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Manuscript Title: A program for the complete expansion of jj-coupled symmetry functions into Slater determinants.
Authors: S. Fritzsche, I.P. Grant
Program title: CESD
Catalogue identifier: ADCB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 92(1995)111
Programming language: Fortran.
Computer: Sun SPARC Station.
Operating system: Sun OS 4.1.2, 5.2, HP-UX.
RAM: 4K words
Word size: 32
Keywords: Atomic physics, Structure, Configuration, Decoupling, Determinant, Jj-coupling, Relativistic.
Classification: 2.1.

Subprograms used:
Cat Id Title Reference
ABJN_v1_0 GRASP CPC 55(1989)425

Nature of problem:
The jj-coupled symmetry functions, which are used in the atomic structure program GRASP, are expanded into Slater determinants.

Solution method:
The atomic or configuration symmetry functions in jj-coupling are projected onto a suitable basis of N-electron Slater determinants. A complete expansion is obtained by considering all determinants with non-vanishing overlap. The module calculates a representation of the symmetry functions in that subspace of determinants.

The symmetry functions may only contain electrons in subshells with angular momenta j<=7/2, i.e. in subshells {s1/2, p1/2, ...., ftau/2, gtau/2}. This is consistent with the basis scheme of the GRASP program [1,2] which does not at present allow two or more equivalent electrons in subshells with j>=9/2. For larger values of j, additional quantum numbers (like the senority, for instance) are needed beyond the total subshell angular momentum to classify the antisymmetric subshell states. The present version is also limited to a maximal number of 5 open subshells.

Unusual features:
A representation in a determinant basis is obtained for configuration symmetry functions (CSF) and/or atomic symmetry functions during the execution of the GRASP program. For the expansion of the atomic states a successful evaluation and diagonalization of either the Dirac-Coulomb or Dirac-Coulomb-Breit Hamiltonian matrix is supposed. The number of determinants in the representation is usually greater or equivalent to the number of CSF in GRASP. The dimensions are equivalent if a complete active space [3] is considered. The maximal number of determinants in the code is only restricted by the dimensions of the associated arrays.

Running time:
Test case 1: 1.8 seconds; test case 2 (supplied in the distributed program): 4 seconds (HP 720); otherwise depends on the size of the employed configuration basis in GRASP.

[1] K.G. Dyall, I.P. Grant, C.T. Johnson, F.A. Parpia and E.P. Plummer, Comput. Phys. Commun. 55(1989)425.
[2] F.A. Parpia, I.P. Grant and C.F. Fischer, private communication (1992); the GRASP-2 program is available from these authors upon application.
[3] F.A. Parpia, W.P. Wijesundera and I.P. Grant, Comput. Phys. Commun. 76(1993)127.