Second-order contributions to the fine structure of helium from all intermediate states

Abstract

For the theoretical assessment of the 2'P helium fine structure to become comparable to the precision measurements that have been made, it is necessary that the theory be calculated through order a~me . In particular, the second-order contribution from the Breit and mass-polarization operators must be evaluated to an accuracy of 1% or so. In this work, for each of five possible intermediate state symmetries the Dalgarno-Lewis method is used to obtain the first-order perturbed wave function, from which the second-order energy follows by integrat&on. Both the perturbed and unperturbed wave functions are expanded in Hylleraas-type series with a progressively larger number of terms, the second-order energies being computed at each stage; up to 455 terms are used for 'P intermediate states and up to 286 for 'P, D, 'D, and 'F. The sequence of second-order energy results for each symmetry is extrapolated to the limit of an infinite number of basis functions to arrive at a final result. The P, 'P, and 'D states will contribute to both the larger and the smaller fine-structure intervals vo, and v», respectively, while 'I' and 'D states affect only v». The total theoretical result, up to order a mc, for vo, is much more accurate than that for v», allowing the finestructure constant 0, to be determined very precisely by comparison of theory to experiment, with the result a ' = 137.036 08(13), good to 0.94 ppm,

The 1986 adjustment of the fundamental physical constants

“…A measurement of the fine structure in atomic He (Lewis, Pichanick, and Hughes, 1970;Frieze et al , 1981;Kponou et al , 1981) can yield a value for n (item 10.2) only if the calculation of the energy levels (Lewis and Serafino, 1978) can be carried out with sufficient precision. Unfortunately, the computational uncertainty is relatively large, and uncalculated terms in the perturbation expansion of the wave-functions of the two-electron system may contribute at the part in 10 level.…”

Analysis of some integrals arising in the atomic three-electron problem

“…(23) leads to (24) W -2,j, -2, a, p)=16m. ( (25) U(j, m, a, b)= g ( -1)"(n -1)!a"X(j+1n, b), (26) (29) X(m, a)= m! (1+a)m+i it is clear that Eq.…”

Hyperfine quenching and precision measurement of the 2P03-2Indelicato1, Birkett2, Briand3 et al. 1992Phys. Rev. Lett.604190View full textAdd to dashboardCite

“…Calculations of the fine-structure splittings generally include the effects of relativity by a perturbation expansion in the parameter (Z«) 2 . The problems associated with this approach at high Z are illustrated by the fact that in ordinary helium (Z=2) the calculations [2] are accurate at the ppm level, whereas the most elaborate calculations [3,4] at Z=64 are accurate at only the few percent level. Accurate experimental measurements performed at high Z can therefore act to stimulate further theoretical work in including relativistic effects in the calculation of two-electron energy levels.…”