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Manuscript Title: A new version of CFPSIB: fractional parentage of identical boson
system. | ||

Authors: Y.-X. Liu, Q.-Z. Han, J.-J. Wang | ||

Program title: RCFPSIB | ||

Catalogue identifier: ACGW_v2_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 85(1995)89 | ||

Programming language: Fortran. | ||

Computer: IBM RISC/6000 320H. | ||

Operating system: AIX 3.2.4, VMS version 4.7. | ||

RAM: 8M words | ||

Word size: 32 | ||

Keywords: Nuclear physics, Identical bosons, Angular momentum, Seniority, Multiplicity, Coefficient of Fractional parentage, Isoscalar factor, Matrix element reduced, Interacting boson model, Unitary group, Orthogonal group. | ||

Classification: 17.18. | ||

Nature of problem:The program calculates all the coefficients of fractional parentage (CFP)[1] of identical boson system, by using the recurrent relations[2] with well-defined seniority. CFP's are the expansion coefficients of symmetrized n-body wave functions in terms of the symmetrized (n-1)- body wave functions and the wave function of the nth boson. It is of fundamental importance in constructing a many-boson wave function with well-defined permutational symmetry and total angular momentum, and in calculating the reduced matrix elements (RME's) of a physical operator. The evaluation of the RME's is the basis of the calculation in nuclear, atomic and molecular physics. Moreover, CFP's of a system with a large number of identical bosons are important in investigating the physical mechanism of nuclear high spin states and superdeformed states[3] and examining the chaotic behaviour in many-boson system[4]. | ||

Solution method:The program RCFPSIB uses the approach developed in Refs [2] to get all the CFP's of an identical boson system. In the approach, the CFP is factorized as a product of the isoscalar factor (ISF) of the reduction U(N) contained in O(N) and that of O(N) contained in O(3). The ISF of the reduction U(N) contained in O(N) has been given analytically. The ISF of the reduction O(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 O(N). It provides an efficient algorithm for computation and is numerically stable for relatively large system. | ||

Reasons for new version:Practical calculations show that the FORTRAN program CFPSIB[5] is not efficient enough for the system including a large number of bosons. After a careful examination on the code, we find out that a lot of repetitious calculations are involved in the program. We then modify it, so that this new version is accomplished. | ||

Restrictions:The program RCFPSIB can evaluate the CFP's of a system with identical bosons. At present, with the control parameters MNU=50, NFS=442, NTL=100, MAL=9, MM=4, the program can handle the system with maximal seniority 50 for d-bosons. With the control parameters MNU=16, NFS=895, NTL=48, MAL=37, MM=6, the program can handle the system with maximal seniority 16 for f-bosons. With the control parameters MNU=10, NFS=988, NTL=40, MAL=50, MM=8, the program can handle the system with maximal seniority 10 for g-bosons. With the control parameters MNU=7, NFS=593, NTL=35, MAL=35, MM=10, the program can handle the system with maximal seniority 7 for h-bosons. With the control parameters MNU=6, NFS=590, NTL=36, MAL=34, MM=12, the program can handle the system with maximal seniority 6 for i=bosons. After these control parametes are enlarged, the system can be enlarged. | ||

Running time:This depends strongly on the number of the bosons and the angular momentum of each boson. For example, it takes about 56 minutes on VAX 8550 to get all the ISF's, RME's and CFP's of a system including 50 d-bosons, about 5 hours for the 16 f-boson system, about 4 hours and 7 minutes for 10 g-bosons system, 31 minutes for 7 h-boson system, 19 minutes for 6 i-boson system. | ||

References: | ||

[1] | R.F. Bacher and S. Gousmit, Phys. Rev. 46(1934)948; G. Racah, Phys. Rev. 62(1942)438; 63(1943)367; 76(1949)1352; 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, J. Phys. A 22(1989)4769. | |

[3] | F. Iachello, Nucl. Phys. A522(1991), 83c, and references therein. | |

[4] | Y. Alhassid, A. Novoselsky and N. Whelan, Phys. Rev. Lett. 65(1990), 2971; N. Whelan and Y. Alhassid, Nucl. Phys. A556(1993), 42. V. Paar, D. Vorkapic and A.E.L. Dieparink, Phys. Rev. Lett. 69, 2184 (1992); P. von Brentano and V. Zamfir, Phys. Lett. B297(1992)219. | |

[5] | Yu-xin Liu, Hong-zhou Sun and En-guang Zhao, Compt. Phys. Commun. 70(1992)154. |

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