相对论类氢原子基态静电多极子极化率：广义Dirac-Coulomb Green函数Sturmian展开的应用
Static electric multipole susceptibilities of the relativistic hydrogen-like atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
摘要：
在一阶微扰理论的框架下，研究了置于具有一定$2^{L}$极性的弱静电场中的狄拉克单电子原子的基态。广义Dirac-Coulomb Green函数的Sturmian展开[R. Szmytkowski，J.Phys.B30（1997）825，erratum：30（1997）2747]被用来导出原子的各种远场和近核静电多极子极化率的封闭形式的解析表达式。远场多极子极化率--极化率$α_{L}$、电磁交叉极化率$α_{\mathrm{E}L\to\mathrm{M}(L\mp1)}$和电磁环磁交叉极化率$α_{\mathrm{E}L\to\mathrm{T}L}$ --可以用一个或两个单位辐角的无限广义超几何函数${}_{3}F_{2}$表示.对应的近核多极极化率公式-电子核屏蔽常数$σ_{\mathrm{E}L\to\mathrm{E}L}$、近核电-磁交叉极化率$σ_{\mathrm{E}L\to\mathrm{M}(L\mp1)}$和近核电-环-磁交叉极化率$σ_{\mathrm{E}L\to\mathrm{T}L}$ -涉及终止${}_{3}F_{2}(1)$系列，并且对于每个$L$，可以用初等函数重写。精确的数值的远场偶极子，四极，八极和hexadecapole的磁化率提供选定的类氢离子。分析准相对论近似，有效的$αZ$，其中$α$是精细结构常数和$Z$是核电荷数的第二顺序，推导出所有类型的远场和近核的磁化率的文件中考虑。
英文摘要：
The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$-polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825, erratum: 30 (1997) 2747] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities --- the polarizabilities $α_{L}$, electric-to-magnetic cross-susceptibilities $α_{\mathrm{E}L\to\mathrm{M}(L\mp1)}$ and electric-to-toroidal-magnetic cross-susceptibilities $α_{\mathrm{E}L\to\mathrm{T}L}$ --- are found to be expressible in terms of one or two non-terminating generalized hypergeometric functions ${}_{3}F_{2}$ with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities --- the electric nuclear shielding constants $σ_{\mathrm{E}L\to\mathrm{E}L}$, near-nucleus electric-to-magnetic cross-susceptibilities $σ_{\mathrm{E}L\to\mathrm{M}(L\mp1)}$ and near-nucleus electric-to-toroidal-magnetic cross-susceptibilities $σ_{\mathrm{E}L\to\mathrm{T}L}$ --- involve terminating ${}_{3}F_{2}(1)$ series and for each $L$ may be rewritten in terms of elementary functions. Exact numerical values of the far-field dipole, quadrupole, octupole and hexadecapole susceptibilities are provided for selected hydrogenic ions. Analytical quasi-relativistic approximations, valid to the second order in $αZ$, where $α$ is the fine-structure constant and $Z$ is the nuclear charge number, are derived for all types of the far-field and near-nucleus susceptibilities considered in the paper.
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