Programs in Physics & Physical Chemistry
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|Manuscript Title: A general program for calculating angular momentum integrals in atomic structure.|
|Authors: A. Hibbert|
|Program title: WEIGHTS|
|Catalogue identifier: ACQL_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 1(1970)359|
|Programming language: Fortran.|
|Computer: ICL 1907.|
|Operating system: QUBE.|
|RAM: 30K words|
|Word size: 24|
|Keywords: Atomic physics, Configuration Interaction, Racah, Coefficients of Fractional Parentage, Recoupling coefficients, Slater integrals, Complex atoms, Wave Function, Bound states, Ls coupling, Theoretical methods.|
|ACQB_v1_0||P SHELL C.F.P.||CPC 1(1969)15|
|ACQC_v1_0||D SHELL C.F.P.||CPC 1(1969)16|
Nature of problem:
In configuration interaction calculations, one wishes to evaluate the matrix of the Hamiltonian operator with respect to a basis set of configuration wave functions. The more difficult part of this procedure is the determination of the two-electron interaction matrix elements. These matrix elements may be written as a weighted sum of radial Slater integrals. The program calculates the coefficients of these integrals.
The coefficients of the Slater integrals are obtained from integration over all spin and angular co-ordinates and (N-2) radial co-ordinates, for an N-electron atom. The scheme for calculating the coefficients is described by Fano, using the techniques of Racah. In this scheme, the coefficients may be expressed as sums over fractional parentage coefficients (Comp. Phys. Commun. 1(1969)15), recoupling coefficients (Comp. Phys. Commun. 1(1970)241), and reduced matrix elements (Fano and Racah). The configurations are defined by the number of electrons in each occupied shell, and the (nl) quantum numbers and angular momentum couplings for each occupied shell.
Any number of electrons in s-, p-, or d-shells are allowed (<=2(2l+1)), but no more than two electrons in any shell of higher orbital angular momentum. This restriction may be relaxed by inclusion of further fractional parentage coefficient packages.
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