Angular momentum distribution in a relativistic configuration: magnetic quantum number analysis

This paper is devoted to the analysis of distribution total magnetic quantum number $M$ in a relativistic subshell with $N$ equivalent electrons momentum $j$. analyzed through its cumulants and their generating function, for which an analytical expression provided. function also allows us get values at any order. Such are useful obtain moments various orders. Since distinct subshells additive this study directly applies configuration. Recursion relations on given. It shown that may be expressed as n-th derivative polynomial. leads recurrence very efficient even case large $j$ or $N$. The numerically studied using Gram-Charlier Edgeworth expansions. inclusion high-order terms improve accuracy representation instance when small angular momenta coexist same However such series does not exhibit convergence high orders considered account first two often provides fair approximation distribution. offers interesting alternative though expansion divergent asymptotic nature.