PROGRAM SUMMARY
Title of program:
RCFP
Catalogue identifier:
ADNA
Ref. in CPC:
134(2001)86
Distribution format: tar gzip file
Operating system: IBM AIX 4.1.2+, Linux 6.1+
High speed store required:
100K words
Number of bits in a word:
64
Number of lines in distributed program, including test data, etc:
9192
Keywords:
Atomic physics, Structure, Atomic many-body perturbation theory,
Complex atom, Configuration interaction, Effective Hamiltonian,
Energy level, Racah algebra, Coefficients (reduced)
of fractional parentage, Matrix element (reduced), Relativistic,
Second quantization, Standard unit tensors, Tensor operators,
9/2-subshell.
Programming language used: Fortran
Computer:
IBM RS 6000 ,
PC Pentium II .
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].
Method of solution:
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.
Restrictions:
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.
Typical 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.
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].
References:
[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.