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Manuscript Title: Calculation of reduced coefficients and matrix elements in jj- coupling.
Authors: G. Gaigalas, S. Fritzsche
Program title: RCFP
Catalogue identifier: ADNA_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 134(2001)86
Programming language: Fortran.
Computer: IBM RS 6000, PC Pentium II.
Operating system: IBM AIX 4.1.2+, Linux 6.1+.
RAM: 100K words
Word size: 64
Keywords: Atomic physics, Structure, Atomic many-body perturbation theory, Complex atom, Configuration interaction, Effective Hamiltonian, Energy level, Racah algebra, Reduced coefficients of fractional parentage, Reduced matrix element, Relativistic, Second quantization, Standard unit tensors, Tensor operators, 9/2-subshell.
Classification: 2.1.

Nature of problem:
The calculation of atomic properties and level structures is based on the evaluation of many-particle matrix elements of physical operators. For symmetry-adapted functions, the matrix element for a given tensor operator A^K of rank K can be expressed as Sigmaj,k coeff(j,k)(gammaj Jj||A^K||gammak Jk) by using the (reduced) coefficients of fractional parentage and the reduced matrix elements of the (unit) standard tensors T^k or W^kqkj. These reduced coefficients and matrix elements are frequently applied to both the configuration interaction and multi-configuration Dirac-Fock method [2] as well as to many-body perturbation theory [3].

Solution method:
A new combination of second quantization and quasispin methods with the theory of angular momentum and irreducible tensor operators leads to a more efficient evaluation of (many-particle) matrix elements and to faster computer codes [4]. Practical implementations of this new scheme will support not only large-scale computations on open-shell atoms but may even help to develop programs for calculating the angular parts of (effective) one- and two-particle operators for many-body perturbation theory (in higher orders) in the future.

For jj-coupled subshells states, our module provides coefficients and matrix elements for all subshells (nj) with j=1/2, 3/2, 5/2, 7/2, and 9/2.

Unusual features:
The interactive version of RCFP can be used as an "electronic tabulation" of standard quantities for evaluating general matrix elements for jj-coupled functions.
All real variables are parametrized by a selected kind parameter and, thus, can be adapted to any required precision if supported by the compiler. Currently, the kind parameter is set to double precision (two 32-bit words) as it is for other components of the RATIP package [1].

Running time:
For large computations, the running time depends on the shell structure and the size of the wave function expansion for a given atomic system. However, the program promptly responds in its interactive mode if only single coefficients and matrix elements are to be calculated.

[1] S. Fritzsche, C.F. Fischer, C.Z. Dong, Comput. Phys. Commun. 124 (2000) 340.
[2] I.P. Grant, H. Quiney, Adv. Atomic Molecular Phys. 23 (1987) 37.
[3] G. Merkelis, G. Gaigalas, J. Kaniauskas, Z. Rudzikas, Izvest. Acad. Nauk SSSR Phys. Ser. 50 (1986) 1403.
[4] G. Gaigalas, Lithuanian J. Phys. 39 (1999) 80.