Programs in Physics & Physical Chemistry
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|Manuscript Title: A Pascal program for calculating the reduced Coulomb Green's functions and their partial waves.|
|Authors: J. Mlodzki, J. Kuszkowski, M. Suffczynski|
|Program title: RCGF|
|Catalogue identifier: ACEP_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 29(1983)341|
|Programming language: Pascal.|
|Computer: CDC 6000.|
|Operating system: SCOPE 3.4.4.|
|RAM: 540K words|
|Word size: 60|
|Keywords: General purpose, Reduced Coulomb Green's function.|
|Classification: 4.5, 5.|
Nature of problem:
The reduced Coulomb Green's function is the coordinate space representation of the sum over intermediate states encountered in bound state second order perturbation theory. This function does not depend on the particular perturbation problem. Thus, it is useful to have it calculated once. When the perturbation Hamiltonian is decomposed into terms of definite angular momentum it is useful to have the partial waves of the Green's function. We therefore present a program for calculating the functions in question.
The formulae for the reduced Coulomb Green's function and its partial waves are lengthy and tedious to evaluate. However, these functions can be expressed in terms of polynomials multipled by known transcendental functions: expotentials, an expotential integral and a logarithm. The main task of the program is to evaluate the coefficients of the polynomials. It is worth stressing that the results are purely analytical and exact because of the use of special data structures, for example a fraction represented by a pair of integers or a polynomial by an array of fractions.
The value of the main quantum number n ranges from 1 to 7, and that of the angular momentum quantum number l from 0 to 7. These restrictions are caused by the limitations of integer arithmetic implemented in the computer used.
Compilation - 11 s, evaluation of the reduced function - 1.6 s, evaluation of the partial wave - 0.8 s.
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