论文标题
在任意离散的能量状态下，狄拉克单电子原子磁性的戈登分解
Gordon decomposition of the magnetizability of a Dirac one-electron atom in an arbitrary discrete energy state
论文作者
论文摘要
我们在任意离散的能量本征中介绍了dirac单电子原子的磁性的戈登分解，并带有一个尖端，无旋转和一动的电荷核$ ze $。假定原子状态的外部磁场被认为是弱，静态和均匀的。使用Szmytkowski在1997年提出的广义Dirac绿色功能的Sturmian扩展，我们得出了Diamagnetic（$χ_{D} $）和Paramagnetic（$χ_{P} $）的封闭形式表达式。我们的计算纯粹是分析性的。 $χ_{p} $的接收公式包含单位参数的通用超几何函数$ {} _ 3f_2 $，而$χ_{d} $是基本形式的。对于原子状态，这两个结果都减少了其他作者先前获得的公式。这项工作是我们最近文章的前传，其中对于某些$ 1 \ leqslant z \ leqslant 137 $的兴奋状态的$χ_{d} $和$χ_{p} $的数值是通过此处衍生的一般表格获得的。
We present a Gordon decomposition of the magnetizability of a Dirac one-electron atom in an arbitrary discrete energy eigenstate, with a pointlike, spinless, and motionless nucleus of charge $Ze$. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, static, and uniform. Using the Sturmian expansion of the generalized Dirac--Coulomb Green function proposed by Szmytkowski in 1997, we derive a closed-form expressions for the diamagnetic ($χ_{d}$) and paramagnetic ($χ_{p}$) contributions to $χ$. Our calculations are purely analytical; the received formula for $χ_{p}$ contains the generalized hypergeometric functions ${}_3F_2$ of the unit argument, while $χ_{d}$ is of an elementary form. For the atomic ground state, both results reduce to the formulas obtained earlier by other author. This work is a prequel to our recent article, where the numerical values of $χ_{d}$ and $χ_{p}$ for some excited states of selected hydrogenlike ions with $1 \leqslant Z \leqslant 137$ were obtained with the use of the general formulas derived here.
