A NEW PROGRAM FOR CALCULATING MATRIX-ELEMENTS IN ATOMIC-STRUCTURE

doi:10.1016/0010-4655(91)90011-9

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A NEW PROGRAM FOR CALCULATING MATRIX-ELEMENTS IN ATOMIC-STRUCTURE

1991-07-01

PRE

Pedro M. Lima *

DOI：10.1016/0010-4655(91)90011-9

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Abstract

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The solution of many problems concerning the electronic structure of atoms requires the evaluation of the matrix elements of the Hamiltonian operator, including the electrostatic interaction. These matrix elements may be expressed as weighted sums of radial integrals. The program we describe in this paper evaluates the coefficients of the Slater integrals and, if these are given, computes all the matrix elements for a given set of configurations. This program has nearly the same purposes as Hibbert's program (Comput. Phys. Commun. 1 (1969) 359) and is also based on the Racach techniques. The main difference between this algorithm and the cited one is the method used to calculate the recoupling coefficients. While Hibbert's programs use Burke's algorithm (Comput. Phys. Commun. 1 (1970) 241) to calculate these coefficients, in our program they are computed using the graphical techniques developed by Jucys et al. (Mathematical Apparatus of the Theory of Angular Momenta, Israel Program for Scientific Translation, Jerusalem, 1962). According to this method, that we describe in another paper (Comput. Phys. Commun. 66 (1991) 89, this issue) the formulae needed to calculate the recoupling coefficients are previously derived and simplified (as a first step of the program). The use of this method may considerably reduce the running time, specially in the case of large configuration interaction matrices.

Keywords:

MATRIX ELEMENTS

ELECTROSTATIC INTERACTION

ANGULAR MOMENTUM

RECOUPLING COEFFICIENTS

COEFFICIENTS OF FRACTIONAL PARENTAGE

LS-COUPLING

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