The study of the 4s4p configuration of the Zn isoelectronic sequence using the relativistic jj-coupling approach

Abstract

The 4s4p configuration of Zn is analyzed using the Relativistic jj-coupling approach. The experimentally determined relativistic Slater integrals are compared with the results of numerical codes, both quasi-and fully-relativistic ones. In this work, they are estimated, semi-empirically, the two J = 1 levels up Z = 70 and the 1 P1 level up Z = 92 by judicious interpolation and extrapolation of energies. The comparison with extensive relativistic configuration-interaction calculations indicates that differences between both approaches are of the order of measurement accuracies.

Some applications of perturbation theory in atomic physics

“…In the non-relativistic and hydrogenic case approximation, the binding energy is given by the well-known Bohr result, which is usually written E nl = − Z/n 2 Ry. Eventually, the first relativistic correction gives us the Bohr-Sommerfeld formula, which we saw in equation (20). It should be noted that, in spectroscopic notation, E nl is used to measure the levels with respect to the fundamental configuration of each ion, which we can denote E 0 .…”

“…The cases where Δn = 0 and Δn = 0 have been studied [14,15]. Both cases are treated according to the Bohr-Sommerfeld formula for one-electron spectra, equation (20).…”

“…(a) Configurations 4s-4p and p n (n = 2, 3, 4). In references [20][21][22], we have analyzed the Zn-like 4s-4p isoelectronic sequence, the ground configurations p 2 (C, Si, Ge, Sn, Zn and Cd sequences), p 3 (N, P and As sequences) and p 4 (O and S sequences). Levels can be faithfully fitted only by means of expressions of the form of (52).…”

Screening parameters for the relativistic hydrogenic model

“…For an "once-off" calculation of the parameters (see section 3.2), the series is evaluated numerically, because the series is convergent. On the other hand, for an "in-line" calculation (see section 3.1), we can solve the integral (22) in an approximate, but accurate enough, analytical form. We explain this in Appendix A.…”

An examination of the consistency of the published levels of the p 2 , p 3 and p 4 isoelectronic sequences using jj-relativistic expressions

“…Although there are extensive calculations using the MCDHF method (cited above), in order to apply the semiempirical method, it can be useful to develop a simplified model utilizing single-configuration expressions or, at the most, accounting for interactions within the same complex. We used this method to study the 4s 4p configuration of the Zn sequence [9].…”