Numerical calculation of relativistic atomic continuum wavefunctions in a frozen-core dirac-fock potential: Application to the 6p < sup> 2 resonances in hg

Document Type

Article

Publication Date

12-14-1991

Abstract

A numerical program that calculates fully relativistic, atomic continuum wavefunctions within the configuration interaction framework of the program of Grant el a! is described. The special features of continuum wavefunctions and the numerical problems that arise are discussed. A central differences method with deferred correction is used to numerically integrate the Dirac-Fock equations. Normalization for the ionic core case is accomplished by three different methods and their features compared: The non-relativistic Strömgren method described by Seaton and Peach, a relativistic wkb method and a less conventional approach of fitting confluent hypergeometric functions to the numerical solution at large radial distances. Asymptotic expressions for normalization were derived, programmed and tested for the case where the energy goes to zero (threshold). Additionally, normalization for the neutral core case by fitting to spherical Bessel and Neumann functions will be briefly described. The program was tested by comparing the numerically obtained continuum wavefunctions with the analytic solution for hydrogen and by examining a Rydberg series of Slater (Rk) integrals. A novel approach for the determination of off-diagonal Lagrange multipliers is also given. Application of this program to the 6p2 resonances in Hg is described and results presented. © 1991 IOP Publishing Ltd.

Publication Title

Journal of Physics B: Atomic, Molecular and Optical Physics

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