On the solution of the nonlinear problem in the theory of the skin effect

Computational investigation of static multipole polarizabilities and sum rules for ground-state hydrogenlike ions

“…One distinction from previous calculations is that results were also reported for calculations where the negative-energy Dirac sea is excluded from the intermediate sum. The agreement with previously derived analytic expressions [7,9,10] for the dipole polarizability could not be better. High-precision calculations of the multipole polarizabilities for = 2,3,4 are also given.…”

“…This was a generalization of an earlier work which gave the O(α 2 Z 2 ) expression for the dipole polarizability [8]. The work on dipole polarizabilities was extended to (αZ) 4 [9], (αZ) 6 [10], and to all orders in terms of a generalized hypergeometric function [11]. Apart from a very recent calculation [6], the expressions for the quadrupole and higher-order polarizabilities have not had independent confirmation.…”

“…The different Z → 0 asymptotes for α ± 1 and α + 1 indicate that the O(α 4 Z 4 ) terms are different for α ± 1 and α + 1 . Expressions for α ± 1 giving terms to O(α 4 Z 4 ) [9], O(α 6 Z 6 ) [10], and to all orders [11] have been derived. The O(α 4 Z 4 ) expression of Zon et al [9] is α Zon Figure 4 plots 10 15 (α ± 1 − α Zon 1 )/Z 2 as a function of Z.…”

“…Expressions for α ± 1 giving terms to O(α 4 Z 4 ) [9], O(α 6 Z 6 ) [10], and to all orders [11] have been derived. The O(α 4 Z 4 ) expression of Zon et al [9] is α Zon Figure 4 plots 10 15 (α ± 1 − α Zon 1 )/Z 2 as a function of Z. The Z → 0 limit of this difference demonstrates that the present calculations are in agreement with the analytic expression to O(α 4 Z 4 ).…”

“…[7]. The value of λ 4 for α ± 1 was set to the value from Zon et al [9]. Table VII lists the numerical values of λ 2i coming from the fit.…”