Isotope shifts of 6s5d $^3$D-states in neutral Barium

a r X i v :0805.2022v 1 [p h y s i c s .a t o m -p h ] 14 M a y 2008EPJ manuscript No.(will be inserted by the editor)Isotope shifts of 6s5d 3D-states in neutral bariumU.Dammalapati a ,S.De,K.Jungmann,and L.WillmannKernfysisch Versneller Instituut,University of Groningen,Zernikelaan 25,9747AA Groningen,The NetherlandsMay 14,2008ser spectroscopy of the low lying 1P and 3D states in atomic barium has been performed.This work contributes substantially to the development of an effective laser cooling and trapping for heavy alkaline earth elements and aims in particular for a better understanding of the atomic wave function of these systems.Isotope shifts and hyperfine structures are ideal probes for the wave functions at the position of the nucleus.This is essential input for a theoretical evaluation of the sensitivity to fundamental symmetry breaking properties like permanent electric dipole moments.We report the first isotope shift measurements of the 3D 1,2-1P 1transitions.A deviation of the King plot from its expected behavior has been observed.Further we have optically resolved the hyperfine structure of the 3D 1,2states.PACS.4 2.62.Fi,39.30.+w,32.80.Pj1IntroductionRecently heavy alkaline earth atoms have attracted at-tention due to high enhancement factors for possible per-manent electric dipole moment (edm’s),both of electrons and nuclei in several isotopes which have nuclear spin.Of particular interest are radium (Ra)isotopes which ex-hibit the largest known enhancement factors for an elec-tron edm and for nucleon edm in nuclei.These arise from close lying states of opposite parity [1,2]in the atomic shell (3P and 3D)or in the nucleus where they are associ-ated with octopole deformations in some nuclei near the region of the valley of stability [3,4].In order to conduct such research a good understanding of the atomic struc-ture,i.e.wave functions,transition probabilities,lifetimes,and hyperfine structure splitting,is needed.At this time atomic structure calculations with independent numerical approaches are underway [5].Sensitive experiments with rare or radioactive isotopes such as Ra require samples of laser cooled and trapped atoms.Experiments are prepared at Argonne National Laboratory,Il,USA [6]and at the TRI µP facility at the Kernfysisch Versneller Instituut,The Netherlands [7,8].The development of an effective method for laser cool-ing and trapping is indispensable.Elaborate laser cooling schemes need to be explored.They involve several lasers at the same time.Barium (Ba),a chemical homologue to Ra,has a similar level structure and is well suited for the development of the technical method due to the copious availability of a large number of stable isotopes.In atomic Ba,the 6s 21S 0-6s6p 1P 1transition (Fig.1)is the strongest transition.It is the only option for laser cooling and trapping in the ground state.The upper state2U.Dammalapati et al.:Isotope shifts of 6s5d 3D-states in Ba36s5d 21Lower λLevel (k)[nm]1P 1λ1 1.19(1)a λir 10.0025(2)a λir 20.0011(2)a λir 30.000031(5)a1S 0791.33D 22923.03D 12775.71P 13D 2τ0.25s[15]1345(14)ns[16]Table 2.Lifetimes of the 1P 1,1D 2,3D 2and 3P 1states.The reference [14,16]quote experimental values and [15]quote cal-culated values.The experimental apparatus (Fig.2)is designed to ful-fill two requirements:First,the production of an atomic beam of metastable D-state atoms by optical pumping.Second,infrared laser spectroscopy of the metastable states.The setup provides two separate interaction zones of the atomic beam with laser beams.We observe the transitions originating from the metastable D-states by fluorescence at the wavelength λ1.In this paper we focus on the 3D states.2.1Isotope selective metastable productionMetastable atoms in the D-states are produced by opti-cal pumping with a laser beam orthogonal to the atomic velocity direction.Isotope selective production can be ac-complished either by driving the 6s 21S 0-6s6p 1P 1transi-tion at wavelength λ1=553.7nm followed by spontaneousIsotope pairIsotope shift [MHz]at λ2-215.15(16)-128.02(39)-259.29(17)-143.0(5)U.Dammalapati et al.:Isotope shifts of6s5d3D-states in Ba34U.Dammalapati et al.:Isotope shifts of 6s5d 3D-states in Ba100020003000-150-100-5050100150200250300138B a136B a134B aIaFrequency [MHz ]C o u n t [1/s ]20004000-150-100-5050100150200250300IbFrequency [MHz ]C o u n t [1/s ]100020003000-150-100-5050100150200250300IIaFrequency [MHz ]C o u n t [1/s ]5000100001500020000-150-100-50050100150200250300IIbFrequency [MHz ]C o u n t [1/s ]Fig. 5.Isotope shift for 138Ba,136Ba,134Ba at wavelength λir 3.Spectra Ia and Ib,respectively IIa and IIb,are taken si-multaneously.(Ia)Selecting 134Ba.Because the isotope shift at wavelength λ2of the pumping transition is small,we pop-ulate also the other isotopes at the same time.(Ib)and (IIa)Selecting 136Ba and (IIb)138Ba.The strength of the signal scales with the natural abundance of the selected isotope.A Lorentzian lineshape is fitted to the resonances.The frequency can be given relative to the transition in 138Ba.3.2Odd isotopes In the odd isotopes we have hyperfine structure multi-plets.The hyperfine levels in the triplet D-states are pop-ulated by locking the diode laser to the 1S 0(F =3/2)-3P 1(F =3/2)transition,which is shifted by -925.6(1.0)MHz relative to the transition in 138Ba.The selection rules al-low to populate the F =1/2,3/2and 5/2states of the 3D 1level for 137Ba and 135Ba.The hyperfine structure splitting of the 3P 1state inBa isotopes with nuclear spin I =3/2has been measured before with high accuracy by optical-rf double-resonance,using a hollow cathode lamp as a light source [21].Thehyperfine structure of the 3D 1state was determined byan atomic beam magnetic resonance method [22].We have measured the hyperfine spectrum of 137Ba and 135Ba isotopes for the 3D 1-1P 1transition simultane-ously by selecting the isotopes through optical pumping using the intercombination line.The laser frequency at λir 3is scanned over the entire set of hyperfine lines which are spreaded over more than 2GHz (Fig.6).All the seven transitions can be fitted with a sum of Lorentzian func-0100020003000400050006000-1.5-1-0.500.51Frequency offset [GHz]F l u o r e s c e n c e [C t s /s ]100020003000400050006000-1.5-1-0.500.51Frequency offset [GHz]F l u o r e s c e n c e [C t s /s ]Fig.6.Measured hyperfine spectra for the 3D 1-1P 1transition for 137Ba and 135Ba.The frequency axis is relative to the same transition in 138Ba.Each frequency point was measured for 1second.tionsF ν=C +7 i =1A iΓ/2)2,(1)where C represents the background counts,i is the index of the hyperfine components,A i is the amplitude of each component,Γis the full width at half maximum and νi is the center of the hyperfine component.From the fit we obtain Γ=20(1)MHz,which is in good agreement withthe natural linewidth of the transition.We derived the isotope shift between the isotopes 137Ba and 135Ba from the measured hyperfine spectra.We deter-mine the difference frequencies ∆ν1(Tab.4)of all seven hyperfine components.With the known hyperfine split-tings of the 3D 1[22]and 1P 1-states [9]we calculate the difference ∆ν2for all hyperfine transitions of the two iso-topes.Thus,the isotope shift ∆νIS is ∆νIS =∆ν1+∆ν2,(2)where the difference in the hyperfine structure ∆ν2for the two isotopes is ∆ν2=[∆νhfs (3D 1)∆νhfs (1P 1)]137(3)−[∆νhfs (3D 1)−(∆νhfs (1P 1)]135.(4)We note that the error is smallest where the transitions nearly coincide in frequency ((5/2→5/2)and (5/2→3/2)).Here,the effect of the uncertainty of the frequency calibra-tion of the fiber laser is minimal.The average over all seven values for ∆νIS yields an isotope shift of -75.3(5)MHz be-tween 137Ba and 135Ba.U.Dammalapati et al.:Isotope shifts of 6s5d 3D-states in Ba5Odd isotopes:3D 1-1P 1transitionTransition ∆ν2[MHz][MHz]-229.3(3.3)-78.4(3.3)1/2→1/297.8(0.6)-143.2(2.6)-81.1(2.6)3/2→3/253.8(0.4)-76.2(2.2)-75.5(2.3)5/2→5/2-68.5(0.3)1.2(1.0)-75.5(1.1)Table 4.Isotope shifts between 137Ba and 135Ba for the6s5d 3D 1-6s6p 1P 1transition.The measured frequency differ-ence ∆ν1of corresponding hyperfine transitions and the differ-ence in thehyperfine splitting ∆ν2of the involved states from literature [9,22]are given.Isotope pair3D 2-1P 1[MHz]-59.3(6)-144.1(1.0)-84.8(8)114(4)39(4)-75.3(5)m pA 1−A 2A 1A 2,(7)where F SMS is a constant for a specific transition and it is insensitive to the nuclear moments.It can be derived from theory.The field shift arises due to the change in the spatial distribution of the nuclear charge between the different isotopes and is-10001000-2500-2000-1500-1000-5005001000∆νM 3D 1 [GHz ]∆νM 3D 2 [G H z ](a)(138,136)(136,134)(138,134)(138,137)1000200030004000-5005001000150020002500300035004000∆νM 1P 1 [GHz ]∆νM 3P 1 [G H z ](b)(138,136)(136,134)(137,135)(138,134)(138,137)(138,135)-2000-10001000-10001000200030004000∆νM 1P 1 [GHz ]∆νM 3D 1 [G H z ](c)(138,136)(136,134)(137,135)(138,134)(138,137)(138,135)Fig.7.King plot for the measured modified isotope shifts ∆M of the 3D 1-1P 1and 3D 2-1P 1transitions in Ba isotopes.A linear correlation is found for the transitions at the wavelengths λir 2and λir 3(a)as well as at the wavelengths λ1and λ2(b).For the the wavelength pair λir 2and λ1we find a deviation (c).There is a linear dependence for pairs of even-even isotopes which differs from the relation for odd-odd and even-odd pairs of isotopes.The data for λ1and λ2are taken from [17].δνF S =F δ r 2 ,(8)where F is a factor depending on the electronic config-uration and r 2 is the expectation value of the square of the radius of the charge distribution in the nucleus.This term provides information on the overlap of the electron wavefunctions with the nucleus.6U.Dammalapati et al.:Isotope shifts of6s5d3D-states in Ba Isotope shifts for different transitions are often com-pared using a King plot[23].Here,the modified isotopeshifts∆νM,which is given asA1A2∆νM=(∆νIS−∆νNMS)×U.Dammalapati et al.:Isotope shifts 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