Lithium Fine Structure in the1s22p2P<

Abstract

The first fully correlated calculations of fine structure in lithium are presented. For the 1s 2 2p 2 states the fine structure is calculated to a computational accuracy of 1 part in 10 6 , including relativistic and QED terms up to O͑a 4 mc 2 ͒, O͑ ͑ ͑͑m͞M͒a 4 mc 2 ͒ ͒ ͒, O͑a 5 mc 2 ͒, and O͑ ͑ ͑͑m͞M͒a 5 mc 2 ͒ ͒ ͒. A comparison is made with other calculations and experiments. A residual discrepancy between theory and experiment of ͑65 6 2͒ 3 10 26 cm 21 is found due to higher-order QED terms. [S0031-9007(97)03922-7] PACS numbers: 31.15. Pf, 31.30.Jv, 32.10.Fn Atomic fine structure is a fundamental testing ground for relativistic and QED effects. For helium, theoretical calculations for the fine structure splittings in 1s 2p 3 P J states have recently been performed up to O͑a 7 ln a͒ mc 2 [1,2]. With future progress in both theory and experiment, comparisons with high precision measurements will potentially yield an atomic physics determination of the fine structure constant a. For lithium, using the level crossing technique, Brog et al.[3] measured the fine structure splitting in 1s 2 2p 2 P J states with an accuracy of 20 ppm (parts per million). The most precise measurement reported in the literature for this splitting was done by Orth et al. [4], using the optical double resonance method. The precision they achieved is 6 ppm. Very recently, Scherf et al.[5] remeasured the 1s 2 2p 2 P J fine structure using the laser-atomic beam spectroscopy method. The precision they obtained is 20 ppm. All these measurements are in excellent agreement. On the theoretical side, there has been a long-standing problem in precise calculations for the lithium 1s 2 2p 2 P J fine structure, including the lowest-order relativistic terms a 4 mc 2 (or a 2 in atomic units) and ͑m͞M͒ a 4 mc 2 , where m is the electron reduced mass and M is the nuclear mass, and the lowestorder QED terms a 5 mc 2 and ͑m͞M͒ a 5 mc 2 . However, recent advances [6-10] in high-precision variational calculations for the lithium atom, using multiple basis sets in Hylleraas coordinates, now make it possible to perform a well-converged calculation for the 1s 2 2p 2 P J fine structure splitting. The purpose of this Letter is to report the first significant theoretical progress in fully correlated calculations for lithium fine structure studies. The key advance is the development of techniques for handling the more highly singular integrals required to calculate matrix elements of the Breit interaction in Hylleraas coordinates.The spin-dependent fine structure splitting can be written in the form [11,12] (in atomic units throughout)where C is a nonrelativistic wave function and H fs is defined by

BREIT–PAULI ENERGIES, TRANSITION PROBABILITIES, AND LIFETIMES FOR 2s, 2p, 3s, 3p, 3d, 4s2LLEVELS OF THE LITHIUM SEQUENCE,Z= 3–8

“…Table B analyzes the fine-structure splitting more carefully. For the 2p 2 P 1/ 2,3/ 2 o state, a very accurate calculation has been reported by Yan and Drake [17] in perfect agreement with experiment for lithium. We also compare the present results with full-core-plus-correlation (FCPC) results obtained by Wang et al [18] that include a small QED correction, increasing the splitting.…”

Fine and hyperfine splitting of the2Pstate in Li andBe+

“…They have been obtained by extrapolation to infinite basis set and uncertainties reflect the numerical convergence. Matrix elements of the fine structure operators have been derived previously by Yan and Drake in [7] and later by us in [15]. Small differences with results of [7] come from the not very large number of basis functions used in that work.…”

“…Matrix elements of the fine structure operators have been derived previously by Yan and Drake in [7] and later by us in [15]. Small differences with results of [7] come from the not very large number of basis functions used in that work. The hyperfine operators have been previously obtained in several works, i.e.…”

Calculations of Magnetic Moments for Three-Electron Atomic Systems

“…For lithium, however, no such calculations have been reported in the literature. The present work is based on our recent advances [13][14][15][16] in high-precision variational calculations for the lithium atom, using multiple basis sets in Hylleraas coordinates.…”