| Abstrakt: |
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 Z e . 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 3F2 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 ⩽ Z ⩽ 137 were obtained with the use of the general formulas derived here. [ABSTRACT FROM AUTHOR] |
