Third-order many-body perturbation theory calculations for the beryllium and magnesium isoelectronic sequences

Relativistic third-order MBPT is applied to obtain energies of ions with two valence electrons in the no virtual-pair approximation (NVPA). A total of 302 third-order Goldstone diagrams are organized into 12 one-body and 23 two-body terms. Only third-order two-body terms and diagrams are presented here, owing to the fact that the one-body terms are identical to the previously studied third-order terms in monovalent ions. Dominant classes of diagrams are identified. The model potential is a Dirac-Hartree-Fock $V^{N-2}$ potential, and B-spline basis functions in a cavity of finite radius are employed in the numerical calculations. The Breit interaction is taken into account through second order of perturbation theory and the lowest-order Lamb shift is also evaluated. Sample calculations are performed for berylliumlike ions with Z = 4--7, and for the magnesiumlike ion P IV. The third-order energies are in excellent agreement with measurement with an accuracy at 0.2% level for the cases considered. Comparisons are made with previous second-order MBPT results and with other calculations. The third-order energy correction is shown to be significant, improving second-order correlation energies by an order of magnitude

Relativistic many-body calculations of the Stark-induced amplitude of the 6P1/2 -7P1/2 transition in thallium

Stark-induced amplitudes for the 6P1/2 - 7P1/2 transition in Tl I are calculated using the relativistic SD approximation in which single and double excitations of Dirac-Hartree-Fock levels are summed to all orders in perturbation theory. Our SD values alpha S = 368 a0 3 and beta S= 298 a 0 3 are in good agreement with the measurements alpha S=377(8) a 0 3$ and beta S = 313(8) a 0 3 by D. DeMille, D. Budker, and E. D. Commins [Phys. Rev. A 50, 4657 (1994)]. Calculations of the Stark shifts in the 6P1/2 - 7P1/2 and 6P1/2 - 7S1/2 transitions are also carried out. The Stark shifts predicted by our calculations agree with the most accurate measured values within the experimental uncertainties for both transitions

Blackbody radiation shift in 87Rb frequency standard

The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature of which the leading contributor is the blackbody radiation (BBR) shift. Experimental measurements of the BBR shifts are difficult. In this work, we have calculated the blackbody radiation shift of the ground-state hyperfine microwave transition in 87Rb using the relativistic all-order method and carried out detailed evaluation of the accuracy of our final value. Particular care is taken to accurately account for the contributions from highly-excited states. Our predicted value for the Stark coefficient, k_S=-1.240(4)\times 10^{-10}\text{Hz/(V/m)}^{2} is three times more accurate than the previous calculation [1].Comment: 7 page