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Manuscript Title: A new Fortran program for CFP's of an identical fermion system.
Authors: J.-J. Wang, Q.-Z. Han, Y.-X. Liu
Program title: CFPSIF
Catalogue identifier: ADAB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 85(1995)99
Programming language: Fortran.
Computer: IBM RISC/6000 320H.
Operating system: AIX 3.2.4, VMS version 4.7.
RAM: 943K words
Word size: 32
Keywords: Nuclear physics, Identical fermions, Angular momentum, Seniority, Multiplicity, Coefficient of Fractional parentage, Isoscalar factor, Matrix element reduced, Model shell, Unitary group, Symplectic group.
Classification: 17.18.

Nature of problem:
The program calculates all the coefficients of fractional parentage (CFPs)[1] of identical fermion system, by using the recurrent relations [2] with well-defined seniority. It is of fundamental importance in constructing a many-particle wave function with well-defined permutational symmetry and total angular momentum CFPs method is one of the most efficient method for construction of such wave functions. It is an iterative method, namely, the n-particle wave function is constructed from (n-1) particle wave functions by coupling one more particle. The reduced matrix elements of any physical tensor operator can be calculated easily with the wave functions expressed in terms of the CFPs. Therefore the calculation of CFPs plays an important role in nuclear physics, atomic and molecular physics.

Solution method:
The program CFPSIF uses the approach developed in Refs [2] to get all the CFP's of an identical fermion system. In the approach, the CFP is factorized as a product of the isoscalar factor (ISF) of the reduction U(N) contained in SP(N) and that of SP(N) contained in O(3). The ISF of the reduction U(N) contained in SP(N) has been given analytically. The ISF of the reduction SP(N) contained in O(3) is evaluated by a recurrent relation. The recurrent relation is presented with well-defined seniority, and the recurrent process is controlled by the multiplicity of an irreducible representation (IRREP) of O(3) in an IRREP of group SP(N). It provides an efficient algorithm for computation and is numerically stable for relatively large system.

The program can evaluate the CFPs of a system including identical fermions, each with single angular momentum j. At present, with the dimension control parameters MNU=6, NFS=40, NFJ=20, the program can handle the system with j <= 11/2. If we take the parameters MNU=8, NFS=300, NFJ=40, the program can handle the system with j <= 15/2. After the parameters MNU, NFS, NFJ et al. are enlarged, the system can be enlarged.

Running time:
This depends strongly on the fermion number and the single angular momentum. For example, it takes about 67 minutes on VAX 8550 to get all the CFPs of a fermion system with j = 15/2, but it takes only about 3 seconds for the fermion system with j = 9/2.

[1] R.F. Bacher and S. Gousmit, Phys. Rev. 46(1934)948; G. Racah, Phys. Rev. 63(1943)367; A.R. Edmonds and B.H. Flowers, Proc. R. Soc. London A 214(1952)515; P.J. Redmond, Proc. R. Soc. London A 222(1954)84; A. DeShalit and I. Talmi, Nuclear Shell Theory (Academic, New York, 1963).
[2] Hong-zhou Sun, Qi-zhi Han, Mei Zhang and Gui-lu Long, Commun. Theor. Phys. 11(1989)441.
[3] Jia-jun Wang, Hong-zhou Sun, High Energy Phys. Nucl. Phys, (in Chinese) 14(1990)842.