This paper is devoted to the analysis of the distribution of the total angular momentum in a relativistic configuration. Using cumulants and generating function formalism this analysis can be reduced to the study of individual subshells with N equivalent electrons of momentum j. An expression as a nth-derivative is provided for the generating function of the J distribution and efficient recurrence relations are established. It is shown that this distribution may be represented by a Gram–Charlier-like series which is derived from the corresponding series for the magnetic quantum number distribution. The numerical efficiency of this expansion is fair when the configuration consists of several subshells, while the accuracy is less good when only one subshell is involved. An analytical expression is given for the odd-order momenta while the even-order ones are expressed as a series which provides an acceptable accuracy though being not convergent. Such expressions may be used to obtain approximate values for the number of transitions in a spin–orbit split array: it is shown that the approximation is often efficient when few terms are kept, while some complex cases require to include a large number of terms.

本文致力于分析相对论构型中总角动量的分布。使用累积量和生成函数形式主义，这种分析可以简化为对具有N 个动量j等效电子的单个子壳层的研究。为J的生成函数提供了作为n次导数的表达式分布和有效递推关系成立。结果表明，该分布可以用类似 Gram-Charlier 的级数表示，该级数源自磁量子数分布的相应级数。当配置由几个子壳组成时，这种扩展的数值效率是公平的，而当只涉及一个子壳时，精度不太好。给出了奇数阶动量的解析表达式，而偶数阶动量被表示为一个级数，虽然不收敛但提供了可接受的精度。此类表达式可用于获得自旋轨道分裂阵列中跃迁数的近似值：结果表明，当保留的项数很少时，近似值通常是有效的，而某些复杂情况需要包含大量项。