High-energy neutrino conversion into electron-W pair in magnetic field and its contribution

合集下载

可见光能量转移,英文

可见光能量转移,英文Visible Light Energy Transfer.Visible light energy transfer is a fundamental process that occurs widely in nature and has numerous applicationsin various fields, ranging from biochemistry and physics to engineering and technology. This process involves the transfer of energy from one excited state to another, typically through photons of visible light.The energy transfer process can be understood by considering the interaction of light with matter. When visible light interacts with matter, it can be absorbed, reflected, refracted, scattered, or emitted. Absorption occurs when the light's energy is transferred to the matter, exciting electrons to higher energy levels. Reflection occurs when the light bounces off the surface of the matter without transferring energy. Refraction occurs when thelight changes direction as it passes through different media, and scattering occurs when the light's direction ischanged due to interactions with particles within the matter.Energy transfer through visible light typically occurs through one of two mechanisms: radiative transfer or non-radiative transfer. Radiative transfer involves the emission and absorption of photons by matter, while non-radiative transfer involves energy transfer through electronic interactions without the emission of photons.In radiative transfer, the excited state of a molecule or atom can decay by emitting a photon, which is then absorbed by another molecule or atom, exciting it to a higher energy state. This process is known as fluorescence or phosphorescence, depending on the lifetime of the excited state. Fluorescence occurs when the excited state decays rapidly, emitting a photon before the energy is lost to the environment, while phosphorescence occurs when the excited state decays slowly, emitting a photon after a delay.Non-radiative transfer, on the other hand, occursthrough electronic interactions between molecules or atoms without the emission of photons. This process can involve energy transfer through electron exchange, dipole-dipole interactions, or electron transfer mechanisms. In these cases, the excited state of one molecule or atom can transfer its energy to another molecule or atom without the emission of a photon, resulting in a more efficient energy transfer process.The efficiency of visible light energy transfer depends on several factors, including the properties of the matter involved, the wavelength of the light, and the environment. For example, the absorption and emission spectra of molecules or atoms determine the wavelengths of light that can be effectively transferred. Additionally, the presence of other molecules or atoms in the environment can affect the rate and efficiency of energy transfer through interactions such as collisions or resonance energy transfer.Visible light energy transfer has numerous applications in various fields. In biochemistry, it plays a crucial rolein photosynthesis, the process by which plants convert light energy into chemical energy. Additionally, visible light energy transfer is used in optical sensors and imaging techniques to detect and quantify molecular interactions and concentrations. In the field of photovoltaics, visible light energy transfer is harnessed to convert sunlight into electrical energy through the photovoltaic effect.Moreover, visible light energy transfer has been extensively studied in the context of organic photochemistry, where it is used to induce chemical reactions through the absorption of visible light. This process, known as photoinduced electron transfer (PET), involves the transfer of an electron from one molecule to another upon absorption of light, leading to chemical transformations. PET reactions are widely used in organic synthesis, photocatalysis, and photovoltaic devices.In summary, visible light energy transfer is a fundamental process that occurs widely in nature and has numerous applications in various fields. It involves thetransfer of energy from one excited state to another through photons of visible light, and can occur through radiative or non-radiative mechanisms. The efficiency of energy transfer depends on the properties of the matter involved, the wavelength of the light, and the environment. Understanding and harnessing the power of visible light energy transfer has the potential to revolutionize fields such as biochemistry, photovoltaics, and organic photochemistry.。

Implications of $bar{nu}_{e}e^{-}to W^{-}gamma$ for high-energy $bar{nu}_e$ observation

$Implications of $bar{nu}_{e}e^{-}to W^{-}gamma$ for high-energy $bar{nu}_e$ observation$

In this Brief Report, we reexamine in some detail the energy spectrum of the ﬁnal-state hard photon in the absorption process ν¯ee− → W −γold. This absorption process has been discussed in Ref. [2], whereas its closely associated resonant absorption process ν¯ee− → W −(→ ν¯µµ−), now referred to as “Glashow resonance”, occurring at Eν¯rees = MW2 /(2me) ∼ 6.3 · 106 GeV, was ﬁrst pointed out in Ref. [3], and was subsequently studied in Ref. [4]. However, to our knowledge, the energy spectrum of the ﬁnal-state photon in ν¯ee− → W −γ has not been studied before. Here, we shall give an estimate of the kinematically allowed average energy for the hard photon and calculate the photon energy spectrum as well as the total cross section of the absorption process ν¯ee− → W −γ.
behaviors of dσ/dy for a few representative values of λ are depicted in Fig. 2. From the

Ultra- and extremely high energy neutrino astronomy

2 Detection Principles and Scientiﬁc Goals
Underwater/ice neutrino telescopes (UNTs) represent a 3-D arrays of photomultipliers deployed deep in the lake, ocean or in the polar ice at the depth of 1 to 4 kilometers to provide with a shield against the sun and moon light background and background of atmospheric muons. Detection principle is based on registration of the Cherenkov photons emitted by charged leptons (including those emitted by secondaries produced along their way in the water or ice and by their decay products) which are generated in CC neutrino interactions νl N −C→C l X (see Fig. 1). Also hadronic showers produced in NC neutrino interactions νl N −N→C νl X inside UNT sensitive volume can be
MeV-range neutrino astronomy have been existing for forty years with two neutrino sources identiﬁed so far,

The sun as a high energy neutrino source

1
νµ νe νe ντ
atm νes of solar atmosphere neutrinos (at the earth) for νe (dashed), νµ (solid), and ντ (dot-dashed line), integrated over the solid angle of the sun. Left: The ﬂuxes without neutrino −γ oscillations, as obtained in [9]. For energies lower than 100 GeV φν ∝ Eν is assumed, and the range from γ = 1.75 to 2.45 is shown. In addition, the plot includes the terrestrial atmospheric horizontal νe (lower dotted) and νµ ﬂux (upper dotted line), also integrated over the solar disk [15]. −5 −3 Right: The corresponding ﬂuxes for the choice ∆m2 eV2 , ∆m2 eV2 , sun = 1.9 × 10 atm = 3.5 × 10 −0.1 0.1 sin θsun = 0.58, and sin θatm = 0.86, averaged over the interval from 10 Eν to 10 Eν . This averaging is justiﬁed by the limited energy resolution of neutrino telescopes, and it smears out rapid neutrino oscillations. solutions to the solar neutrino problem and long baseline experiments, the SuperKamiokande data on terrestrial atmospheric neutrinos can be used to narrow down these parameters to a few cases. In this article we investigate, for the various mixing matrices and corresponding mass diﬀerences, the inﬂuence of neutrino oscillations on the expected event rate of solar atmosphere neutrinos.

Gamma-Ray Bursts, Cosmic-Rays and Neutrinos

a r X i v :a s t r o -p h /0002243v 1 11 F eb 20001Gamma-Ray Bursts,Cosmic-Rays and Neutrinos∗Eli Waxman†‡aaDept.of Condensed Matter Physics,Weizmann Institute of Science,Rehovot 76100,IsraelThe γ-ray burst (GRB)model for production of ultra-high-energy,>1019eV,cosmic-rays is based on the hypothesis that GRBs arise from the dissipation of the kinetic energy of relativistic ﬁreballs at cosmological distances.Recent observations of delayed low energy emission,“afterglow,”from GRB sources strongly support the validity of this hypothesis.Observations also provide quantitative support for the model.The inferred physical ﬁreball parameters imply that protons may be accelerated to >1020eV,and the inferred GRB energy generation rate is similar to that required to account for the observed ﬂux of ultra-high-energy cosmic-rays (UHECRs).Strong suppression of cosmic-ray ﬂux is expected in this model above 1019.7eV,due to proton interaction with microwave background photons.Strong deviations from model ﬂux derived under the assumption of uniform source distribution is expected above 1020eV,due to source discreteness and due to inhomogeneities in source distribution.In particular,the ﬂux above 1020.5eV is expected to be dominated by few,narrow spectrum sources.While model predictions can not be tested (with high conﬁdence level)using present data,the predicted signatures should be observed with the planned Auger and Telescope-Array UHECR detectors.A natural consequence of the GRB model of UHECR production is the conversion of a large fraction,∼10%,of the ﬁreball energy to accompanying burst of ∼1014eV and ∼1018eV neutrinos.A km 2neutrino detector would observe several tens of events per year correlated with GRBs,and test for neutrino properties (e.g.ﬂavor oscillations,for which upward moving τ’s would be a unique signature,and coupling to gravity)with an accuracy many orders of magnitude better than is currently possible.1.IntroductionThe origin of GRBs,bursts of 0.1MeV—1MeV photons lasting for a few seconds,remained un-known for over 20years,primarily because GRBs were not detected prior to 1997at wave-bands other than γ-rays (see [1]for review of γ-ray ob-servations).The isotropic distribution of bursts over the sky suggested that GRB sources lie at cosmological distances,and general phenomeno-logical considerations were used to argue that the bursts are produced by the dissipation of the ki-netic energy of a relativistic expanding ﬁreball (see [2]for review).Adopting the cosmological ﬁreball hypothesis,it was shown that the physical conditions in the ﬁreball dissipation region allow Fermiaccelera-2model is brieﬂy described in§2.1,and proton ac-celeration in GRBﬁreballs is discussed in§2.2. Recent claims,according to which protons can not be accelerated to>1020eV in theﬁreball [11],are shown in§2.2to be erroneous.Implica-tions of recent afterglow observations to high en-ergy particle production are discussed in§3.It is shown that,contrary to some recent claims[12], the GRB energy generation rate implied by af-terglow observations is similar to the energy gen-eration rate required to account for theﬂux of >1019eV cosmic-rays.Model predictions are shown to be consistent with the observed UHECR spectrum in§4.Predictions of the GRB model for UHECR pro-duction,that can be tested with future UHECR experiments,are discussed in§5.Implications of the detection by the AGASA experiment of mul-tiple high energy events with consistent arrival di-rections[13]is also discussed in§5.High energy neutrino production inﬁreballs and its implica-tions for future high energy neutrino detectors are discussed in§6.2.UHECR from GRBﬁreballs2.1.Theﬁreball modelIn theﬁreball model of GRBs[14],a compact source,of linear scale r0∼107cm,produces a wind characterized by an average luminosity L∼1052erg s−1and mass loss rate˙M=L/ηc2. At small radius,the wind bulk Lorentz factor,Γ, grows linearly with radius,until most of the wind energy is converted to kinetic energy andΓsat-urates atΓ∼η∼300.Variability of the source on time scale∆t,resulting inﬂuctuations in the wind bulk Lorentz factorΓon similar time scale, then leads to internal shocks[15]in the expanding ﬁreball at a radiusr i≈Γ2c∆t=3×1013Γ2300∆t10ms cm,(1) whereΓ=300Γ300,∆t=10∆t10ms ms.If the Lorentz factor variability within the wind is sig-niﬁcant,internal shocks would reconvert a sub-stantial part of the kinetic energy to internal energy.It is assumed that this energy is then radiated asγ-rays by synchrotron and inverse-Compton emission of shock-accelerated electrons.In this model,the observedγ-ray variability time,∼r i/Γ2c≈∆t,reﬂects the variability time of the underlying source,and the GRB duration, T∼10s,reﬂects the duration over which energy is emitted from the source.A large fraction of bursts detected by BATSE show variability on the shortest resolved time scale,∼10ms[16], and some show variability on shorter time scales,∼1ms[17].This sets the constraint on under-lying source size,r0<c∆t∼107cm.The wind must be expanding relativistically,with a Lorentz factorΓ∼300,in order that theﬁreball pair-production optical depth be small for observed high energy,∼100MeV,GRB photons[18]. The wind Lorentz factor is expected toﬂuctu-ate on time scales ranging from the source dy-namical time,∆t,to the wind duration T,lead-ing to internal collisions over a range of radii, r∼r i=Γ2c∆t to r∼Γ2cT.Internal shocks are generally expected to be“mildly”relativistic in theﬁreball rest frame,i.e.characterized by Lorentz factorγi−1∼1,since adjacent shells within the wind are expected to expand with Lorentz factors which do not diﬀer by more than an order of magnitude.As theﬁreball expands,it drives a relativistic shock(blastwave)into the surrounding gas.At early time,theﬁreball is little aﬀected by this external interaction.At late time,most of the ﬁreball energy is transferred to the surrounding gas,and theﬂow approaches self-similar expan-sion.For typicalﬁreball parameters,the transi-tion to self-similar expansion occurs at a radius r∼Γ2cT.At this radius,mildly relativistic re-verse shocks propagate into theﬁreball ejecta and decelerate it[19].The reverse shocks disappear on(observed)times scale T,and theﬂow becomes self-similar at later time,with a single,relativis-tic decelerating shock propagating into the sur-rounding medium.Plasma conditions in the re-verse shocks are similar to those of internal shocks arising from variability on time scale∼T,since both are mildly relativistic and occur at similar radii.In the discussion that follows we therefore do not discuss the reverse shocks separately from the internal shocks.The shock driven into the ambient medium continuously heats new gas,and accelerates rel-3 ativistic electrons that may produce by syn-chrotron emission the delayed radiation,“after-glow,”observed on time scales of days to months.As the shock-wave decelerates,the emission shiftswith time to lower frequency.2.2.Fermi acceleration in GRBsIn theﬁreball model,the observed GRB andafterglow radiation is produced by synchrotronemission of shock accelerated electrons.In theregion where electrons are accelerated,protonsare also expected to be shock accelerated.Thisis similar to what is thought to occur in super-novae remnant shocks[20].We consider belowproton acceleration in internal(and reverse)ﬁre-ball shocks.Since the internal shocks are mildlyrelativistic,we expect results related to particleacceleration in sub-relativistic shocks(see,e.g.,[20]for review)to be valid for the present sce-nario.In particular,the predicted energy distri-bution of accelerated protons is dN p/dE p∝E−2p.Two constraints must be satisﬁed byﬁreballwind parameters in order to allow proton accel-eration to E p>1020eV in internal shocks[3]:ξB/ξe>0.02Γ2300E2p,20L−1γ,52,(2)andΓ>130E3/420∆t−1/410ms.(3)Here,E p=1020E p,20eV,Lγ=1052Lγ,52erg/s is theγ-ray luminosity,ξB is the fraction of the wind energy density which is carried by magnetic ﬁeld,4πr2cΓ2(B2/8π)=ξB L,andξe is the frac-tion of wind energy carried by shock accelerated electrons.Since the electron synchrotron cool-ing time is short compared to the wind expansion time,electrons lose their energy radiatively and L is related to the observedγ-ray luminosity by Lγ≈ξe L.Theﬁrst condition must be satisﬁed in order for the proton acceleration time t a to be smaller than the wind expansion time.The sec-ond condition must be satisﬁed in order for the synchrotron energy loss time of the proton to be larger than t a.From Eqs.(2)and(3),we infer that a dissipa-tive ultra-relativistic wind,with luminosity and variability time implied by GRB observations,satisﬁes the constraints necessary to allow the ac-celeration of protons to energy>1020eV,pro-vided that the wind bulk Lorentz factor is large enough,Γ>100,and that the magneticﬁeld is close to equipartition with electrons.The for-mer condition,Γ>100,is remarkably similar to that inferred based onγ-ray spectra.There is no theory at present that allows a basic princi-ples calculation of the strength of the magnetic ﬁeld.However,magneticﬁeld close to equiparti-tion,ξB∼1,is required in order to account for the observedγ-ray emission(see also§3).We have assumed in the discussion so far that theﬁreball is spherically symmetric.However, since a jet-likeﬁreball behaves as if it were a conical section of a sphericalﬁreball as long as the jet opening angle is larger thanΓ−1,our re-sults apply also for a jet-likeﬁreball(we are inter-ested only in processes that occur when the wind is ultra-relativistic,Γ∼300,prior to signiﬁcant ﬁreball deceleration).For a jet-like wind,L in our equations should be understood as the lumi-nosity theﬁreball would have carried had it been spherically symmetric.It has recently been pointed out in[11]that conditions at the external,highly relativistic shock driven by theﬁreball into the ambient gas are not likely to allow proton acceleration to ultra-high energy.Although correct,this observa-tion is irrelevant to the scenario considered here based on[3],since in this scenario protons are accelerated in internal,mildly relativisticﬁreball shocks.3.Implications of afterglow observations In addition to providing support to the valid-ity of the qualitativeﬁreball scenario described in §2.1[7],afterglow observations provide quantita-tive constraints onﬁreball model parameters. The determination of GRB redshifts implies that the characteristic GRBγ-ray luminosity and emitted energy,in the0.05to2MeV band, are Lγ∼1052erg/s and Eγ∼1053erg respec-tively(e.g.[8]),an order of magnitude higher than the values assumed prior to afterglow de-tection(here,and throughout the paper,we as-sume an open universe,Ω=0.2,Λ=0,and4H0=75km/s Mpc).The increased GRB lumi-nosity scale implies that the constraint(2)on theﬁreball magneticﬁeld is less stringent than pre-viously assumed.Due to present technical limitations of the ex-periments,afterglow radiation is observed in mostcases only on time scale>>10s.At this stage,radiation is produced by the external shock driveninto the surrounding gas,and afterglow observa-tions therefore do not provide direct constraintson the magneticﬁeld energy fractionξB at theinternal and reverse shocks,where protons are ac-celerated to ultra-high energy.In one case,how-ever,that of GRB990123,reverse shock emissionwas detected over∼10s time scale[21,22].Forthis case,the inferred value ofξB[23]is consis-tent with the constraint(2).Clearly,more ob-servations are required to determine whether thiscondition is generally satisﬁed.The observed GRB redshift distribution im-plies a GRB rate of R GRB∼10/Gpc3yr at z∼1.The present,z=0,rate is less well constrained,since most observed GRBs originate at redshifts1≤z≤2.5[24].Present data are consis-tent with both no evolution of GRB rate withredshift,and with strong evolution(following,e.g.,the luminosity density evolution of QSOs orthe evolution of star formation rate),in whichR GRB(z=1)/R GRB(z=0)∼8[24].The energyobserved inγ-rays reﬂect theﬁreball energy inaccelerated electrons.Afterglow observations im-ply that accelerated electrons and protons carrysimilar energy[8].Thus,the inferred z=0rateof cosmic-ray production by GRBs is similar tothe generation rate ofγ-ray energy,E2(d˙n CR/dE)z=0=1044ζerg/Mpc3yr,(4)whereζis in the range of∼1to∼8.Thisenergy generation rate is remarkably similar tothat implied by the observed UHECRﬂux(see§4).4using(following[25])the GRB energy observed in the50to300keV band,where only a small fraction of the0.05to2MeVγ-ray energy is observed.5Galactic source of protons dominates theﬂux at high energy E>1019eV.In Fig.1we compare the UHECR spectrum, reported by the Fly’s Eye[26],the Yakutsk[31], and the AGASA[28]experiments,with that pre-dicted by the GRB model.The proton genera-tion rate is assumed to evolve in redshift follow-ing QSO luminosity evolution[32].Note,that the cosmic-ray spectrum at energy>1019eV is little aﬀected by modiﬁcations of the cosmological pa-rameters or of the redshift evolution of cosmic-ray generation rate,since cosmic-rays at this energy originate from distances shorter than several hun-dred Mpc.The spectrum andﬂux at E>1019eV is mainly determined by the present(z=0)gen-eration rate and spectrum.The absoluteﬂux measured at3×1018eV diﬀers between the var-ious experiments,corresponding to a systematic ≃10%(≃20%)over-estimate of event energies in the AGASA(Yakutsk)experiment compared to the Fly’s Eye experiment(see also[27]).In Fig. 1,the Yakutsk energy normalization is used. The suppression of modelﬂux above1019.7eV is due to energy loss of high energy protons in interaction with the microwave background,i.e. to the“GZK cutoﬀ”[33].Both Fly’s Eye and Yakutsk data show a deﬁcit in the number of events,compared to the number expected based on extrapolation of the J∝E−2.61power-lawﬁt, consistent with the predicted suppression.The deﬁcit is,however,only at a2σconﬁdence level [3].The AGASA data is consistent with Fly’s Eye and Yakutsk results below1020eV.A discrepancy may be emerging at higher energy,>1020eV, where the Fly’s Eye and Yakutsk experiments de-tect1event each,and the AGASA experiment detects6events for similar exposure.Theﬂux above1020eV is dominated by sources at distances<30Mpc[5](see§5).Since the distribution of known astrophysical systems (e.g.galaxies,clusters of galaxies)is inhomoge-neous on scales of tens of Mpc,signiﬁcant devi-ations from model predictions presented in Fig. 1for a uniform source distribution are expected above1020eV.It has recently been shown[34] that clustering of cosmic-ray sources leads to a standard deviation,σ,in the expected number, N,of events above1020eV,given byσ/N=0.9(d0/10Mpc)0.9,where d0is the unknown scale length of the source correlation function and d0∼10Mpc forﬁeld galaxies.An order of magnitude increase in the exposure of UHECR experiments,compared to that avail-able at present,is required to test for the exis-tence of the GZK cutoﬀ[5].Such exposure would allow this test through an accurate determination of the spectrum in the energy range of1019.7eV to1020eV,where the eﬀects of source inhomo-geneities are expected to be small[5,34].More-over,an order of magnitude increase in exposure will also allow to determine the source correlation length d0,through the detection of anisotropies in the arrival directions of∼1019.5eV cosmic-rays over angular scales ofΘ∼d0/30Mpc[34]. Finally,we note that preliminary results from the HiRes experiment were presented in this con-ference[35],reporting7events beyond1020eV for an exposure similar to that of the Fly’s Eye.It is diﬃcult to decide how to interpret this result, since the discrepancy between HiRes and Fly’s Eye results is present not only above1020eV but also at lower energy,where Fly’s Eye,AGASA and Yakutsk experiments are in agreement:13 events above6×1019eV are reported in the pre-liminary HiRes analysis,while only5events at that energy range are reported by the Fly’s Eye. We therefore believe that unambiguous conclu-sions based on the recent HiRes data can only be drawn after a complete analysis of the HiRes data is published.5.GRB model predictions for plannedUHECR experimentsThe energy of the most energetic cosmic ray detected by the Fly’s Eye experiment is in ex-cess of2×1020eV,and that of the most energetic AGASA event is∼2×1020eV.On a cosmo-logical scale,the distance traveled by such ener-getic particles is small:<100Mpc(50Mpc)for the AGASA(Fly’s Eye)event(e.g.,[36]).Thus, the detection of these events over a∼5yr period can be reconciled with the rate of nearby GRBs,∼1per100yr out to100Mpc,only if there is a large dispersion,≥100yr,in the arrival time of protons produced in a single burst.6The required dispersion is likely to occur due to the combined eﬀects of deﬂection by random magneticﬁelds and energy dispersion of the par-ticles[3].A proton of energy E propagating over a distance D through a magneticﬁeld of strength B and correlation lengthλis deﬂected by an an-gleθs∼(D/λ)1/2λ/R L,which results in a time delay,compared to propagation along a straight line,τ(E,D)≈θ2s D/4c∝B2λ.The random en-ergy loss UHECRs suﬀer as they propagate,ow-ing to the production of pions,implies that at any distance from the observer there is someﬁ-nite spread in the energies of UHECRs that are observed with a givenﬁxed energy.For protons with energies>1020eV the fractional RMS en-ergy spread is of order unity over propagation distances in the range10−100Mpc(e.g.[36]). Since the time delay is sensitive to the particle energy,this implies that the spread in arrival time of UHECRs with given observed energy is com-parable to the average time delay at that energy,τ(E,D).The magneticﬁeld required in order to pro-duce a spreadτ(E=1020eV,D=100Mpc)> 100yr,is well below the current upper bound on the inter-galactic magneticﬁeld,Bλ1/2≤10−9G Mpc1/2[37],which allows a spreadτ∼105yr.We discuss below some implications, unique to the GRB model,of time delays induced by magnetic-ﬁeld deﬂection.5.1.The highest energy sourcesThe rapid increase with energy of the pion production energy loss rate eﬀectively introduces a cutoﬀdistance,D c(E),beyond which sources do not contribute to theﬂux above E.The function D c(E)is shown in Fig. 2.We de-ﬁne a critical energy E c,for which the aver-age number of sources at D<D c(E c)is1, 4π7ﬂux(obtained for spatially and temporally homo-geneous UHECR volume emissivity).At E>E c, theﬂux will generally be much lower than the average,because there will be no burst within a distance D c(E)having taken place suﬃciently re-cently.There is,however,a signiﬁcant probabil-ity to observe one source with aﬂux higher than the average.A source similar to the brightest one in Fig.2appears∼5%of the time.At anyﬁxed time a given burst is observed in UHECRs only over a narrow range of energy, because if a burst is currently observed at some energy E then UHECRs of much lower(higher) energy from this burst will arrive(have arrived) mainly in the future(past).For energies above the pion production threshold,E>1019.7eV,the dispersion in arrival times of UHECRs withﬁxed observed energy is comparable to the average de-lay at that energy.This implies that the spec-tral width∆E of the source at a given time is of order the average observed energy,∆E∼E. Thus,bursting UHECR sources should have nar-rowly peaked energy spectra,and the brightest sources should be diﬀerent at diﬀerent energies. For steady state sources,on the other hand,the brightest source at high energies should also be the brightest one at low energies,its fractional contribution to the overallﬂux decreasing to low energy only as D c(E)−1.A detailed numerical analysis of the time dependent energy spectrum of bursting sources is given in[39].The AGASA experiment reported the presence of one triplet and three doublets of UHECRs with angular separations(within each multiplet)≤2.5◦,roughly consistent with the measure-ment error,among a total of47UHECRs with E≥4×1019eV[13].The probability to have found such multiplets by chance is∼1%.There-fore,this observation favors the bursting source model,although more data are needed to conﬁrm it.Testing the GRB model predictions described above requires an exposure10times larger than that of present experiments.Such increase is ex-pected to be provided by the planned Auger[40] and Telescope Array[41]detectors.5.2.Spectra of Sources at E<4×1019eV For nearby,D<100Mpc,sources contributing at E≤4×1019eV,pion production energy loss is negligible,and particle energy may be considered constant along the propagation path.In this case, the spectral shape of individual sources depends primarily on the magneticﬁeld correlation length [42].Ifλ≫Dθs(D,E)≃D(D/λ)1/2λ/R L,all UHECRs that arrive at the observer are essen-tially deﬂected by the same magneticﬁeld struc-tures,and the absence of random energy loss during propagation implies that all rays with a ﬁxed observed energy would reach the observer with exactly the same direction and time de-lay.At aﬁxed time,therefore,the source would appear mono-energetic and point-like(In real-ity,energy loss due to pair production results in aﬁnite but small spectral and angular width,∆E/E∼δθ/θs≤1%[42]).If,on the other hand,λ≪Dθs(D,E),the de-ﬂection of diﬀerent UHECRs arriving at the ob-server are essentially independent.Even in the absence of any energy loss there are many paths from the source to the observer for UHECRs of ﬁxed energy E that are emitted from the source at an angleθ≤θs relative to the source-observer line of sight.Along each of the paths,UHECRs are deﬂected by independent magneticﬁeld struc-tures.Thus,the source angular size would be of orderθs and the spread in arrival times would be comparable to the characteristic delayτ,leading to∆E/E∼1(The spectral shape of sources is given in analytic form for this case in[42]).For D=30Mpc and E≃1019eV,theθs D=λline divides the allowed region(for the GRB model)in the B–λplane atλ∼1Mpc.Thus, measuring the spectral width of bright sources would allow to determine if theﬁeld correlation length is much larger,much smaller,or compara-ble to1Mpc.6.High energy Neutrinos6.1.GRB neutrinos,∼1014eVProtons accelerated in theﬁreball to high en-ergy lose energy through photo-meson interaction withﬁreball photons.The decay of charged pions8produced in this interaction,π+→µ++νµ→e ++νe +(E b γ/1MeV)Γ4300∆t 10ms .(6)Thus,acceleration of protons to high energy ininternal ﬁreball shocks would lead to conversion of a signiﬁcant fraction of proton energy to high energy neutrinos.IfGRBs are the sources of UHECRS,then us-ing Eq.(6)and the UHECR generation rate given by Eq.(4)with ζ≃1,the expected GRB neu-trino ﬂux is [44]E 2νΦνx ≈1.5×10−9 f πcm 2s sr,(7)where νx stands for νµ,¯νµand νe .The neutrino spectrum (7)is modiﬁed at high energy,where neutrinos are produced by the decay of muons and pions whose life time ex-ceeds the characteristic time for energy loss due to adiabatic expansion and synchrotron emission[43,45,44].The synchrotron loss time is deter-mined by the energy density of the magnetic ﬁeld in the wind rest frame.For the characteristic pa-rameters of a GRB wind,synchrotron losses are the dominant eﬀect,leading to strong suppression of νﬂux above ∼1016eV.We note,that the results presented above were derived using the “∆-approximation,”i.e.assum-ing that photo-meson interactions are dominated by the contribution of the ∆-resonance.It has recently been shown [46],that for photon spectraharder than dN γ/dE γ∝E −2γ,the contribution of non-resonant interactions may be important.Since in order to interact with the hard part ofthe photon spectrum,E γ<E bγ,the proton en-ergy must exceed the energy at which neutrinosof energy E bνare produced,signiﬁcant modiﬁca-tion of the ∆-approximation results is expectedonly for E ν≫E bν,where the neutrino ﬂux is strongly suppressed by synchrotron losses.6.2.Afterglow neutrinos,∼1018eVProtons are expected to be accelerated to >1020eV in both internal shocks due to variability of the underlying source,and in the reverse shocks driven into the ﬁreball ejecta at the initial stage of interaction of the ﬁreball with its surrounding gas,which occurs on time scale T ∼10s,compa-rable to the duration of the GRB itself.Optical–UV photons are radiated by electrons accelerated in shocks propagating backward into the ejecta,and may interact with accelerated protons.The interaction of these low energy,10eV–1keV,pho-tons and high energy protons produces a burst of duration ∼T of ultra-high energy,1017–1019eV,neutrinos [as indicated by Eq.(5)]via photo-meson interactions [47].Afterglows have been detected in several cases;reverse shock emission has only been identiﬁed for GRB 990123[21].Both the detections and the non-detections are consistent with shocks oc-curring with typical model parameters [22],sug-gesting that reverse shock emission may be com-mon.The predicted neutrino emission depends,however,upon parameters of the surrounding medium that can only be estimated once more ob-servations of the prompt optical afterglow emis-sion are available.9If the density of gas surrounding theﬁreball is typically n∼1cm−3,a value typical to the inter-stellar medium and consistent with GRB990123 observations,then the expected neutrino inten-sity is[47]E2νΦνx≈10−10 Eνcm2s sr,(8)whereβ=1/2forǫob.ν>1017eV andβ=1for ǫob.ν<1017eV.Here too,νx stands forνµ,¯νµand νe.The neutrinoﬂux is expected to be strongly suppressed at energy>1019eV,since protons are not expected to be accelerated to energy≫1020eV.The neutrinoﬂux due to interaction with re-verse shock photons may be signiﬁcantly higher than that given in Eq.(8),if the density of gas surrounding theﬁreball is signiﬁcantly higher than the value we have assumed,i.e.if n≫1cm−3.6.3.ImplicationsTheﬂux of∼1014eV neutrinos given in Eq.(7)implies that large area,∼1km2,high-energy neutrino telescopes,which are being constructed to detect cosmologically distant neutrino sources (see[48]for review),would observe several tens of events per year correlated with GRBs.The detec-tion rate of ultra-high energy,∼1018eV,after-glow neutrinos implied by Eq.(8)is much lower. The∼1018eV neutrinoﬂux depends,however, on parameters of the surrounding medium which can be estimated only once more observations of reverse shock emission are available.One may look for neutrino events in angular coincidence,on degree scale,and temporal co-incidence,on time scale of seconds,with GRBs [43].Detection of neutrinos from GRBs could be used to test the simultaneity of neutrino and pho-ton arrival to an accuracy of∼1s(∼1ms for short bursts),checking the assumption of special relativity that photons and neutrinos have the same limiting speed.These observations would also test the weak equivalence principle,accord-ing to which photons and neutrinos should suﬀer the same time delay as they pass through a grav-itational potential.With1s accuracy,a burst at 100Mpc would reveal a fractional diﬀerence in limiting speed of10−16,and a fractional diﬀerence in gravitational time delay of order10−6(con-sidering the Galactic potential alone).Previous applications of these ideas to supernova1987A (see[49]for review),where simultaneity could be checked only to an accuracy of order several hours,yielded much weaker upper limits:of or-der10−8and10−2for fractional diﬀerences in the limiting speed and time delay respectively.The model discussed above predicts the pro-duction of high energy muon and electron neu-trinos.However,if the atmospheric neutrino anomaly has the explanation it is usually given, oscillation toντ’s with mass∼0.1eV[50],then one should detect equal numbers ofνµ’s andντ’s. Up-goingτ’s,rather thanµ’s,would be a dis-tinctive signature of such oscillations.Sinceντ’s are not expected to be produced in theﬁreball, looking forτ’s would be an“appearance experi-ment.”To allowﬂavor change,the diﬀerence in squared neutrino masses,∆m2,should exceed a minimum value proportional to the ratio of source distance and neutrino energy[49].A burst at 100Mpc producing1014eV neutrinos can test for ∆m2≥10−16eV2,5orders of magnitude more sensitive than solar neutrinos.REFERENCES1.Fishman,G.J.&Meegan,C.A.,ARA&A33,415(1995).2.Piran,T.,in Unsolved Problems In Astro-physics,eds.J.N.Bahcall and J.P.Ostriker, 343-377(Princeton,1996).3.Waxman,E.,Phys.Rev.Lett.75,386(1995).4.Vietri,M.,Ap.J.453,883(1995).5.Waxman,E.,Ap.J.452,L1(1995).6.Waxman,E.,in Proc.Nobel Symposium Par-ticle Physics and The Universe(Haga Slott, Sweden,August1998),eds.L.Bergstrom,P.Carlson,&C.Fransson(astro-ph/9911395).7.M´e sz´a ros,P.,in Proc.Cosmic Explosions(Maryland,U.S.A.,Oct.1999),ed.M.Livio (astro-ph/9912474).8.Freedman,D.L.,&Waxman,E.,submittedto Ap.J.(astro-ph/9912214).9.Waxman,E.,Ap.J.485,L5(1997);Wijers,R.A.M.J.,Rees,M.J.&M´e sz´a ros,P.,MN-。

胺基保护——邻苯二甲酰亚胺脱保护

New1H-Pyrazole-Containing Polyamine Receptors Able ToComplex L-Glutamate in Water at Physiological pH ValuesCarlos Miranda,†Francisco Escartı´,‡Laurent Lamarque,†Marı´a J.R.Yunta,§Pilar Navarro,*,†Enrique Garcı´a-Espan˜a,*,‡and M.Luisa Jimeno†Contribution from the Instituto de Quı´mica Me´dica,Centro de Quı´mica Orga´nica Manuel Lora Tamayo,CSIC,C/Juan de la Cier V a3,28006Madrid,Spain,Departamento de Quı´mica Inorga´nica,Facultad de Quı´mica,Uni V ersidad de Valencia,c/Doctor Moliner50, 46100Burjassot(Valencia),Spain,and Departamento de Quı´mica Orga´nica,Facultad deQuı´mica,Uni V ersidad Complutense de Madrid,A V plutense s/n,28040Madrid,SpainReceived April16,2003;E-mail:enrique.garcia-es@uv.esAbstract:The interaction of the pyrazole-containing macrocyclic receptors3,6,9,12,13,16,19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene1[L1],13,26-dibenzyl-3,6,9,12,13,16,-19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene2[L2],3,9,12,13,16,22,-25,26-octaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene3[L3],6,19-dibenzyl-3,6,9,12,13,-16,19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene4[L4],6,19-diphenethyl-3,6,9,12,13,16,19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetraene5[L5],and 6,19-dioctyl-3,6,9,12,13,16,19,22,25,26-decaazatricyclo-[22.2.1.111,14]-octacosa-1(27),11,14(28),24-tetra-ene6[L6]with L-glutamate in aqueous solution has been studied by potentiometric techniques.The synthesis of receptors3-6[L3-L6]is described for the first time.The potentiometric results show that4[L4]containing benzyl groups in the central nitrogens of the polyamine side chains is the receptor displaying the larger interaction at pH7.4(K eff)2.04×104).The presence of phenethyl5[L5]or octyl groups6[L6]instead of benzyl groups4[L4]in the central nitrogens of the chains produces a drastic decrease in the stability[K eff )3.51×102(5),K eff)3.64×102(6)].The studies show the relevance of the central polyaminic nitrogen in the interaction with glutamate.1[L1]and2[L2]with secondary nitrogens in this position present significantly larger interactions than3[L3],which lacks an amino group in the center of the chains.The NMR and modeling studies suggest the important contribution of hydrogen bonding andπ-cation interaction to adduct formation.IntroductionThe search for the L-glutamate receptor field has been andcontinues to be in a state of almost explosive development.1 L-Glutamate(Glu)is thought to be the predominant excitatory transmitter in the central nervous system(CNS)acting at a rangeof excitatory amino acid receptors.It is well-known that it playsa vital role mediating a great part of the synaptic transmission.2However,there is an increasing amount of experimentalevidence that metabolic defects and glutamatergic abnormalitiescan exacerbate or induce glutamate-mediated excitotoxic damageand consequently neurological disorders.3,4Overactivation ofionotropic(NMDA,AMPA,and Kainate)receptors(iGluRs)by Glu yields an excessive Ca2+influx that produces irreversible loss of neurons of specific areas of the brain.5There is much evidence that these processes induce,at least in part,neuro-degenerative illnesses such as Parkinson,Alzheimer,Huntington, AIDS,dementia,and amyotrophic lateral sclerosis(ALS).6In particular,ALS is one of the neurodegenerative disorders for which there is more evidence that excitotoxicity due to an increase in Glu concentration may contribute to the pathology of the disease.7Memantine,a drug able to antagonize the pathological effects of sustained,but relatively small,increases in extracellular glutamate concentration,has been recently received for the treatment of Alzheimer disease.8However,there is not an effective treatment for ALS.Therefore,the preparation of adequately functionalized synthetic receptors for L-glutamate seems to be an important target in finding new routes for controlling abnormal excitatory processes.However,effective recognition in water of aminocarboxylic acids is not an easy task due to its zwitterionic character at physiological pH values and to the strong competition that it finds in its own solvent.9†Centro de Quı´mica Orga´nica Manuel Lora Tamayo.‡Universidad de Valencia.§Universidad Complutense de Madrid.(1)Jane,D.E.In Medicinal Chemistry into the Millenium;Campbell,M.M.,Blagbrough,I.S.,Eds.;Royal Society of Chemistry:Cambridge,2001;pp67-84.(2)(a)Standaert,D.G.;Young,A.B.In The Pharmacological Basis ofTherapeutics;Hardman,J.G.,Goodman Gilman,A.,Limbird,L.E.,Eds.;McGraw-Hill:New York,1996;Chapter22,p503.(b)Fletcher,E.J.;Loge,D.In An Introduction to Neurotransmission in Health and Disease;Riederer,P.,Kopp,N.,Pearson,J.,Eds.;Oxford University Press:New York,1990;Chapter7,p79.(3)Michaelis,E.K.Prog.Neurobiol.1998,54,369-415.(4)Olney,J.W.Science1969,164,719-721.(5)Green,J.G.;Greenamyre,J.T.Prog.Neurobiol.1996,48,613-63.(6)Bra¨un-Osborne,H.;Egebjerg,J.;Nielsen,E.O.;Madsen,U.;Krogsgaard-Larsen,P.J.Med.Chem.2000,43,2609-2645and references therein.(7)(a)Shaw,P.J.;Ince,P.G.J.Neurol.1997,244(Suppl2),S3-S14.(b)Plaitakis,A.;Fesdjian,C.O.;Shashidharan,S Drugs1996,5,437-456.(8)Frantz,A.;Smith,A.Nat.Re V.Drug Dico V ery2003,2,9.Published on Web12/30/200310.1021/ja035671m CCC:$27.50©2004American Chemical Society J.AM.CHEM.SOC.2004,126,823-8339823There are many types of receptors able to interact with carboxylic acids and amino acids in organic solvents,10-13yielding selective complexation in some instances.However,the number of reported receptors of glutamate in aqueous solution is very scarce.In this sense,one of the few reports concerns an optical sensor based on a Zn(II)complex of a 2,2′:6′,2′′-terpyridine derivative in which L -aspartate and L -glutamate were efficiently bound as axial ligands (K s )104-105M -1)in 50/50water/methanol mixtures.14Among the receptors employed for carboxylic acid recogni-tion,the polyamine macrocycles I -IV in Chart 1are of particular relevance to this work.In a seminal paper,Lehn et al.15showed that saturated polyamines I and II could exert chain-length discrimination between different R ,ω-dicarboxylic acids as a function of the number of methylene groups between the two triamine units of the receptor.Such compounds were also able to interact with a glutamic acid derivative which has the ammonium group protected with an acyl moiety.15,16Compounds III and IV reported by Gotor and Lehn interact in their protonated forms in aqueous solution with protected N -acetyl-L -glutamate and N -acetyl-D -glutamate,showing a higher stability for the interaction with the D -isomer.17In both reports,the interaction with protected N -acetyl-L -glutamate at physiological pH yields constants of ca.3logarithmic units.Recently,we have shown that 1H -pyrazole-containing mac-rocycles present desirable properties for the binding of dopam-ine.18These polyaza macrocycles,apart from having a highpositive charge at neutral pH values,can form hydrogen bonds not only through the ammonium or amine groups but also through the pyrazole nitrogens that can behave as hydrogen bond donors or acceptors.In fact,Elguero et al.19have recently shown the ability of the pyrazole rings to form hydrogen bonds with carboxylic and carboxylate functions.These features can be used to recognize the functionalities of glutamic acid,the carboxylic and/or carboxylate functions and the ammonium group.Apart from this,the introduction of aromatic donor groups appropriately arranged within the macrocyclic framework or appended to it through arms of adequate length may contribute to the recognition event through π-cation interactions with the ammonium group of L -glutamate.π-Cation interactions are a key feature in many enzymatic centers,a classical example being acetylcholine esterase.20The role of such an interaction in abiotic systems was very well illustrated several years ago in a seminal work carried out by Dougherty and Stauffer.21Since then,many other examples have been reported both in biotic and in abiotic systems.22Taking into account all of these considerations,here we report on the ability of receptors 1[L 1]-6[L 6](Chart 2)to interact with L -glutamic acid.These receptors display structures which differ from one another in only one feature,which helps to obtain clear-cut relations between structure and interaction(9)Rebek,J.,Jr.;Askew,B.;Nemeth,D.;Parris,K.J.Am.Chem.Soc.1987,109,2432-2434.(10)Seel,C.;de Mendoza,J.In Comprehensi V e Supramolecular Chemistry ;Vogtle,F.,Ed.;Elsevier Science:New York,1996;Vol.2,p 519.(11)(a)Sessler,J.L.;Sanson,P.I.;Andrievesky,A.;Kral,V.In SupramolecularChemistry of Anions ;Bianchi,A.,Bowman-James,K.,Garcı´a-Espan ˜a,E.,Eds.;John Wiley &Sons:New York,1997;Chapter 10,pp 369-375.(b)Sessler,J.L.;Andrievsky,A.;Kra ´l,V.;Lynch,V.J.Am.Chem.Soc.1997,119,9385-9392.(12)Fitzmaurice,R.J.;Kyne,G.M.;Douheret,D.;Kilburn,J.D.J.Chem.Soc.,Perkin Trans.12002,7,841-864and references therein.(13)Rossi,S.;Kyne,G.M.;Turner,D.L.;Wells,N.J.;Kilburn,J.D.Angew.Chem.,Int.Ed.2002,41,4233-4236.(14)Aı¨t-Haddou,H.;Wiskur,S.L.;Lynch,V.M.;Anslyn,E.V.J.Am.Chem.Soc.2001,123,11296-11297.(15)Hosseini,M.W.;Lehn,J.-M.J.Am.Chem.Soc.1982,104,3525-3527.(16)(a)Hosseini,M.W.;Lehn,J.-M.Hel V .Chim.Acta 1986,69,587-603.(b)Heyer,D.;Lehn,J.-M.Tetrahedron Lett.1986,27,5869-5872.(17)(a)Alfonso,I.;Dietrich,B.;Rebolledo,F.;Gotor,V.;Lehn,J.-M.Hel V .Chim.Acta 2001,84,280-295.(b)Alfonso,I.;Rebolledo,F.;Gotor,V.Chem.-Eur.J.2000,6,3331-3338.(18)Lamarque,L.;Navarro,P.;Miranda,C.;Ara ´n,V.J.;Ochoa,C.;Escartı´,F.;Garcı´a-Espan ˜a,E.;Latorre,J.;Luis,S.V.;Miravet,J.F.J.Am.Chem.Soc .2001,123,10560-10570.(19)Foces-Foces,C.;Echevarria,A.;Jagerovic,N.;Alkorta,I.;Elguero,J.;Langer,U.;Klein,O.;Minguet-Bonvehı´,H.-H.J.Am.Chem.Soc.2001,123,7898-7906.(20)Sussman,J.L.;Harel,M.;Frolow,F.;Oefner,C.;Goldman,A.;Toker,L.;Silman,I.Science 1991,253,872-879.(21)Dougherty,D.A.;Stauffer,D.A.Science 1990,250,1558-1560.(22)(a)Sutcliffe,M.J.;Smeeton,A.H.;Wo,Z.G.;Oswald,R.E.FaradayDiscuss.1998,111,259-272.(b)Kearney,P.C.;Mizoue,L.S.;Kumpf,R.A.;Forman,J.E.;McCurdy,A.;Dougherty,D.A.J.Am.Chem.Soc.1993,115,9907-9919.(c)Bra ¨uner-Osborne,H.;Egebjerg,J.;Nielsen,E.;Madsen,U.;Krogsgaard-Larsen,P.J.Med.Chem.2000,43,2609-2645.(d)Zacharias,N.;Dougherty,D.A.Trends Pharmacol.Sci.2002,23,281-287.(e)Hu,J.;Barbour,L.J.;Gokel,G.W.J.Am.Chem.Soc.2002,124,10940-10941.Chart 1.Some Receptors Employed for Dicarboxylic Acid and N -AcetylglutamateRecognitionChart 2.New 1H -Pyrazole-Containing Polyamine Receptors Able To Complex L -Glutamate inWaterA R T I C L E SMiranda et al.824J.AM.CHEM.SOC.9VOL.126,NO.3,2004strengths.1[L1]and2[L2]differ in the N-benzylation of the pyrazole moiety,and1[L1]and3[L3]differ in the presence in the center of the polyamine side chains of an amino group or of a methylene group.The receptors4[L4]and5[L5]present the central nitrogens of the chain N-functionalized with benzyl or phenethyl groups,and6[L6]has large hydrophobic octyl groups.Results and DiscussionSynthesis of3-6.Macrocycles3-6have been obtained following the procedure previously reported for the preparation of1and2.23The method includes a first dipodal(2+2) condensation of the1H-pyrazol-3,5-dicarbaldehyde7with the corresponding R,ω-diamine,followed by hydrogenation of the resulting Schiff base imine bonds.In the case of receptor3,the Schiff base formed by condensation with1,5-pentanediamine is a stable solid(8,mp208-210°C)which precipitated in68% yield from the reaction mixture.Further reduction with NaBH4 in absolute ethanol gave the expected tetraazamacrocycle3, which after crystallization from toluene was isolated as a pure compound(mp184-186°C).In the cases of receptors4-6, the precursor R,ω-diamines(11a-11c)(Scheme1B)were obtained,by using a procedure previously described for11a.24 This procedure is based on the previous protection of the primary amino groups of1,5-diamino-3-azapentane by treatment with phthalic anhydride,followed by alkylation of the secondary amino group of1,5-diphthalimido-3-azapentane9with benzyl, phenethyl,or octyl bromide.Finally,the phthalimido groups of the N-alkyl substituted intermediates10a-10c were removed by treatment with hydrazine to afford the desired amines11a-11c,which were obtained in moderate yield(54-63%).In contrast with the behavior previously observed in the synthesis of3,in the(2+2)dipodal condensations of7with 3-benzyl-,3-phenethyl-,and3-octyl-substituted3-aza-1,5-pentanediamine11a,11b,and11c,respectively,there was not precipitation of the expected Schiff bases(Scheme1A). Consequently,the reaction mixtures were directly reduced in situ with NaBH4to obtain the desired hexaamines4-6,which after being carefully purified by chromatography afforded purecolorless oils in51%,63%,and31%yield,respectively.The structures of all of these new cyclic polyamines have been established from the analytical and spectroscopic data(MS(ES+), 1H and13C NMR)of both the free ligands3-6and their corresponding hydrochloride salts[3‚4HCl,4‚6HCl,5‚6HCl, and6‚6HCl],which were obtained as stable solids following the same procedure previously reported18for1‚6HCl and2‚6HCl.As usually occurs for3,5-disubstituted1H-pyrazole deriva-tives,either the free ligands3-6or their hydrochlorides show very simple1H and13C NMR spectra,in which signals indicate that,because of the prototropic equilibrium of the pyrazole ring, all of these compounds present average4-fold symmetry on the NMR scale.The quaternary C3and C5carbons appear together,and the pairs of methylene carbons C6,C7,and C8are magnetically equivalent(see Experimental Section).In the13C NMR spectra registered in CDCl3solution, significant differences can be observed between ligand3,without an amino group in the center of the side chain,and the N-substituted ligands4-6.In3,the C3,5signal appears as a broad singlet.However,in4-6,it almost disappears within the baseline of the spectra,and the methylene carbon atoms C6and C8experience a significant broadening.Additionally,a remark-able line-broadening is also observed in the C1′carbon signals belonging to the phenethyl and octyl groups of L5and L6, respectively.All of these data suggest that as the N-substituents located in the middle of the side chains of4-6are larger,the dynamic exchange rate of the pyrazole prototropic equilibrium is gradually lower,probably due to a relation between proto-tropic and conformational equilibria.Acid-Base Behavior.To follow the complexation of L-glutamate(hereafter abbreviated as Glu2-)and its protonated forms(HGlu-,H2Glu,and H3Glu+)by the receptors L1-L6, the acid-base behavior of L-glutamate has to be revisited under the experimental conditions of this work,298K and0.15mol dm-3.The protonation constants obtained,included in the first column of Table1,agree with the literature25and show that the zwitterionic HGlu-species is the only species present in aqueous solution at physiological pH values(Scheme2and Figure S1of Supporting Information).Therefore,receptors for(23)Ara´n,V.J.;Kumar,M.;Molina,J.;Lamarque,L.;Navarro,P.;Garcı´a-Espan˜a,E.;Ramı´rez,J.A.;Luis,S.V.;Escuder,.Chem.1999, 64,6137-6146.(24)(a)Yuen Ng,C.;Motekaitis,R.J.;Martell,A.E.Inorg.Chem.1979,18,2982-2986.(b)Anelli,P.L.;Lunazzi,L.;Montanari,F.;Quici,.Chem.1984,49,4197-4203.Scheme1.Synthesis of the Pyrazole-Containing MacrocyclicReceptorsNew1H-Pyrazole-Containing Polyamine Receptors A R T I C L E SJ.AM.CHEM.SOC.9VOL.126,NO.3,2004825glutamate recognition able to address both the negative charges of the carboxylate groups and the positive charge of ammonium are highly relevant.The protonation constants of L 3-L 6are included in Table 1,together with those we have previously reported for receptors L 1and L 2.23A comparison of the constants of L 4-L 6with those of the nonfunctionalized receptor L 1shows a reduced basicity of the receptors L 4-L 6with tertiary nitrogens at the middle of the polyamine bridges.Such a reduction in basicity prevented the potentiometric detection of the last protonation for these ligands in aqueous solution.A similar reduction in basicity was previously reported for the macrocycle with the N -benzylated pyrazole spacers (L 2).23These diminished basicities are related to the lower probability of the tertiary nitrogens for stabilizing the positive charges through hydrogen bond formation either with adjacent nonprotonated amino groups of the molecule or with water molecules.Also,the increase in the hydrophobicity of these molecules will contribute to their lower basicity.The stepwise basicity constants are relatively high for the first four protonation steps,which is attributable to the fact that these protons can bind to the nitrogen atoms adjacent to the pyrazole groups leaving the central nitrogen free,the electrostatic repulsions between them being therefore of little significance.The remaining protonation steps will occur in the central nitrogen atom,which will produce an important increase in the electrostatic repulsion in the molecule and therefore a reduction in basicity.As stated above,the tertiary nitrogen atoms present in L 4-L 6will also contribute to this diminished basicity.To analyze the interaction with glutamic acid,it is important to know the protonation degree of the ligands at physiological pH values.In Table 2,we have calculated the percentages ofthe different protonated species existing in solution at pH 7.4for receptors L 1-L 6.As can be seen,except for the receptor with the pentamethylenic chains L 3in which the tetraprotonated species prevails,all of the other systems show that the di-and triprotonated species prevail,although to different extents.Interaction with Glutamate.The stepwise constants for the interaction of the receptors L 1-L 6with glutamate are shown in Table 3,and selected distribution diagrams are plotted in Figure 1A -C.All of the studied receptors interact with glutamate forming adduct species with protonation degrees (j )which vary between 8and 0depending on the system (see Table 3).The stepwise constants have been derived from the overall association constants (L +Glu 2-+j H +)H j LGlu (j -2)+,log j )provided by the fitting of the pH-metric titration curves.This takes into account the basicities of the receptors and glutamate (vide supra)and the pH range in which a given species prevails in solution.In this respect,except below pH ca.4and above pH 9,HGlu -can be chosen as the protonated form of glutamate involved in the formation of the different adducts.Below pH 4,the participation of H 2Glu in the equilibria has also to be considered (entries 9and 10in Table 3).For instance,the formation of the H 6LGlu 4+species can proceed through the equilibria HGlu -+H 5L 5+)H 6LGlu 4+(entry 8,Table 3),and H 2Glu +H 4L 4+)H 6LGlu 4(entry 9Table 3),with percentages of participation that depend on pH.One of the effects of the interaction is to render somewhat more basic the receptor,and somewhat more acidic glutamic acid,facilitating the attraction between op-positely charged partners.A first inspection of Table 3and of the diagrams A,B,and C in Figure 1shows that the interaction strengths differ markedly from one system to another depending on the structural features of the receptors involved.L 4is the receptor that presents the highest capacity for interacting with glutamate throughout all of the pH range explored.It must also be remarked that there are not clear-cut trends in the values of the stepwise constants as a function of the protonation degree of the receptors.This suggests that charge -charge attractions do not play the most(25)(a)Martell,E.;Smith,R.M.Critical Stability Constants ;Plenum:NewYork,1975.(b)Motekaitis,R.J.NIST Critically Selected Stability Constants of Metal Complexes Database ;NIST Standard Reference Database,version 4,1997.Table 1.Protonation Constants of Glutamic Acid and Receptors L 1-L 6Determined in NaCl 0.15mol dm -3at 298.1KreactionGluL 1aL 2aL 3bL 4L 5L 6L +H )L H c 9.574(2)d 9.74(2)8.90(3)9.56(1)9.25(3)9.49(4)9.34(5)L H +H )L H 2 4.165(3)8.86(2)8.27(2)8.939(7)8.38(3)8.11(5)8.13(5)L H 2+H )L H 3 2.18(2)7.96(2) 6.62(3)8.02(1) 6.89(5)7.17(6)7.46(7)L H 3+H )L H 4 6.83(2) 5.85(4)7.63(1) 6.32(5) 6.35(6) 5.97(8)L H 4+H )L H 5 4.57(3) 3.37(4) 2.72(8) 2.84(9) 3.23(9)L H 5+H )L H 6 3.18(3) 2.27(6)∑log K H n L41.135.334.233.634.034.1aTaken from ref 23.b These data were previously cited in a short communication (ref 26).c Charges omitted for clarity.d Values in parentheses are the standard deviations in the last significant figure.Scheme 2.L -Glutamate Acid -BaseBehaviorTable 2.Percentages of the Different Protonated Species at pH 7.4H 1L aH 2LH 3LH 4LL 11186417L 21077130L 3083458L 4083458L 51154323L 6842482aCharges omitted for clarity.A R T I C L E SMiranda et al.826J.AM.CHEM.SOC.9VOL.126,NO.3,2004outstanding role and that other forces contribute very importantly to these processes.26However,in systems such as these,which present overlapping equilibria,it is convenient to use conditional constants because they provide a clearer picture of the selectivity trends.27These constants are defined as the quotient between the overall amounts of complexed species and those of free receptor and substrate at a given pH[eq1].In Figure2are presented the logarithms of the effective constants versus pH for all of the studied systems.Receptors L1and L2with a nonfunctionalized secondary amino group in the side chains display opposite trend from all other receptors. While the stability of the L1and L2adducts tends to increase with pH,the other ligands show a decreasing interaction. Additionally,L1and L2present a close interaction over the entire pH range under study.The tetraaminic macrocycle L3is a better(26)Escartı´,F.;Miranda,C.;Lamarque,L.;Latorre,J.;Garcı´a-Espan˜a,E.;Kumar,M.;Ara´n,V.J.;Navarro,mun.2002,9,936-937.(27)(a)Bianchi,A.;Garcı´a-Espan˜a,c.1999,12,1725-1732.(b)Aguilar,J.A.;Celda,B.;Garcı´a-Espan˜a,E.;Luis,S.V.;Martı´nez,M.;Ramı´rez,J.A.;Soriano,C.;Tejero,B.J.Chem.Soc.,Perkin Trans.22000, 7,1323-1328.Table3.Stability Constants for the Interaction of L1-L6with the Different Protonated Forms of Glutamate(Glu) entry reaction a L1L2L3L4L5L6 1Glu+L)Glu L 3.30(2)b 4.11(1)2HGlu+L)HGlu L 3.65(2) 4.11(1) 3.68(2) 3.38(4) 3Glu+H L)HGlu L 3.89(2) 4.48(1) 3.96(2) 3.57(4) 4HGlu+H L)H2Glu L 3.49(2) 3.89(1) 2.37(4) 3.71(2)5HGlu+H2L)H3Glu L 3.44(2) 3.73(1) 2.34(3) 4.14(2) 2.46(4) 2.61(7) 6HGlu+H3L)H4Glu L 3.33(2) 3.56(2) 2.66(3) 4.65(2) 2.74(3) 2.55(7) 7HGlu+H4L)H5Glu L 3.02(2) 3.26(2) 2.58(3) 4.77(2) 2.87(3) 2.91(5) 8HGlu+H5L)H6Glu L 3.11(3) 3.54(2) 6.76(3) 4.96(3) 4.47(3) 9H2Glu+H4L)H6Glu L 2.54(3) 3.05(2) 3.88(2) 5.35(3) 3.66(4) 3.56(3) 10H2Glu+H5L)H7Glu L 2.61(6) 2.73(4) 5.51(3) 3.57(4) 3.22(8) 11H3Glu+H4L)H7Glu L 4.82(2) 4.12(9)a Charges omitted for clarity.b Values in parentheses are standard deviations in the last significantfigure.Figure1.Distribution diagrams for the systems(A)L1-glutamic acid, (B)L4-glutamic acid,and(C)L5-glutamicacid.Figure2.Representation of the variation of K cond(M-1)for the interaction of glutamic acid with(A)L1and L3,(B)L2,L4,L5,and L6.Initial concentrations of glutamate and receptors are10-3mol dm-3.Kcond)∑[(H i L)‚(H j Glu)]/{∑[H i L]∑[H j Glu]}(1)New1H-Pyrazole-Containing Polyamine Receptors A R T I C L E SJ.AM.CHEM.SOC.9VOL.126,NO.3,2004827receptor at acidic pH,but its interaction markedly decreases on raising the pH.These results strongly suggest the implication of the central nitrogens of the lateral polyamine chains in the stabilization of the adducts.Among the N-functionalized receptors,L4presents the largest interaction with glutamate.Interestingly enough,L5,which differs from L4only in having a phenethyl group instead of a benzyl one,presents much lower stability of its adducts.Since the basicity and thereby the protonation states that L4and L5 present with pH are very close,the reason for the larger stability of the L4adducts could reside on a better spatial disposition for formingπ-cation interactions with the ammonium group of the amino acid.In addition,as already pointed out,L4presents the highest affinity for glutamic acid in a wide pH range,being overcome only by L1and L2at pH values over9.This observation again supports the contribution ofπ-cation inter-actions in the system L4-glutamic because at these pH values the ammonium functionality will start to deprotonate(see Scheme2and Figure1B).Table4gathers the percentages of the species existing in equilibria at pH7.4together with the values of the conditional constant at this pH.In correspondence with Figure1A,1C and Figure S2(Supporting Information),it can be seen that for L1, L2,L5,and L6the prevailing species are[H2L‚HGlu]+and[H3L‚HGlu]2+(protonation degrees3and4,respectively),while for L3the main species are[H3L‚HGlu]+and[H4L‚HGlu]2+ (protonation degrees4and5,respectively).The most effective receptor at this pH would be L4which joins hydrogen bonding, charge-charge,andπ-cation contributions for the stabilization of the adducts.To check the selectivity of this receptor,we have also studied its interaction with L-aspartate,which is a competitor of L-glutamate in the biologic receptors.The conditional constant at pH7.4has a value of3.1logarithmic units for the system Asp-L4.Therefore,the selectivity of L4 for glutamate over aspartate(K cond(L4-glu)/K cond(L4-asp))will be of ca.15.It is interesting to remark that the affinity of L4 for zwiterionic L-glutamate at pH7.4is even larger than that displayed by receptors III and IV(Chart1)with the protected dianion N-acetyl-L-glutamate lacking the zwitterionic charac-teristics.Applying eq1and the stability constants reported in ref17,conditional constants at pH7.4of 3.24and 2.96 logarithmic units can be derived for the systems III-L-Glu and IV-L-Glu,respectively.Molecular Modeling Studies.Molecular mechanics-based methods involving docking studies have been used to study the binding orientations and affinities for the complexation of glutamate by L1-L6receptors.The quality of a computer simulation depends on two factors:accuracy of the force field that describes intra-and intermolecular interactions,and an adequate sampling of the conformational and configuration space of the system.28The additive AMBER force field is appropriate for describing the complexation processes of our compounds,as it is one of the best methods29in reproducing H-bonding and stacking stabiliza-tion energies.The experimental data show that at pH7.4,L1-L6exist in different protonation states.So,a theoretical study of the protonation of these ligands was done,including all of the species shown in5%or more abundance in the potentiometric measurements(Table4).In each case,the more favored positions of protons were calculated for mono-,di-,tri-,and tetraprotonated species.Molecular dynamics studies were performed to find the minimum energy conformations with simulated solvent effects.Molecular modeling studies were carried out using the AMBER30method implemented in the Hyperchem6.0pack-age,31modified by the inclusion of appropriate parameters. Where available,the parameters came from analogous ones used in the literature.32All others were developed following Koll-man33and Hopfinger34procedures.The equilibrium bond length and angle values came from experimental values of reasonable reference compounds.All of the compounds were constructed using standard geometry and standard bond lengths.To develop suitable parameters for NH‚‚‚N hydrogen bonding,ab initio calculations at the STO-3G level35were used to calculate atomic charges compatible with the AMBER force field charges,as they gave excellent results,and,at the same time,this method allows the study of aryl-amine interactions.In all cases,full geometry optimizations with the Polak-Ribiere algorithm were carried out,with no restraints.Ions are separated far away and well solvated in water due to the fact that water has a high dielectric constant and hydrogen bond network.Consequently,there is no need to use counteri-ons36in the modelization studies.In the absence of explicit solvent molecules,a distance-dependent dielectric factor quali-tatively simulates the presence of water,as it takes into account the fact that the intermolecular electrostatic interactions should vanish more rapidly with distance than in the gas phase.The same results can be obtained using a constant dielectric factor greater than1.We have chosen to use a distance-dependent dielectric constant( )4R ij)as this was the method used by Weiner et al.37to develop the AMBER force field.Table8 shows the theoretical differences in protonation energy(∆E p) of mono-,bi-,and triprotonated hexaamine ligands,for the (28)Urban,J.J.;Cronin,C.W.;Roberts,R.R.;Famini,G.R.J.Am.Chem.Soc.1997,119,12292-12299.(29)Hobza,P.;Kabelac,M.;Sponer,J.;Mejzlik,P.;Vondrasek,put.Chem.1997,18,1136-1150.(30)Cornell,W.D.;Cieplak,P.;Bayly,C.I.;Gould,I.R.;Merz,K.M.,Jr.;Ferguson,D.M.;Spelmeyer,D.C.;Fox,T.;Caldwell,J.W.;Kollman,P.A.J.Am.Chem.Soc.1995,117,5179-5197.(31)Hyperchem6.0(Hypercube Inc.).(32)(a)Fox,T.;Scanlan,T.S.;Kollman,P.A.J.Am.Chem.Soc.1997,119,11571-11577.(b)Grootenhuis,P.D.;Kollman,P.A.J.Am.Chem.Soc.1989,111,2152-2158.(c)Moyna,G.;Hernandez,G.;Williams,H.J.;Nachman,R.J.;Scott,put.Sci.1997,37,951-956.(d)Boden,C.D.J.;Patenden,put.-Aided Mol.Des.1999, 13,153-166.(33)/amber.(34)Hopfinger,A.J.;Pearlstein,put.Chem.1984,5,486-499.(35)Glennon,T.M.;Zheng,Y.-J.;Le Grand,S.M.;Shutzberg,B.A.;Merz,K.M.,put.Chem.1994,15,1019-1040.(36)Wang,J.;Kollman,P.A.J.Am.Chem.Soc.1998,120,11106-11114.Table4.Percentages of the Different Protonated Adducts[HGlu‚H j L](j-1)+,Overall Percentages of Complexation,andConditional Constants(K Cond)at pH7.4for the Interaction ofGlutamate(HGlu-)with Receptors L1-L6at Physiological pH[H n L‚HGlu]an)1n)2n)3n)4∑{[H n L‚HGlu]}K cond(M-1)L13272353 2.44×103L2947763 4.12×103L31101324 3.99×102L423737581 2.04×104L51010222 3.51×102L6121224 3.64×102a Charges omitted for clarity.A R T I C L E S Miranda et al. 828J.AM.CHEM.SOC.9VOL.126,NO.3,2004。

核物理专业英语词汇指南

核物理专业英语词汇指南摘要：本文介绍了核物理专业的一些基本概念和常用词汇，以及它们的英文表达和发音。

本文旨在帮助核物理专业的学生和研究者提高英语水平，更好地进行国际交流和学术研究。

本文分为以下几个部分：核物理基本概念核反应和放射性核材料和燃料核设施和反应堆核安全和防护核能利用和发展核物理基本概念核物理是研究原子核的结构、性质、相互作用和变化的物理学分支。

核物理涉及到许多基本粒子，如质子、中子、电子、光子、中微子等，以及它们之间的四种基本力：强相互作用力、弱相互作用力、电磁力和引力。

核物理还涉及到许多重要的现象，如裂变、聚变、衰变、辐射等，以及它们在能量转换、物质转化和时间演化中的作用。

下面是一些核物理基本概念和常用词汇的英文表达和发音：中文英文发音元素element/ˈelɪmənt/粒子particle/ˈpɑːrtɪkl/离子ion/ˈaɪən/分子molecule/ˈmɒlɪkjuːl/原子atom/ˈætəm/原子的atomic/əˈtɒmɪk/原子核nucleus (pl. nuclei)/ˈnjuːklɪəs/ (/ˈnjuːkliaɪ/)核的nuclear/ˈnjuːklɪə(r)/质子proton/ˈprəʊtɒn/中子neutron/ˈnjuːtrɒn/电子electron/ɪˈlektrɒn/核子nucleon/ˈnjuːklɪən/化学性质chemical property/ˈkemɪkl ˈprɒpəti/带正电的positively charged/ˈpɒzətɪvli ˈtʃɑːdʒd/带负电的negatively charged/ˈneɡətɪvli ˈtʃɑːdʒd/不带电的uncharged/ʌnˈtʃɑːdʒd/电中性的electrically neutral/ɪlektrɪkli ˈnjuːtrəl/（元素）周期表periodic table/pɪərɪədɪk ˈteɪbl/原子序数atomic number/ətɒmɪk ˈnʌmbə(r)/质量数mass number/mæs ˈnʌmbə(r)/轨道电子orbital electron/ˈɔ:bɪtl ɪlektrɒn/同位素isotope/ˈaɪsətəʊp/天然存在的naturally occurring/ˈnætʃrəli əˈkɜ:rɪŋ/中文英文发音人工的artificial/ˌɑ:tɪˈfɪʃl/化学键chemical bond/ˈkemɪkl bɒnd/化合物compound/ˈkɒmpaʊnd/上标superscript/ˈsu:pəskrɪpt/下标subscript/ˈsʌbskrɪpt/氢hydrogen/ˈhaɪdrədʒən/重氢，氘heavy hydrogen, deuterium/hevi ˈhaɪdrədʒən, dju:ˈtɪəriəm/重氢核，氘核deuterion/dju:ˈtɪəriən/超重氢，氚tritium/ˈtrɪtiəm/氦helium/ˈhi:liəm/结合能binding energy/ˈbaɪndɪŋ ˈenədʒi/动能kinetic energy/kɪˈnetɪk ˈenədʒi/势能potential (energy)/pəˈtenʃl (ˈenədʒi)/跃迁jump/dʒʌmp/核力nuclear force/ˈnju:klɪə fɔ:s/排斥repulsion/rɪˈpʌlʃn/吸引attraction/əˈtrækʃn/轰击bombardment/bɒmˈbɑ:dmənt/发射（出）emission (n.), emit (v.)/ɪˈmɪʃn, ɪˈmɪt/能级energy level/ˈenədʒi ˌlevl/裂变fission/ˈfɪʃn/聚变fusion/ˈfju:ʒn/衰变decay/dɪˈkeɪ/核反应和放射性核反应是指原子核的结构或组成发生变化的过程，通常伴随着能量和粒子的释放或吸收。

光电转化效率英文

光电转化效率英文Photovoltaic Efficiency: Harnessing the Power of LightThe quest for renewable and sustainable energy sources has been a driving force in the scientific community for decades. Among the various technologies that have emerged, photovoltaic (PV) systems have garnered significant attention due to their ability to directly convert sunlight into electrical energy. The efficiency of this conversion process, known as photovoltaic efficiency, is a crucial factor in determining the overall performance and viitability of solar energy as a viable alternative to traditional fossil fuels.At its core, the photovoltaic effect is a phenomenon in which the absorption of light by a semiconductor material generates electron-hole pairs that can be separated and collected to produce an electric current. The efficiency of this process is determined by a complex interplay of various factors, including the properties of the semiconductor material, the design of the PV cell, and the conditions under which the system operates.One of the primary factors influencing photovoltaic efficiency is the ability of the semiconductor material to absorb a wide range of thesolar spectrum. Ideally, the semiconductor should be able to absorb as much of the incident solar radiation as possible, converting it into usable electrical energy. This is where the concept of bandgap energy comes into play. The bandgap is the energy difference between the valence band and the conduction band of the semiconductor material, and it determines the range of wavelengths that the material can effectively absorb.Researchers have dedicated significant efforts to developing semiconductor materials with optimized bandgap energies to maximize the absorption of solar radiation. Silicon, the most widely used semiconductor in PV systems, has a bandgap energy of around 1.1 eV, which allows it to absorb a significant portion of the visible and near-infrared regions of the solar spectrum. However, there are other semiconductor materials, such as gallium arsenide (GaAs) and cadmium telluride (CdTe), that have bandgap energies more closely matched to the solar spectrum, potentially offering higher photovoltaic efficiencies.Another crucial factor in photovoltaic efficiency is the ability of the PV cell to effectively separate and collect the generated electron-hole pairs. This process is influenced by the design and structure of the PV cell, including the choice of electrode materials, the quality of the semiconductor-electrode interface, and the presence of any recombination centers or defects within the cell. Researchers haveexplored various device architectures, such as heterojunction and tandem designs, to optimize the charge separation and collection processes, ultimately improving the overall photovoltaic efficiency.The performance of a PV system is also heavily dependent on the operating conditions, such as temperature and irradiance levels. Increased temperatures can lead to a decrease in the bandgap energy of the semiconductor material, which can result in a lower open-circuit voltage and a reduction in photovoltaic efficiency. Conversely, higher irradiance levels can enhance the generation of electron-hole pairs, potentially increasing the current output and overall efficiency.To address these challenges, researchers have developed various strategies to improve photovoltaic efficiency. One approach is the use of advanced materials, such as perovskites and organic semiconductors, which have shown promising results in terms of efficiency and cost-effectiveness. Perovskite solar cells, for example, have demonstrated rapid advancements in efficiency, reaching over 25% in laboratory settings, making them a compelling alternative to traditional silicon-based PV technologies.Another approach is the development of tandem or multi-junction solar cells, which combine multiple semiconductor materials with different bandgap energies. By stacking these materials in a strategicmanner, the system can effectively capture a broader range of the solar spectrum, leading to higher overall photovoltaic efficiencies. These tandem designs have the potential to surpass the theoretical efficiency limits of single-junction solar cells, paving the way for even more efficient PV systems.In addition to material and device innovations, researchers have also explored techniques to optimize the system-level performance of PV installations. This includes the development of advanced tracking systems, which can adjust the orientation of the solar panels to follow the sun's path, maximizing the amount of incident solar radiation. Furthermore, the integration of energy storage solutions, such as batteries or thermal storage, can help overcome the intermittency of solar energy, enabling a more reliable and consistent power supply.The quest for higher photovoltaic efficiency is not just a scientific pursuit but also a critical step towards the widespread adoption of solar energy as a viable alternative to traditional fossil fuels. As the world grapples with the pressing challenges of climate change and the need for sustainable energy solutions, the continued advancement of photovoltaic technology holds the promise of a future powered by the abundant and renewable energy of the sun.。

Neutrino Event Rates from Gamma Ray Bursts

a rXiv:as tr o-ph/998138v38Oct1999University of Wisconsin -Madison MADPH-99-1134astro-ph/9908138August 1999Neutrino Event Rates from Gamma Ray Bursts F.Halzen and D.W.Hooper Department of Physics,University of Wisconsin,Madison,WI 53706Received August 13,1999;accepted October 7,1999ABSTRACTWe recalculate the diﬀuseﬂux of high energy neutrinos produced by Gamma Ray Bursts(GRB)in the relativisticﬁreball model.Although we conﬁrm that the average single burst produces only∼10−2high energy neutrino events in a detector with1km2eﬀective area,i.e.about10events per year,we show that the observed rate is dominated by burst-to-burstﬂuctuations which are very large.Weﬁnd event rates that are expected to be larger by one order of magnitude,likely more,which are dominated by a few very bright bursts.This greatly simpliﬁes their detection.Subject headings:gamma rays:bursts1.High Energy Neutrinos from Relativistic FireballsThe evidence has been steadily accumulating that GRB emission is the result of a relativistically expandingﬁreball energized by a process involving neutron stars or black holes(Piran1999).In the early stage,theﬁreball cannot emit eﬃciently because the radiation is trapped due to the very large optical depth.Theﬁreball’s energy is dissipated in kinetic energy until it becomes optically thin and produces the observed display.This scenario can accommodate the observed energy-and time scales provided the bulk Lorentz factorγof the expanding shock is∼300.The production of high energy neutrinos is anticipated:protons,accelerated in the kinetic phase of the shock,interact with photons producing charged pions which are the parents of neutrinos(Waxman&Bahcall1997).Standard particle physics andﬁreball phenomenology are suﬃcient to compute the neutrinoﬂux(Waxman&Bahcall1997; Halzen1998)as well as the observed rates in high energy neutrino telescopes.The observation of GRB neutrinos over a cosmological baseline has scientiﬁc potential beyond testing the“best-buy”ﬁreball model:the observations can test with unmatched precision special relativity and the equivalence principle,and study oscillating neutrinoﬂavors over the ultimate baseline of z≃1.The anticipated neutrinoﬂux traces the broken power-law spectrum observed for the photons,which provide the target material for neutrino production:Aφ=for E>E B,(2)E2where A is a normalization constant which is determined from energy considerations andE B≈700TeV(Halzen1998).The total energy in GRB neutrinos is given byF tot=c2fπt hubble˙ρE,(3)where fπis the fraction of proton energy that goes into pion production,t hubble is10Byrs and˙ρE is the injection rate into protons accelerated to high energies in the kineticﬁreball. This is a critical parameter in the calculations;it can beﬁxed,for instance,by assuming that GRB are the source of the highest energy cosmic rays beyond the ankle(Waxman 1995;Milgrom&Usov1995;Vietri1995)in the spectrum,or˙ρE≃4×1044erg Mpc−3yr−1 (Halzen1998).The factor fπrepresent the fraction of total energy going into pion production.It is calculated by known particle physics and is of order15%(Waxman& Bahcall1997;Halzen1998).We remind the reader that these assumptions reproduce the observed average photon energy per burst if equal energy goes into the hadronic and electromagnetic component of theﬁreball(Waxman&Bahcall1997).Now,normalizing theﬂux for this total energy:F tot=AE.(4)Approximating E B−E min≃E B,the integration constant is found to be1.20×10−12TeV cm−2s−1sr−1.The quantities fπand E B are calculated using Eqs.(4) and(5)in Waxman and Bahcall(1997).The GRB parameters entering these equations are chosen following Halzen(1998)and assumed to be independent ofγ.We assumedE max=107TeV.Given the neutrinoﬂuxφ,the event rates in a neutrino detector are obtained by a straightforward method(Halzen1998):N= φ(E)Pν→µdE,(5) where Pν→µis the detection probability for neutrinos of muonﬂavor.It is determined,as a function of energy,by the neutrino cross sections and the range of the secondary muon(Gaisser,Halzen&Stanev1995;Gandhi et al.1996).We obtain an observed neutrinoﬂux of order10yr−1km−2assuming103bursts per year.This result is somewhat lower but not inconsistent with those obtained previously.One should keep in mind that neutrinos can also be produced,possibly with higher ﬂuxes,in other stages of theﬁreball,e.g.when it expands through the interstellar medium (Katz1994;Halzen&Jaczko1996;Vietri1998;Boettcher&Dermer1998).2.Burst-to-Burst FluctuationsWe here want to draw attention to the fact that this result should not be used without consideration of the burst-to-burstﬂuctuations which are very large indeed;see also Dermer,Boettcher&Chiang(1999).We will,in fact,conclude that from an observational point of view the relevant rates are determined by theﬂuctuations,and not by the average burst.Our calculations are performed byﬂuctuating individual bursts according to the model described above with i)the square of the distance which is assumed to follow a Euclidean or cosmological distribution,ii)with the energy assuming that the neutrino rate depends linearly on energy and follows a simple step function with ten percent of GRB producing more energy than average by a factor of ten,and one percent by a factor of100, and,most importantly,iii)ﬂuctuations in theγfactor around its average value of300. Theﬂuctuations inγaﬀect the value of fπwhich varies approximately asγ−4(Waxman& Bahcall1997)as well as the position of the break energy which varies asγ2.For a detailed discussion see Halzen(1998).Both eﬀects are taken into account.Clearly a factor of ten variation ofγleads to a change inﬂux by roughly4orders of magnitude.The origin of the largeﬂuctuations withγshould be a general property of boosted accelerators.With high luminosities emitted over short times,the large photon densityrenders the GRB opaque unlessγis very large.Only transparent sources with large boost factors emit photons.They are however relatively weak neutrino sources because the actual photon target density in theﬁreball is diluted by the large Lorentz factor.This raises the unanswered question whether there are bursts with lowerγ-factors. Because of absorption such sources would emit less photons of lower energy and could have been missed by selection eﬀects;they would be spectacular neutrino sources.Some have argued(Stern1999)for γ ∼30on the basis that the unusualﬂuctuations in the morphology of GRB can only be produced in a relatively dense,turbulent medium.3.Monte Carlo Simulation ResultsWe will illustrate the eﬀect ofﬂuctuations by Monte Carlo simulation of GRB.For a Euclidean distribution the calculation can be performed analytically;in other cases the Monte Carlo method evaluates the integrals.The overwhelming eﬀect ofﬂuctuations is demonstrated in sample results shown in Figs.1–3and Table1,a–c.Not knowing the distribution ofγ-factors around its average,we have parametrized it as a Gaussian with widthsσ,σ′below and above the average value of300.We choseσ′to be either0or300, to illustrate the eﬀect of allowing GRB with Lorentz factors up to103with a Gaussian probability.The critical,and unknown,parameter isσ.It may,in fact,be more important than any other parameter entering the calculation.As far as we know,neither theory nor experiment provide compelling information at this point.Note that we requireσ>70in order to allow a signiﬁcant part of the bursts to haveγ-factors less than102,or one third the average value;see Table1.The value ofσ′is less critical.A value of300allows for Lorentz factors as large as103.The dominant eﬀect of this is a renormalization of the neutrino rates because a fraction of the bursts now have a largeγ-factor and,as a consequence,a low neutrinoﬂux.We discuss some quantitative examples next.Firstly,even in the absence of the dominantﬂuctuations inγ,the rate of9detected neutrinos per year over103bursts,becomes30–90in the presence ofﬂuctuations in energy and distance.The range covers a variety of assumptions for GRB distributions,which range from Euclidean to cosmological;the issue is not important here because other factors dominate theﬂuctuations.Every2years there will be an event with7neutrinos in a single burst.Forσ=70,the rate is∼600per year in a kilometer square detector,with23 individual bursts yielding more than4neutrinos and7yielding more than10in a single year!The results for other values ofσare tabulated in Table1.The number of events per year for a range of values ofσis shown in Fig.1.The frequency of GRB producing seven or more neutrinos is shown in Fig.2.The neutrino multiplicity of bursts forσ=30,60 and75is shown in Fig.3.Note that absorption in the source eventually reduces the overall rates whenγis much smaller than average,orσlarger than60.This factor is included in our calculations(Halzen1998).To this point we have assumed that all quantitiesﬂuctuate independently.Interestingly, the value ofσ=70is obtained in the scenario where insteadﬂuctuations inγare a consequence ofﬂuctuations in energy.In order not to double count,ﬂuctuations in energy itself,which only contribute a factor of3to the neutrino rate anyway,should be omitted.Even though bursts with somewhat lowerγproduce neutrinos with reduced energy, compared to700TeV,over a longer time-scale than1second,the signatures of these models are spectacular.Existing detectors with eﬀective area at the1–10%of a kilometer squared, should produce results relevant to the open question on the distribution of bulk Lorentz factors in theﬁreball model.Independent of the numerics,the fact that a single GRB with high energy,close proximity and a relatively low Lorentz factor can reasonably produce more detectable neutrino events than all other GRB over several years time,renders the result of thestraightforward diﬀuseﬂux calculation observationally misleading.Our calculations suggest that it is far more likely that neutrino detectors detect one GRB with favorable characteristics,than hundreds with average values.Clearly,our observations are relevant for other GRB models,as well as for blazars and any other boosted sources.They are also applicable to photons and may represent the underlying mechanism for the fact that the TeV extra-galactic sky consists of a few bursting sources.We expect no direct correlation between neutrino and high energy gamma sources because cosmic events with abundant neutrino production are almost certainly opaque to high energy photons.4.ConclusionsAlthough the average event rates predicted with typical GRB parameters appear somewhat discouraging to present and future Cerenkov neutrino detector experiments, theﬂuctuations in these calculations are more signiﬁcant and aﬀect the prospects for detection.We speculated on the distribution of the parameters entering theﬁreball model calculation and used a Monte Carlo simulation to estimate the actual event rates.The result of these simulations show that a kilometer scale detector could be expected to observe tens or hundreds of events per year.To improve on the reliability of this estimate,a well deﬁned distribution for the Lorentz factor must be determined.Contrariwise,not observing neutrino GRB after years of observation will result in a strong limit on the number of accelerated protons in the kinetic phase of the burst,or inﬁne-tuned,high values of the Lorentz boost factor.AcknowledgementsThis research was supported in part by the U.S.Department of Energy under Grant No.DE-FG02-95ER40896and in part by the University of Wisconsin Research Committee with funds granted by the Wisconsin Alumni Research Foundation.We thank G.Barouch, T.Piran and E.Waxman for discussions.REFERENCESBoettcher,M&Dermer,C.D.1998,astro-ph/9801027,ApJ,499,L131Dermer,C.D.,Boettcher,M.&Chiang,J.1999,ApJ Lett,in pressFor a review,see Gaisser,T.K.,Halzen,F.&Stanev,T.1995,Phys.Rep.,258(3),173 Gandhi,R.,Quigg,C.,Reno,M.H.&Sarcevic,I.1996,Astropart.Phys.,5,81 Halzen,F.1998,astro-ph/9810368,Lectures on Neutrino Astronomy:Theory and Experiment,given at the Theoretical Advanced Study Institute in ElementaryParticle Physics(TASI98),“Neutrinos in Physics and Astrophysics:From10−33to 10+28cm”,Boulder,Colorado,May31–June261998Halzen,F.&Jaczko,G.1996,Phys.Rev.D,54,2774Katz,J.I.1994,ApJ,432,L27Milgrom,M.&Usov,V.1995,ApJ,449,L37For a recent review,see Piran,T.1999,astro-ph/9810256,Phys.Rep.,314,575Stern,B.1999,astro-ph/9902203,in“High Energy Processes in Accreting Black Holes”,ed.J.Poutanen and R.Svensson(ASP Conf.Series),Vol.161,277Vietri,M.1995,ApJ,453,883Vietri,M.1998,Phys.Rev.Lett.80,3690Waxman,E.1995,Phys.Rev.Lett.,75,386Waxman,E.&Bahcall,J.N.1997,Phys.Rev.Lett.,78,2292Fig. 1.—Rate of high energy neutrino events in a detector with1km2eﬀective area as a function of the range of the bulk Lorentz factorγ.The range is assumed to be Gaussian with widthσbelow the average of300,andσ′above.The latter is taken to be either0,or300.Fig. 2.—Yearly rate of individual neutrino bursts with more than7events in a detector with1km2eﬀective area as a function of the range of the bulk Lorentz factorγ.The range is assumed to be Gaussian with widthσbelow the average of300,andσ′above.The latter is taken to be either0,or300.Fig. 3.—Neutrino multiplicity distribution in individual GRB in a detector with1km2 eﬀective area.The range of the bulk Lorentz factorγis assumed to be Gaussian with width σ=30,60and75below the average of300,andσ′taken to be0.Table1:High energy neutrino events in a detector with1km2eﬀective area as a function of the range of the bulk Lorentz factorγ.The range is assumed to be Gaussian with widthσbelow the average of300,andσ′above.The latter is taken to be either0,or300.Shown as a function ofσis the total number of neutrinos,as well as the yearly number of individual bursts with more than4,7,and11high energy neutrinos.For comparison,the middle line shows the result when allﬂuctuations are removed.σ′=0800.040.15 1.0919.8378.91276331812750.010.080.6817.481.88142715107000.040.3914.884.8611231276500.020.2012.187.74831810660000.099.4690.5394168455000.04 6.8693.1326136350000.01 4.5295.5271115245000 2.6297.422794240000 1.2898.7193832350000.4499.616773130000099.9146621000001008610.50.2Result if energy and distance are not allowed to vary:Percent of Lorentz Factors by Range GRB≥X Events/yrσ0–1010–5050–100100–200200–300Events/yr≥4≥7≥11。

新型无机闪烁体的能量分辨率(中英文对照)

成都理工大学学生毕业设计（论文）外文译文极，（b）光电子是后来ηNph，（c）这些∝ηNph电子在第一倍增极和到达（d）倍增极的k（k = 1，2…）放大后为δk 并且我们假设δ1=δ2=δ3=δk=δ的，并且δ/δ1≈1的。

我们可以得出：R2=Rlid2=5.56δ/[∝ηNph（δ-1）] ≈5.56/Nel （3）Nel表示第一次到达光电倍增管的数目。

在试验中，δ1≈10＞δ2=δ3=δk，因此，在实际情况下，我们可以通过（3）看出R2的值比实际测得大。

请注意，对于一个半导体二极管（不倍增极结构）（3）也适用。

那么Nel就是是在二极管产生电子空穴对的数目。

在物质不均匀，光收集不完整，不相称和偏差的影响从光电子生产过程中的二项式分布及电子收集在第一倍增极不理想的情况下，例如由于阴极不均匀性和不完善的重点，我们有：R2=Rsci2+Rlid2≈5.56[(νN-1/Nel)+1/Nel] (4)νN光子的产生包括所有非理想情况下的收集和1/Nel的理想情况。

为了说明，我们在图上显示，如图1所示。

ΔE/E的作为伽玛射线能量E的函数，为碘化钠：铊闪烁耦合到光电倍增管图。

1。

对ΔE/E的示意图（全曲线）作为伽玛射线能量E功能的碘化钠：铊晶体耦合到光电倍增管。

虚线/虚线代表了主要贡献。

例如见[9,10]。

对于Rsci除了1/（Nel）1/2的组成部分，我们看到有两个组成部分，代表在0-4％的不均匀性，不完整的光收集水平线，等等，并与在0-400代表非相称keV的最大曲线。

表1给出了E=662Kev时的数值（137Cs）在传统的闪烁体资料可见。

从图一我们可以清楚的看到在低能量E＜100Kev，如果Nel，也就是Nph增大的话，是可以提高能量分辨率的。

这是很难达到的，因为光额产量已经很高了（见表1）在能量E＞300Kev时，Rsci主要由能量支配其能量分辨率，这是没办法减小Rsci 的。

然而，在下一节我们将会讲到，可以用闪烁体在高能量一样有高的分辨率。

宽入射角高效宽带超表面太赫兹线极化转换器

第19卷第3期太赫兹科学与电子信息学报Vo1．19，No．3 2021年6月 Journal of Terahertz Science and Electronic Information Technology Jun．，2021 文章编号：2095-4980(2021)03-0361-05宽入射角高效宽带超表面太赫兹线极化转换器尹波，马越*，张晓玲，刘伽利，夏禾禾，张玉瑶，梁景瑞(重庆邮电大学光电工程学院，重庆 400065)摘要：为解决当前太赫兹频段下的极化转换器件带宽窄和带内转换率低的问题，设计了一款基于超表面的高效率太赫兹线极化转换器。

通过在两端增加一对谐振枝节的方法，将原本的单谐振频点变为2个，增加了极化转换器的工作带宽。

另一方面，利用超表面在电磁谐振时的高阻抗表面特性，获得了极低的同极化反射系数，提高了带内的总体转换效率。

仿真结果显示，该结构能够在0.401~0.555 THz的宽频带范围内实现高效率的线极化转换，相对带宽约为32.5%，带内转换率高于95%。

在理论分析方面，通过对高转换率频率下的表面电流与相位的仿真，阐明了宽带高转换率的机理。

研究了该结构对于太赫兹波入射角度的依赖性，结果表明，该结构在0°~40°的入射角范围内均可保持较好的极化转换性能。

同时，这款极化转换器具有设计简单的优点，这些工作能够对宽带高效的超表面极化转换器件设计提供设计思路。

关键词：超表面；太赫兹；极化转换器中图分类号：O441 文献标志码：A doi：10.11805/TKYDA2020518Terahertz high-efficiency broadband metasurface polarization converter withwide incident angleYIN Bo，MA Yue*，ZHANG Xiaoling，LIU Jiali，XIA Hehe，ZHANG Yuyao，LIANG Jingrui (Institute of Photoelectric，Chongqing University of Post and Telecommunication，Chongqing 400065，China)Abstract：A high-efficiency broadband polarization converter based on metasurface is proposed in order to broaden the working bandwidth of the polarization converter in terahertz band as well asimproving the polarization conversion ratio. By adding a couple of resonating branches, the original singleresonating point is increased to two, dramatically increasing the working bandwidth of the polarizationconverter. The low co-polarized reflectance is acquired through the characteristic of high-resistancesurface when the metasurface is under electro-magnetic resonance, which could enhance the overallpolarization conversion rate. The simulation results illustrate that this structure is able to achieve highpolarization conversion in 0.401-0.555 THz with conversion ratio above 95%. The mechanism forhigh-efficiency broadband polarization conversion is discussed through simulating the reflect phase andsurface current distribution. The dependence of the structure on the incident angle of terahertz waves isstudied. The results show that this structure is able to maintain high conversion ratio at incident anglewithin 0°-40°. In addition, this design has advantage of simple structure. These works can help in thedesign of broadband efficient metasurface polarization converter.Keywords：metasurface；terahertz；polarization converter极化在电磁波的传输中扮演了十分重要的角色。

光光转换效率英文

光光转换效率英文介绍光光转换效率英文是指太阳能电池将光能转化为电能的效率。

在太阳能领域，光光转换效率是一个重要的指标，影响着太阳能电池的实际应用和经济效益。

光光转换效率的提高可以有效地提高太阳能电池的性能和产能，加速太阳能产业的发展。

本文将详细探讨光光转换效率的英文表达，包括相关术语和常用表述。

术语及表述在讨论光光转换效率英文之前，先介绍一些与光光转换效率相关的术语： 1. Photovoltaic conversion efficiency：光伏转换效率 2. Incident light：入射光 3. Absorption：吸收 4. Electron-hole pair：电子空穴对 5. Exciton：激子 6. Charge carrier：载流子 7. Energy band gap：能带间隙 8. Open-circuit voltage：开路电压 9. Short-circuit current：短路电流 10. Fill factor：填充因子 11. Power conversion efficiency：功率转换效率光光转换效率的影响因素光光转换效率受多种因素的影响，下面将逐一介绍这些因素及其英文表述。

材料选择1.Band gap engineering：能带调控2.Semiconducting material：半导体材料3.Absorption coefficient：吸收系数4.Doping concentration：掺杂浓度结构设计1.Surface texture：表面处理2.Anti-reflection coating：抗反射涂层3.Tandem structure：串联结构4.Multi-junction solar cells：多结太阳能电池光学特性1.Quantum efficiency：量子效率2.Reflectance：反射率3.Transmittance：透过率4.Light trapping：光捕获电子输运1.Mobility：迁移率2.Diffusion length：扩散长度3.Recombination：复合4.Tunneling effect：隧穿效应界面特性1.Heterojunction：异质结2.Contact resistance：接触电阻3.Interface trap density：界面态密度4.Passivation：表面钝化设备参数1.Open-circuit voltage：开路电压2.Short-circuit current：短路电流3.Fill factor：填充因子4.Power conversion efficiency：功率转换效率提高光光转换效率的方法在太阳能电池领域，提高光光转换效率是一个持续的研究方向。

基于伽马射线的类轴子粒子探测及暗物质子晕搜寻研究

第62卷第2期天文学报Vol.62No.2 2021年3月ACTA ASTRONOMICA SINICA Mar.,2021doi:10.15940/ki.0001-5245.2021.02.010博士学位论文摘要选登基于伽马射线的类轴子粒子探测及暗物质子晕搜寻研究夏子晴†(中国科学院紫金山天文台南京210023)目前已经有很多观测证据表明宇宙中存在着大量暗物质,其能量密度占据了目前宇宙总能量密度的1/4.根据高精度的数值模拟和引力透镜观测,我们已经对从矮星系到星系团中的暗物质空间分布有了较好的理解,但是对于暗物质究竟是什么我们还一无所知.由此,物理学家提出了很多假想的粒子模型.其中比较著名的粒子模型有:弱相互作用大质量粒子(WIMP)、轴子和类轴子(ALP).弱相互作用大质量粒子只存在弱相互作用和引力相互作用,可以相互湮灭(或者衰变)成稳定的高能粒子,包括伽马光子、带电粒子和中微子.从而使我们可以通过探测其湮灭(或者衰变)产生的高能粒子来间接探测弱相互作用大质量粒子.ALP可以在电磁场中与光子相互转化,这一特性使得我们可以通过寻找伽马射线能谱中的光子-类轴子振荡结构来间接探测类轴子.本文中的研究主要是利用公开的费米大面积望远镜(Fermi Large Area Telescope,Fermi-LAT)的数据和已发表的大气切伦科夫望远镜High Energy Stereoscopic System(H.E.S.S.)能谱数据,对暗物质粒子(轴子和类轴子、弱相互作用大质量粒子)进行间接探测.银河系中广泛存在着磁场,因此在河内源的能谱中可能存在着由光子和类轴子相互转化而形成的振荡结构.首先我们选取了3个在银盘上且非常明亮的超新星遗迹作为目标源(分别是IC443、W44和W51C),利用Fermi-LAT对这3个超新星遗迹的观测来寻找光子-类轴子振荡信号.在IC443的能谱中,我们找到了疑似的振荡结构,但是其对应的类轴子参数空间已经被太阳轴子望远镜CAST(CERN(European Centre for Nuclear Research)Axion Solar Telescope)排除.我们猜测,由于IC443是个空间延展的源,其能谱中出现的疑似的振荡结构可能是来自不同区域伽马射线辐射叠加的结果.然后我们选取了10个明亮的位于银盘上的TeV源,利用H.E.S.S.发表的能谱数据继续搜寻类轴子.然而我们并没有找到明显的光子-类轴子振荡信号,随后计算出了对类轴子参数空间的限制.这是首次利用天文观测数据在高质量区域(100neV)对解释河外TeV伽马射线反常弱吸收的类轴子模型参数空间进行排除.我们还利用Fermi-LAT伽马射线观测,搜寻了来自暗物质子晕结构的弱相互作用大质量粒子湮灭信号.目前有大量数值模拟的结果显示,像银河系这样的星系中存在大量的暗物质子晕结构.暗物质粒子可以湮灭或者衰变产生伽马射线.因此质量足够大且距我们足够近的暗物质子晕可能会以稳定延展伽马射线源的形式出现,同时没有其他波段的对应天体.以此为标准,我们找到了一个可能的暗物质子晕候选体3FGL J1924.8−1034,但是由于Fermi-LAT角分辨率的局限,我们不能排除它是由两个(及以上)邻近点源组成的可能.由于高的质光比,矮椭球星系一直被认为是暗物质间接探测的理想目标.我们搜寻了银河系附近矮椭球星系的伽马射线辐射,来探测弱相互作用大质量粒子的信号.分析发现来自Reticulum II方向的伽马射线信号是随时间稳步增长的.随后我们对所有目标源进行了联合分析,得到的联合伽马射线信†2019-06-20获得博士学位,导师:紫金山天文台伍健研究员和范一中研究员;21-12天文学报62卷号已经超过了4σ的局域置信度.在暗物质间接探测中,主要困难在于如何把暗物质湮灭或衰变产物的信号从天体物理背景中分离出来.如果是搜寻具有某些独特特征的能谱,如线谱和箱型能谱,在这方面遇到的困难就要小一些,因为通常的天体物理辐射过程难以出现这种特殊结构的能谱.在本文的工作中,我们还利用了Fermi-LAT数据来搜寻暗物质粒子可能产生的特征能谱(包括线谱和箱型能谱)信号.我们分别在银河系卫星星系和银河系内的暗物质子晕结构(通过N体模拟)寻找潜在的线谱信号.由于没有发现明显信号,我们随后计算出了暗物质湮灭成两个光子的湮灭截面的相应上限.随后我们还在矮椭球星系中,研究了由暗物质湮灭或衰变所产生的中间粒子衰变发出的箱型伽马射线能谱信号.Probe Axion-like Particles(ALPs)and Search for Dark Matter Subhalo with the Gamma-rayObservationsXIA Zi-qing(Purple Mountain Observatory,Chinese Academy of Sciences,Nanjing210023)The presence of a large amount of dark matter(DM)in the Universe has already been convincingly established.DM is believed to make up a quarter of the energy density of the current Universe.Thanks to high-resolution numerical simulations made possible by modern supercomputers and the gravitational lensing observations,the distribution of DM in structures ranging from dwarf galaxies to clusters of galaxies has been understood better than before.But the nature of DM remains unknown.Various hypothetical particles have been proposed,such as weakly-interacting mas-sive particles(WIMPs),axion,axion-like particles(ALPs),sterile neutrino and gravitino. WIMPs may be able to annihilate with each other(or alternatively decay)into stable high-energy particle pairs,including gamma-rays,charged particles and neutrinos.ALPs and photons can convert to each other in electromagneticﬁelds through the Primakoﬀprocess, which could result in the detectable spectral oscillation phenomena in the gamma-rays ob-servation.My research mainly focused on the indirect detection of dark matter,such as ALPs and WIMPs,using publicly available Fermi Large Area Telescope(Fermi-LAT)data and the the published data of High Energy Stereoscopic System(H.E.S.S.)observation.The conversion between photons and ALPs in the Milky Way magneticﬁeld could result in the detectable oscillation phenomena in the gamma-ray spectra of the Galactic sources. First,we search for such oscillation eﬀects in the spectra of supernova remnants caused by the photon-ALP conversion,using the Fermi LAT data.The inclusion of photon-ALP oscillations yields an improvedﬁt to theγ-ray spectrum of IC443,which gives a statistical signiﬁcance of4.2σin favor of such spectral oscillation.However,the best-ﬁt parameters of ALPs are in tension with the CAST(CERN(European Centre for Nuclear Research)Axion Solar Telescope)limits.Secondly,we use the H.E.S.S.observations of some TeV sources in the Galactic plane to exclude the highest ALP mass region(i.e.,ALP mass m a∼10−7eV) that accounts for the anomalously weak absorption of TeV gamma-rays for theﬁrst time.A Milky Way-like galaxy is predicted to host tens of thousands of galactic DM subhalos. Annihilation of WIMPs in massive and nearby subhalos could generate detectable gamma-rays,appearing as unidentiﬁed,spatially-extended and stable gamma-ray sources.We search for such sources in the third Fermi Large Area Telescope source List(3FGL)and report21-22期夏子晴:基于伽马射线的类轴子粒子探测及暗物质子晕搜寻研究3the identiﬁcation of a new candidate,3FGL J1924.8−1034.3FGL J1924.8−1034is found spatially-extended at a high conﬁdence level of5.4σ.No signiﬁcant variability has been found and its gamma-ray spectrum is wellﬁtted by the dark matter annihilation into b¯b with a mass of∼43GeV.All these facts make3FGL J1924.8−1034a possible dark matter subhalo candidate.However,due to the limited angular resolution,the possibility that the spatial extension of3FGL J1924.8−1034is caused by the contamination from the other un-resolved point source can not be ruled out.The Milky Way dwarf spheroidal galaxy is considered one of the most ideal targets for indirect detection of dark matter due to their high dark matter density and low astrophysical backgrounds.We search for gamma-ray emission from nearby Milky Way dwarf spheroidal galaxies and candidates with Fermi-LAT data.Intriguingly,the peak TS(Test Statistic) value of the weak emission from Reticulum II rises continually.We alsoﬁnd that the combination of all these nearby sources will result in a more signiﬁcant(>4σ)gamma-ray signal.A commonly encountered obstacle in indirect searches for dark matter is how to disentangle possible signals from astrophysical backgrounds.Gamma-ray features,in particular monochromatic gamma-ray lines and boxlike spectral features,provide smoking gun signatures.We analyze the Fermi LAT observation of Milky Way satellites and the local volume dark matter subhalo population(with N-body simulation)to search for potential line signals,respectively.The corresponding upper limits on the cross section of DM annihilation into two photons are derived,without signiﬁcant signal found.Then we study the box-shaped DM signals,which is generated by the decay of intermediate particles produced by DM annihilation or decay,with Fermi-LAT observations of dwarf spheroidal galaxies.21-3。

CONVERSION OF HIGH-ENERGY PHOTONS INTO ELECTRICITY

专利名称：CONVERSION OF HIGH-ENERGY PHOTONSINTO ELECTRICITY发明人：Michl Binderbauer,Toshiki Tajima申请号：US13521220申请日：20110101公开号：US20130125963A1公开日：20130523专利内容由知识产权出版社提供专利附图：摘要：Systems and methods for the conversion of energy of high-energy photons into electricity which utilize a series of materials with differing atomic charges to takeadvantage of the emission of a large multiplicity of electrons by a single high-energy photon via a cascade of Auger electron emissions. In one embodiment, a high-energy photon converter preferably includes a linearly layered nanometric-scaled wafer made up of layers of a first material sandwiched between layers of a second material having an atomic charge number differing from the atomic charge number of the first material. Inother embodiments, the nanometric-scaled layers are configured in a tubular or shell-like configuration and/or include layers of a third insulator material.申请人：Michl Binderbauer,Toshiki Tajima地址：Irvine CA US,Irvine CA US国籍：US,US更多信息请下载全文后查看。

稀土上转换发光英语

稀土上转换发光英语Rare Earth Upconversion Luminescence.Introduction.Rare earth upconversion luminescence, often referred to as upconversion, is a phenomenon in which low-energy photons are converted into higher-energy photons through the interaction of photons with ions doped into a host lattice. This process allows for the emission of visible light from infrared excitation, which has numerous applications in various fields, including solar cells, biological imaging, and optical displays.Background.Upconversion luminescence was first discovered in the 1960s, but its potential applications were not immediately recognized. It was primarily studied in the context ofsolid-state physics and spectroscopy. However, with theadvancement of nanotechnology and the development of nanostructured materials, upconversion has gained significant attention due to its unique properties and potential applications.Working Principle.Upconversion luminescence occurs when photons interact with ions doped into a host lattice, typically rare earth ions such as erbium (Er3+) or ytterbium (Yb3+). These ions have multiple energy levels, and when excited by infrared light, they absorb multiple photons and transition to higher energy levels. Subsequently, they decay back to lower energy levels, emitting visible photons in the process.The key to efficient upconversion is the energy transfer process between the ions. Ytterbium ions, with their strong absorption cross-section and efficient energy transfer properties, are often used as sensitizers to transfer energy to other rare earth ions. This energy transfer process can occur either through a directinteraction between the ions or indirectly through the host lattice.Applications.1. Solar Cells: Upconversion luminescence can enhance the efficiency of solar cells by converting infrared photons, which are not typically absorbed by silicon-based solar cells, into visible photons that can be effectively utilized. This process leads to an increase in the solar cell's photocurrent and hence its efficiency.2. Biological Imaging: Upconversion luminescence has found applications in biological imaging due to its ability to emit visible light from infrared excitation. This feature allows for deeper tissue penetration and reduced autofluorescence background, making it suitable for in vivo imaging. Additionally, the long luminescence lifetime of upconversion materials can provide temporal resolution for biological processes.3. Optical Displays: Upconversion luminescence haspotential applications in optical displays, particularly in the development of color-tunable displays. By doping different rare earth ions into a host lattice, it is possible to emit different colors of light, enabling multicolor displays. Additionally, the ability to tune the emission wavelength of upconversion materials offers flexibility in display design.Challenges and Future Directions.Although upconversion luminescence has shown promising applications, there are still challenges that need to be addressed. One of the key challenges is the low external quantum efficiency of upconversion materials, which limits their practical applications. Future research efforts should focus on improving the efficiency of upconversion processes and exploring new materials and structures that can enhance the energy transfer process.Another challenge is the stability and durability of upconversion materials under various environmental conditions. Many upconversion materials are sensitive totemperature, humidity, and other external factors, whichcan affect their performance. Therefore, there is a need to develop more stable and robust upconversion materials that can withstand harsh environments.Despite these challenges, the future of upconversion luminescence looks promising. With continued research and development, it is expected that upconversion materialswill find widespread applications in various fields, including solar cells, biological imaging, optical displays, and more.In conclusion, rare earth upconversion luminescence isa fascinating phenomenon with numerous potential applications. Its unique ability to convert infrared light into visible light offers new opportunities in various fields, and with continued research and development, it is likely to play a significant role in future technologies.。

High Energy Tau Neutrinos

a r X i v :h e p -p h /0111436v 1 29 N o v 20011High Energy Tau NeutrinosJane H.MacGibbon a and Ubi F.Wichoski b∗aCode SN3,NASA Johnson Space Center,Houston Texas 77058USAbDepto.de F´ısica,CENTRA-IST,Av.Rovisco Pais,1-Lisbon 1049-001PortugalThe intrinsic tau neutrino ﬂux from cosmological and astrophysical sources has usually been considered negligible in com-parison to the electron and muon neutrino ﬂuxes.However,the inclusion of the tau neutrino component coming from hadronic decay at the source can signiﬁcantly modify the tau neutrino spectrum expected at Earth.We report our results on the high energy tau neutrino production and its implications for the observation of high energy neutrino events.1.INTRODUCTIONPresently much effort is being expended to resolve the ﬂavor of the incoming neutrino ﬂux (for a review see [1]).One motivation for doing this is that the absolute sensitivity,or relative sensitivity compared with background,may be signiﬁcantly greater for one neutrino species than for other species [2].Another primary motivation for identifying the neutrino ﬂa-vor is to test the hypothesis that neutrinos undergo ﬂavor oscillation as they propagate from source to Earth.Because the non-oscillation production of ντis assumed to be negligible relative to νe and νµpro-duction,and the cascade ντproduced by collisions of primary νe and νµﬂux with the relic cosmic neu-trino background is orders of magnitude less than the primary νe and νµﬂux,any detected ντcomponent from a source outside the Solar System is currently expected to be indicative of oscillation.In this paper,we brieﬂy report some results of our investigation into high energy ντproduction,presented elsewhere [3].We illustrate that the ντcomponent at the high energy end in the hadronic decays is signiﬁcantly higher than previously assumed and that this can have observa-tional consequences.2.NEUTRINO PRODUCTIONHigh energy neutrinos are expected to be produced by several cosmological and astrophysical sources,dx=152decaying jet [6].This distribution continues down toE∼1GeV .When convolved with the π±decay,Eq.(1)leads to a similarly dominant E −3/2term in the νe and νµspectra at x 0.1and dN νe ,νµ/dE →0as x →1.(For a full derivation of the νe and νµspectra using fragmentation function (1)see [7].)Because ντproduction is suppressed compared with other species,it has been assumed in previous astrophysical and cosmological ﬂux calculations that the ντspectrum from hadronic jets is orders of magni-tude less than the νe and νµspectra at all x .This is not so,once the energy of the jets surpasses the tau lep-ton and heavy quark masses.While indeed the total number of ντproduced per jet is less than 10−3of the total number of νe and νµ,the high x tau neutrinos are predominantly produced by the initial decays of the heavier quarks with shorter lifetimes (the greatest contribution comes from the t quark decay)and the νe and νµare produced by the ﬁnal state cluster decays of the much lighter pions.This leads to signiﬁcantly greater relative contribution from ντat high x than previously assumed.The fragmentation distribution (1)is no longer relevant for the tau neutrino.In Fig.1we show the ντspectrum,together with the νe and νµspectra,generated by the decay of 10TeV q ¯q jets.To simulate these spectra we used the QCD event generator HERWIG [12]and the process e +e −→q i ¯q i (g ),i =all q ﬂavors.Consistent spectra are obtained with PYTHIA/JETSET (see [3]).Note that in the region 0.1 x 1,the tau neutrinos make up more than one tenth of the total neutrino contribu-tion.Note also that below x 0.1,dN ντ/dE falls off with roughly an E −1/2slope,and not the E −3/2slope of the νe and νµspectra.From our 300GeV –75TeV simulations,we ﬁnd that the ντspectrum generated by q ¯q jet decay can be parametrized asdN ντ2m J0.15E ντm J1/2−0.06E ντdQdt=Γs (T BH ,Q )kT BH−(−1)2s−1,(3)where Γs is the absorption probability for species,s is the spin,and T BH is the black hole temperature.The neutrino ﬂux from the evaporating PBH including hadronic decays is shown in Fig.3.3.CONCLUSIONSPrevious work has assumed the ντcomponent in TeV –UHE hadronic decays to be negligible com-34681012142123l o g 10(E 2F (E )) [e V m -2 s r -1 s e c -1]log 10(E) [eV]Muon Neutrino Electron NeutrinoTau Neutrino from Decays Tau Neutrino from CascadesFigure 2.The neutrino spectra from VHS cosmic strings with a mass per unit length of Gµ=10−8.The dash-dotted curve is the ντcomponent produced by cascades off the relic neutrino background [13]and the thick solid line is the the ντcomponent produced by hadronic decays.pared with the νe and νµcomponents,at all neu-trino energies.We ﬁnd that this is not so once the decays are sufﬁciently energetic to include the heav-ier quarks.In particular,for neutrino energies in the decade below the energy of the initial decaying par-ticle,the tau neutrino component is of similar mag-nitude to the νe and νµcomponents.Below these energies the ντspectrum exhibits a slope of slightly less than E −1/2compared with the E −3/2slope of the νe and νµspectra.This analysis modiﬁes the ex-pected spectra in many astrophysical and cosmologi-cal high energy neutrino production scenarios.As a consequence,the observation of a signiﬁcant ντto νµratio at a given energy in high energy neutrino tele-scopes and detectors may be due to hadronic decay at the source and not νµ→ντoscillation in transit.Acknowledgments:It is a pleasure to thank M.Sey-mour and in particular B.Webber for advice,and R.Brandenberger and A.Heckler for encouragement.REFERENCES1. E.Kh.Akhmedov,Neutrino Physics ,hep-ph/0001264v2(2000).2.S.I.Dutta,M.H.Reno,and I.Sarcevic,Phys.Rev.D 62,123001(2000).202122232425262728-1-0.500.511.522.53l o g 10(d 2N /d E d t ) [G e V -1 s e c -1]log 10(E) [GeV]Muon Neutrino Electron NeutrinoTau NeutrinoFigure 3.The neutrino ﬂux from a T BH ∼100GeV evaporating PBH at a redshift (1+z )∼1[3].The dashed line represents νµ,the dotted line represents νe ,and the solid line represents ντ.3.J.H.MacGibbon and U.F.Wichoski,Tau Neu-trinos from Astrophysical and Cosmological Sources (2001),to be submitted;J.H.MacGib-bon,U.F.Wichoski,and B.R.Webber,Proc.of the 27th International Cosmic Ray Conference ,Hamburg,2001,p.1157(hep-ph/0106337).4.H.Athar,G.Parente,and E.Zas,Phys.Rev.D62,093010(2000);A.Husain,Cosmic Tau Neu-trinos ,hep-ph/0004083.5.For a review see P.Bhattacharjee and G.Sigl,Phys.Rep.327,109(2000).6. C.Hill,D.Schramm,and T.Walker,Phys.Rev.D 36,1007(1987).7.Ubi F.Wichoski,Jane H.MacGibbon,and RobertH.Brandenberger,High Energy Neutrino,Pho-ton and Cosmic Ray Fluxes from VHS Cosmic Strings ,hep-ph/9805419(to appear in PRD).8.I.M.Albuquerque,L.Hui,and E.W.Kolb,Phys.Rev.D 64,083504(2001).9.J.H.MacGibbon and B.J.Carr,Astrophys.J.371,447(1991).10.J.H.MacGibbon and B.R.Webber,Phys.Rev.41,3052(1990).11.F.Halzen,B.Keszthelyi,and E.Zas,Phys.Rev.D 52,3239(1995).12.G.Corcella et al.,JHEP 0101,010(2001).13.S.Yoshida et al.,Astrophys.J.479,547(1997).。

Innovations in Waste-to-Energy Conversion

Innovations in Waste-to-Energy Conversion Waste-to-energy conversion is a process of generating energy from waste materials. This process has gained significant attention in the past few years due to its potential to reduce waste and generate clean energy. Innovations in waste-to-energy conversion have been made to improve the efficiency, sustainability, and environmental impact of this process. In this response, we will discuss some of the recent innovations in waste-to-energy conversion and their benefits.One of the recent innovations in waste-to-energy conversion is the use of advanced gasification technology. Gasification is a process that converts solid waste into a gas that can be used to generate electricity or produce other useful products. Advanced gasification technology uses high temperatures and pressure to convert waste into a clean gas that contains very low levels of pollutants. This technology has several benefits, including high efficiency, low emissions, and the ability to handle a wide range of waste materials.Another innovation in waste-to-energy conversion is the use of anaerobic digestion. Anaerobic digestion is a biological process that breaks down organic waste materials into biogas, which can be used to generate electricity or produce other useful products. This technology has several benefits, including low emissions, high efficiency, and the ability to handle a wide range of organic waste materials. Additionally, anaerobic digestion produces a nutrient-rich byproduct that can be used as fertilizer.Innovations in waste-to-energy conversion have also been made in the area of thermal conversion. Thermal conversion is a process that uses heat to convert waste into energy. This process can be used to generate electricity or produce other useful products. One of the recent innovations in thermal conversion is the use of plasma gasification. Plasma gasification uses high temperatures and pressure to convert waste into a clean gas that can be used to generate electricity or produce other useful products. This technology has several benefits, including high efficiency, low emissions, and the ability to handle a wide range of waste materials.Another innovation in waste-to-energy conversion is the use of pyrolysis. Pyrolysis is a process that uses heat in the absence of oxygen to convert waste into a liquid or gas that can be used to generate electricity or produce other useful products. This technology has several benefits, including high efficiency, low emissions, and the ability to handle a wide range of waste materials. Additionally, pyrolysis produces a biochar byproduct that can be used as a soil amendment.Innovations in waste-to-energy conversion have also been made in the area of mechanical-biological treatment. Mechanical-biological treatment is a process that uses mechanical and biological processes to treat waste materials before they are converted into energy. One of the recent innovations in mechanical-biological treatment is the use of bioreactors. Bioreactors are tanks that contain microorganisms that break down organic waste materials. This technology has several benefits, including low emissions, high efficiency, and the ability to handle a wide range of waste materials.In conclusion, innovations in waste-to-energy conversion have made significant progress in recent years. These innovations have improved the efficiency, sustainability, and environmental impact of waste-to-energy conversion processes. Advanced gasification technology, anaerobic digestion, plasma gasification, pyrolysis, and bioreactors are just a few examples of the recent innovations in waste-to-energy conversion. These technologies have several benefits, including high efficiency, low emissions, and the ability to handle a wide range of waste materials. As waste-to-energy conversion technology continues to evolve, we can expect to see even more innovations that will further improve the efficiency and sustainability of this process.。

科技英语：澳洲科学家将太阳能光电转换率提升至40%

UNSW Australia's solar researchers have converted over 40% of the sunlight hitting a solar system into electricity, the highest efficiency ever reported. The record efficiency was achieved in outdoor tests in Sydney, before being independentlyconfirmed by the National Renewable Energy Laboratory (NREL) at their outdoor test facility in the United States.The work was funded by the Australian Renewable Energy Agency (ARENA) and supported by the Australia-US Institute for Advanced Photovoltaics (AUSIAPV)."This is the highest efficiency ever reported for sunlight conversion1 into electricity," UNSW Scientia Professor and Director of the Advanced Centre for Advanced Photovoltaics (ACAP) Professor Martin Green said."We used commercial solar cells, but in a new way, so these efficiency improvements are readily accessible to the solar industry," added Dr Mark Keevers, the UNSW solar scientist who managed the project.The 40% efficiency milestone2 is the latest in a long line of achievements by UNSW solar researchers spanning four decades. These include the first photovoltaic system to convert sunlight to electricity with over 20% efficiency in 1989, with the new result doubling this performance."The new results are based on the use of focused sunlight, and are particularly relevant to photovoltaic power towers being developed in Australia," Professor Green said.1 conversionn.转化，转换，转变参考例句：He underwent quite a conversion.他彻底变了。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

a r X i v :h e p -p h /0208111v 2 17 F eb 2003INFNCA-TH0205High-energy neutrino conversion into electron-W pair in magneticﬁeld and its contribution to neutrino absorptionAndrea Erdas 1,2,3,∗and Marcello Lissia 2,1,†1Dipart.di Fisica dell’Universit`a di Cagliari,S.P.Sestu Km 1,I-09042Monserrato (CA),Italy 2Ist.Naz.Fisica Nucleare (I.N.F.N.)Cagliari,S.P.Sestu Km 1,I-09042Monserrato (CA),Italy 3Department of Physics and Astronomy,The Johns Hopkins University,Baltimore,MD 21218(August 9,2002;revised November 22,2002)Abstract We calculate the conversion rate of high-energy neutrinos propagating in constant magnetic ﬁeld into an electron-W pair (ν→W +e )from the imagi-nary part of the neutrino ing the exact propagators in constant magnetic ﬁeld,the neutrino self-energy has been calculated to all orders in the ﬁeld within the Weinberg-Salam model.We obtain a compact formula in the limit of B ≪B cr ≡m 2/e .We ﬁnd that above the process thresholdE (th )≈2.2·1016eV ×(B cr /B )this contribution to the absorption of neutrinosyields an asymptotic absorption length ≈1.1m ×(B cr /B )2×(1016eV /E).14.60.Lm,95.30.CqTypeset using REVT E XI.INTRODUCTIONThe study of creation,propagation,energy loss,and absorption of neutrinos in magnetic ﬁeld is important in several astrophysical contexts and in the early cosmology[1].Neutrino self-energy and dispersion relation is modiﬁed in magnetized media[2–4],and processes where neutrinos radiate electron-positron pairs(ν→ν+e++e−)[5–7]or gammas(ν→ν+γ)[8,9,7]have been investigated in the range of energies where it is possible to use an eﬀective four-fermion interaction and rates have been obtained in the limits of weak and strong magneticﬁelds.As an example of the importance of macroscopic magneticﬁeld as an eﬀective source of energy loss for energetic neutrinos,we recall that the estimate[5]for the rateν→ν+e++e−in the strong magneticﬁeld near the surface of a neutron star is about ten times the rate of pair production in the Coulombﬁeld near the nucleus of metallic iron.Conversion of neutrinos in W-lepton pairs in the presence of magneticﬁelds(νl→W+l) should be considered when studying the propagation of neutrinos of suﬃciently high energies: we shall show that in this limit this process gives an important contribution to neutrino absorption.A similar process,νγ→l W+,has been studied by Seckel[10],who shows that at energies above the threshold for W production this process is competitive withννscattering at the same center of mass energies.The process we are considering,where an extremely energetic neutrino creates a real W, is a second order process in the weak coupling constant g,while the radiation of a e+e−pair through a virtual W or a virtual Z is a fourth order process.Therefore,there is an energy above which the conversion into an electron-W pair becomes the dominant process. In addition,since we use the electro-weak lagrangian and not an eﬀective low-energy theory, our result is valid also at very high energies,much higher than the W mass;actually,the W-electron decay rate contributes signiﬁcantly to neutrino absorption only in this limit. Notice that eventually the real W decays and that in about10.5%of cases theﬁnal state contains a neutrino of the sameﬂavor(e.g.,νe→W+e→νe e+e−),so that the process canbe thought of as the radiation of a lepton pair;in about21%of cases theﬁnal state contains a neutrino of diﬀerentﬂavor(e.g.,νe→W+e→νµµe),and in the remaining68.5%of cases theﬁnal state contains hadrons.In this paper we use Schwinger’s proper time method[11]to calculate the neutrino self-energy in homogeneous magneticﬁelds and then we obtain the probability of decay into W-electron pair by extracting the imaginary part of the self-energy.A similar strategy was used by Tsai and Erber[12]to extract the photon pair creation probability from the vacuum polarization in intense homogeneous magneticﬁelds.In Section2we brieﬂy review the notation and derive the one-loop neutrino self-energy in constant magneticﬁeld[2],in Section3we obtain the imaginary part of the self-energy and the rate of W-electron pairs creation in magneticﬁeld.The ensuing discussion and conclusions are in Section4.II.NEUTRINO SELF-ENERGY IN A CONSTANT MAGNETIC FIELDIn this section we review the calculation of the one-loop neutrino self-energy in a homo-geneous magneticﬁeld,using the exact fermion and gauge boson propagators in a constant magneticﬁeld[2].We consider a magneticﬁeld with magnitude B pointing along the pos-itive z-direction.The only non-vanishing components of the electromagneticﬁeld strength tensor Fµνare F12=−F21=B.The exact expression for the electron S(x′,x′′)[11,13] and W boson Gµν(x′,x′′)[2]propagators in a constant magneticﬁeld are obtained using Schwinger’s proper time method:S(x′,x′′)=φ∗(x′,x′′) d4ke ik·(x′−x′′)Gµν(k),(2)(2π)4where the translationally invariant parts of the propagators areS(k)=i ∞0ds×exp −is m2−iǫ+k2 +k2⊥tan eBs cos eBs , andGµν(k)=i ∞0ds eBs e−is(M2−iǫ)[gµν +(e2eF s)µν⊥] + kµ+kλFµλtan eBs B +i eM2 .(4) In the rest of the paper we shall drop the inﬁnitesimal imaginary contribution to the masses −iǫ,which determines the correct boundary conditions;if necessary it can be easily reintro-duced:m2→m2−iǫand M2→M2−iǫ.In our notation,−e and m are the charge and mass of the electron,M the W-mass,x the gauge parameter,σ3=σ12=iFµνxνand,therefore,the phase factor in Eqs.(1)and(2),which is independent of 2the integration path,is[13]φ(x′,x′′)=exp ie x′x′′dxµAµ(x) =exp i esin2(eBs).(6)BNote that the W and Goldstone scalar propagator were obtained in Ref.[2]by introducing a new gaugeﬁxing term(EGF)which is manifestly invariant under electromagnetic gauge transformations.The advantage of the EGF gauge is that the electromagnetic potential has no cross couplings with the W and Goldstoneﬁelds and,therefore,these twoﬁelds do not mix in the presence of a magneticﬁeld.In the remainder of this paper we focus our attention on electron-type neutrinos,the generalization toµandτ-neutrino is straightforward.For the purpose of this work,it would seem convenient to work in the unitary gauge(x→∞),where the unphysical scalarsdisappear.However,the W-propagator is quite cumbersome in this gauge.We prefer to work in the Feynman gauge(x=1),where the expression of the propagator is much simpler. In principle the choice of the Feynman gauge carries the price of calculating an additional bubble diagram:the one with the Goldstone scalar.But this scalar bubble diagram does not contribute to leading order,since it is suppressed by a factor of m2/M2≈4.04·10−11,and can be neglected.Therefore,we only need to calculate the bubble diagram with a W-boson:ΣW(x′,x′′)=ig22γL=1−γ5(2π)4e ip·(x′−x′′)ΣW(p)(9)asΣW(p)=−ig2(2π)4 ∞0ds1cos z2e−is1(m2+q2 +q2⊥tan z1z2)×γRγµ (m−q )e−iz1σ3−q⊥z1+z2p ,k⊥+tan z1ΣW(p)=g2(z1+z2)sin(z1+z2)e−i(m2/eB)[z1+z2M2/m2+(z1+z2)ϕ0]× z2sin(z1+z2)p⊥γL+(c.t.)(13)whereϕ0=z1z2m2+sin z1sin z2m2.(14)and the appropriate counter-terms(c.t.)are deﬁned such that(c.t.)=−ΣW(p) B=0,p=0−p ∂ΣW(p)eB (z1+z2)≡1m2z2ηz2(4π)2 eB sinβzM2/m20du e−iz[1−ηu+u+ϕ0]×ηu p e iσ3βz(1+ηu)+sin[βzηu]M2+sin[βz(1−ηu)]sin[βzηu]M2.(18) III.RATE OF W-ELECTRON PAIR CREATIONBecause of the oscillating phase exp(−iz),the main contribution to the integral over z comes from the region where z<∼1.If we are only interested in neutrinos that travel througha“moderate”magneticﬁeld eB≪m2=eB cr,this meansβ≪1,we can expand the terms in the integrand in power series ofβz≪1.Furthermore,sinceΣW is quite small,of order g2eB/M2,as it can be inferred from the expression(17)or from the explicit calculation in Ref.[2],we can set p=0inΣW.After this is all done,we obtainΣW(p)≃g2M2 2p⊥γL∞0dzz M2/m20duu 23(ηu)2×e−iz[1+u−ηu+1m2(eBmM2,(20)which can be read from the ratio of the z and z3term in the exponential of Eq.(19)or inferred from kinematical considerations and the momentum change of a virtual e−W pair in a magneticﬁeld.At low energies,ξ≪1,the z3term in the exponential can be dropped,the self-energy is real and we obtain the result of Ref.[2];at high energies,ξ≫1,the self-energy acquires an imaginary part that we shall calculate in the following.In this last case we writeΣW asΣW(p)=2(4π)2 eB3ξ2z2u2](21)where we have dropped all nonleading terms inηu and extended the integration in du to ∞,due to the fact that the main contribution to the integral in du comes from the region u<∼1because of the oscillating phase exp(−izu)and thatη=m2/M2is extremely small.The integral in dz of the imaginary part of the self-energy can be performed with the substitution z=y√3 ∞0y sin 33y3) dy(22)obtainingℑΣW(p)=−2(4π)2 eB√u K2/3 √ξ23 3/2 .(23) Theﬁnal integration in du yieldsℑΣW(p)=−g2M2 2 1+√eBp⊥ e−√eBp⊥,(24) and,therefore,the absorption coeﬃcient,α=−2p⊥ℑΣW(p),isα=g2¯h c m B cr2 1+√m Mc B e−√m Mc B.(25)From the exponential in Eq.(25)we can read the threshold for the process1:if we deﬁne ξ(th)=√3Mc2MB≈2.2·1016eVB cr12π¯h c p⊥cM2 2=g2¯h cm B cr 2=0.935 p⊥c B cr 2m−1,(27)where we have used the numerical value G F/(¯h c)3=g2/[√1The kinematical threshold is obviously given by the sum of the masses M+m,below which the rate is rigorously zero:this threshold is lost in our expansion,but it is unimportant as long as the eﬀective threshold,below which the process is exponentially suppressed,is very much larger than M+m.2In principle the full result would have additional dependences on the lepton mass coming from terms that containη=(m/M)2and that we have disregarded being extremely small for electrons; these corrections are larger for muons and especially taus,but still small.IV.DISCUSSION AND CONCLUSIONSIn Figure1we show the absorption coeﬃcient forνe→W+e as function of the neutrino transverse energy E≡p⊥c for several values of the magneticﬁeld B:B=10−1B cr,B= 10−2B cr,B=10−3B cr,B=10−4B cr,and B=10−5B cr with B cr=m2/e=4.4·1010Gauss. It is evident that the process has an energy threshold that grows for smaller values of B, as quantitatively described by Eq.(26).If we consider the angular coeﬃcient,which is one, and the spacing between the curves above the threshold,weﬁnd thatαgrows linearly with E and quadratically with B,in agreement with Eq.(27).The same Figure1is valid forνµ(ντ),if one multiplies both the horizonal and the vertical scale times(mµ/m e)=206.768266 ((mτ/m e)=3477.6).In Figure2we compare the processνe→W+e with the processν→ν+e++e−that has a much lower threshold;this threshold can be estimated from the dimensionlessﬁeld dynamical parameter characteristic to this processκ≡eBp⊥/m3,which is analogous toξof Eq.(20)with the substitution M→m:the threshold is smaller by a factor of about m2/M2≈4·10−11.The curves plotted as function ofκshow clearly that the thresholds of both processes are function only of the product Bp⊥,see Eq.(26).For the process ν→ν+e++e−we use the result shown in Eq.(8)of Ref.[6]:α(ν→νe+e−)=G2F(g2V+g2A)B cr 2ln(κ)−ln(3)24 ,(28)which the authors claim valid for E≪M3/eB(κ≪(M/m)3≈4·1015):we plot Eq.(8) of Ref.[6],see Eq.(28),up toκ=1015.We show results only for B=0.1B cr(top curves) and B=0.001B cr(bottom curves).We see that the processν→ν+e++e−(dashed curves)dominates below the threshold ofν→W+e(solid curves),but above this threshold ν→W+e is almost two orders of magnitude larger(about a factor50).Therefore,above the threshold E≈(mM2)/eB(κ≈(M/m)2≈2·1010),the eﬀective lagrangian(four fermion interaction)cannot be used.The rate ofν→ν+e++e−can instead be estimated using the rate ofν→W+e,which gives the total adsorption,times the branching ratio of W→νe+e,which is(10.66±0.20)%.In conclusion,we have calculated the absorption rate of very high energy neutrinos in magneticﬁeld.Our main result is given by the compact formula in Eq.(25)valid for electron neutrinos.The result for muon or tau neutrinos can be obtained by substituting the electron mass m with the muon or tau mass remembering that the electron mass m appears also in B cr=m2/e.This process is exponentially suppressed,and,therefore,it can be disregarded,for en-ergies below a threshold energy inversely proportional to the magneticﬁeld;for aﬁeld one tenth of the criticalﬁeld this energy is of the order of1017eV,see Eq.(26)and Fig.1.Above this threshold the absorption coeﬃcient grows linearly with energy and quadrat-ically with theﬁeld as shown in Eq.(27):for aﬁeld one tenth of the criticalﬁeld and an energy of1018eV the absorption coeﬃcient is about one inverse meter(see Fig.1).Above the threshold this process substitutes the radiation of e+e−pairs as dominant mechanism forνabsorption in magneticﬁeld(see Fig.2).ACKNOWLEDGMENTSA.Erdas wishes to thank Gordon Feldman for helpful discussions and the High Energy Theory Group of the Johns Hopkins University for the hospitality extended to him during his several visits.This work is partially supported by M.I.U.R.(Ministero dell’Istruzione,dell’Universit`a e della Ricerca)under Coﬁnanziamento P.R.I.N.2001.REFERENCES∗Electronic address:andrea.erdas@ca.infn.it†Electronic address:marcello.lissia@ca.infn.it[1]G.G.Raﬀelt,Stars as Laboratories for Fundamental Physics(University of ChicagoPress,Chicago,1996).[2]A.Erdas and G.Feldman,Nucl.Phys.B343,597(1990).[3]A.Erdas,C.W.Kim,and T.H.Lee,Phys.Rev.D58,085016(1998).[4]A.Erdas and C.Isola,Phys.Lett.B494262(2000).[5]A.V.Borisov,A.I.Ternov,and V.Ch.Zhukovsky,Phys.Lett.B318,489(1993).[6]A.V.Kuznetsov,N.V.Mikheev,Phys.Lett.B394,123(1997).[7]A.A.Gvozdev,A.V.Kuznetsov,N.V.Mikheev,and L.A.Vassilevskaya,Phys.Atom.Nucl.61,1031(1998).[8]A.A.Gvozdev,N.V.Mikheev,and L.A.Vassilevskaya,Phys.Rev.D54,5674(1996).[9]A.N.Ioannisian and G.G.Raﬀelt,Phys.Rev.D55,7038(1997).[10]D.Seckel,Phys.Rev.Lett.80,900(1998).[11]J.Schwinger,Phys.Rev.82,664(1951).[12]W.Tsai and T.Erber,Phys.Rev.D10,492(1974).[13]W.Dittrich and M.Reuter,Eﬀective Lagrangians in Quantum Electrodynamics,LectureNotes in Physics(Springer-Verlag,Berlin,1985).FIG.1.Neutrino absorption coeﬃcient for the processνe→W+e in inverse meters as func-tion of the neutrino transverse energy(E≡p⊥c)in eV forﬁve values of the magneticﬁeld:B=10−1B cr,B=10−2B cr,B=10−3B cr,B=10−4B cr,B=10−5B cr going from top to bottom,with B cr=4.4·1010Gauss.The same curves apply forνµ(ντ),if both the horizonal and the vertical scale are multiplied times(mµ/m e)=206.768266((mτ/m e)=3477.6).FIG.2.Neutrino absorption coeﬃcients for the processesνe→W+e,(solid curves)and ν→ν+e++e−(dashed curves)in inverse meters as function of the dimensionless characteristicparameterκ≡eBp⊥/m3for two values of the magneticﬁeld:B=10−1B cr and B=10−3B crgoing from top to bottom.。