5 p 2 P j \5 d 2 D 3Õ2 transition matrix elements in atomic 87 Rb S. B. Bayram,* M. Havey, ² M. Rosu, and A. Sieradzan Department of Physics, Central Michigan University, Mt. Pleasant, Michigan 48859 A. Derevianko ‡ and W. R. Johnson Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556 Received 1 February 2000; published 7 April 2000 A combined precision experimental and theoretical study of 5 p 2 P j →5 d 2 D 3/2 electric-dipole transition matrix elements in atomic 87 Rb has shown that they are dominated by electron correlation. The relative size and sign of the measured matrix element ratio is found to be 1.0688, in very good agreement with the value of 1.135 obtained from relativistic third-order many-body perturbation theory. PACS numbers: 32.70.Cs, 31.30.Jv, 31.15.Md, 32.80.-t Determination of multipole matrix elements, quantities that define a scale of interaction between electromagnetic radiation and atomic matter 1, remains a fundamental prob- lem of considerable theoretical and experimental interest. Such quantities are important to a wide range of basic and applied problems, including determination of astrophysical abundances of atoms in stellar atmospheres 2 and analysis of atomic parity-violation experiments 3. As opposed to observables related to energy intervals in atoms or mol- ecules, which may be determined to a precision of 10 -11 4,5, the best measurements of atomic dipole matrix ele- ments have only recently achieved a precision of 5 10 -4 6. And despite remarkable advances in the devel- opment of relativistic many-body techniques in atomic phys- ics, calculations of electric-dipole matrix elements for heavier atoms such as cesium have been limited to an accu- racy of about 0.5% 7,9,10. Nevertheless, at this level in- sight into important physical effects determining the matrix elements may be given. For example, a recent report of cal- culation of magnetic dipole matrix elements associated with ns 2 S 1/2 →n ' s 2 S 1/2 transitions in the alkali-metal atoms has revealed that negative-energy states can produce significant anomalies in the magnetic transition strength 11. A number of novel techniques have recently been applied to precise absolute and relative measurements of the strength of resonance transitions in the heavier alkali-metal atoms. These have included refined lifetime measurements in atomic-beam experiments 12, photoassociative spectros- copy of cold atoms confined to atomic traps 13–15, and direct measurements of the natural width of the 3 s 2 S 1/2 →3 p 2 P 3/2 transition in Na 16. Meticulous light-absorption measurements have determined the relative strength of the Cs resonance transitions 17 to 5 10 -4 . It has also been shown 18 that the frequency dependence of polarized Ray- leigh and Raman scattering of light from atoms depends sen- sitively on the relative strengths of radiative transitions be- tween manifolds of atomic levels. Further, recent experi- ments 19 on the 5 s 2 S 1/2 →5 p 2 P j →8 s 2 S 1/2 transition in atomic Rb demonstrated that precision measurements of the polarization dependence of the two-photon transition rate in atoms can yield sum rules for combinations of atomic electric-dipole matrix elements. We have made a combined experimental and theoretical study of the 5 s 2 S 1/2 →5 p 2 P j →5 d 2 D 3/2 transition in atomic 87 Rb. In this case, precision measurements of the nonreso- nant two-photon, two-color linear depolarization spectrum show remarkable polarization-dependent interference struc- ture which is partly due to the near degeneracy of the two photons driving the process. From the measurements it was possible to extract the ratio of the reduced excited-state tran- sition matrix elements for two contributing pathways: 5 p 2 P 3/2 →5 d 2 D 3/2 and 5 p 2 P 1/2 →5 d 2 D 3/2 . The ratio of re- duced matrix elements for the multiplet transition shows a significant departure from the nonrelativistic limit of unity. To understand the results, we have performed third-order many-body perturbation theory 7 calculations of the matrix elements, including spin-orbit and relativistic effects in an ab initio fashion. The calculations reveal that, although the main departure appears in the Dirac-Hartree-Fock values, excep- tionally large correlation contributions dominate the excited- state transition matrix elements. The experimental scheme is illustrated in the inset to Fig. 1, which shows low-lying energy levels for atomic Rb. Two independently tunable lasers having frequencies  1 and  2 are adjusted to satisfy the two-photon resonance condition  1 + 2 = 0 , where  0 is the resonance frequency of the 5 s 2 S 1/2 →5 d 2 D 3/2 transition. Averaged over hyperfine structure,  0 =25 700.56 cm -1 . In the weak laser fields of the present experiment, there are two contributing virtual levels; these are indicated by the horizontal broken lines in Fig. 1. In the present case, these merge when one laser fre- quency is offset from the 5 s 2 S 1/2 →5 p 2 P 3/2 transition by about 33.7 cm -1 . In this paper detuning is defined as  1 = 1 - 3/2 , where  3/2 =12 816.58 cm -1 is the resonance frequency of the 5 s 2 S 1/2 →5 p 2 P 3/2 transition. For the 5 s 2 S 1/2 →5 p 2 P 1/2 transition,  1/2 =12 578.96 cm -1 . De- tection of atoms promoted to the 5 d 2 D 3/2 levels is achieved by monitoring the 6 p 2 P j →5 s 2 S 1/2 fluorescence around 420 nm. *Present address: University of Michigan, Ann Arbor, MI. ² Permanent address: Old Dominion University, Norfolk, VA. ‡ Present address: Harvard Smithsonian Center for Astrophysics, Cambridge, MA. RAPID COMMUNICATIONS PHYSICAL REVIEW A, VOLUME 61, 050502R 1050-2947/2000/615/0505024/$15.00 ©2000 The American Physical Society 61 050502-1