A computer program for two-particle generalized coefficients of fractional parentage

详细信息    查看全文

• 作者：A. Deveikis ; A. Juodagalvis
• 关键词：Nuclear shell model ; Coefficients of fractional parentage ; Antisymmetric A-particle states ; jt-coupling
• 刊名：Computer Physics Communications
• 出版年：2008
• 出版时间：15 October 2008
• 年：2008
• 卷：179
• 期：8
• 页码：607-613
• 全文大小：151 K

文摘

We present a FORTRAN90 program GCFP for the calculation of the generalized coefficients of fractional parentage (generalized CFPs or GCFP). The approach is based on the observation that the multi-shell CFPs can be expressed in terms of single-shell CFPs, while the latter can be readily calculated employing a simple enumeration scheme of antisymmetric A-particle states and an efficient method of construction of the idempotent matrix eigenvectors. The program provides fast calculation of GCFPs for a given particle number and produces results possessing numerical uncertainties below the desired tolerance. A single j-shell is defined by four quantum numbers, (e,l,j,t).

A supplemental C++ program parGCFP allows calculation to be done in batches and/or in parallel.

Program summary

Program title: GCFP, parGCFP

Catalogue identifier: AEBI_v1_0

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEBI_v1_0.html

Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html

No. of lines in distributed program, including test data, etc.: 17 199

No. of bytes in distributed program, including test data, etc.: 88 658

Distribution format: tar.gz

Programming language: FORTRAN 77/90 (GCFP), C++ (parGCFP)

Computer: Any computer with suitable compilers. The program GCFP requires a FORTRAN 77/90 compiler. The auxiliary program parGCFP requires GNU-C++ compatible compiler, while its parallel version additionally requires MPI-1 standard libraries

Operating system: Linux (Ubuntu, Scientific) (all programs), also checked on Windows XP (GCFP, serial version of parGCFP)

RAM: The memory demand depends on the computation and output mode. If this mode is not 4, the program GCFP demands the following amounts of memory on a computer with Linux operating system. It requires around 2 MB of RAM for the A=12 system at E_x2. Computation of the A=50 particle system requires around 60 MB of RAM at E_x=0 and 70 MB at E_x=2 (note, however, that the calculation of this system will take a very long time). If the computation and output mode is set to 4, the memory demands by GCFP are significantly larger. Calculation of GCFPs of A=12 system at E_x=1 requires 145 MB. The program parGCFP requires additional 2.5 and 4.5 MB of memory for the serial and parallel version, respectively.

Classification: 17.18

Nature of problem: The program GCFP generates a list of two-particle coefficients of fractional parentage for several j-shells with isospin.

Solution method: The method is based on the observation that multishell coefficients of fractional parentage can be expressed in terms of single-shell CFPs [1]. The latter are calculated using the algorithm [2,3] for a spectral decomposition of an antisymmetrization operator matrix Y. The coefficients of fractional parentage are those eigenvectors of the antisymmetrization operator matrix Y that correspond to unit eigenvalues. A computer code for these coefficients is available [4]. The program GCFP offers computation of two-particle multishell coefficients of fractional parentage. The program parGCFP allows a batch calculation using one input file. Sets of GCFPs are independent and can be calculated in parallel.

Restrictions: A<86 when E_x=0 (due to the memory constraints); small numbers of particles allow significantly higher excitations, though the shell with j11/2 cannot get full (it is the implementation constraint).

Unusual features: Using the program GCFP it is possible to determine allowed particle configurations without the GCFP computation. The GCFPs can be calculated either for all particle configurations at once or for a specified particle configuration. The values of GCFPs can be printed out with a complete specification in either one file or with the parent and daughter configurations printed in separate files. The latter output mode requires additional time and RAM memory. It is possible to restrict the (J,T) values of the considered particle configurations. (Here J is the total angular momentum and T is the total isospin of the system.) The program parGCFP produces several result files the number of which equals to the number of particle configurations. To work correctly, the program GCFP needs to be compiled to read parameters from the standard input (the default setting).

Running time: It depends on the size of the problem. The minimum time is required, if the computation and output mode (CompMode) is not 4, but the resulting file is larger. A system with A=12 particles at E_x=0 (all 9411 GCFPs) took around 1 sec on a Pentium4 2.8 GHz processor with 1 MB L2 cache. The program required about 14 min to calculate all 1.3×10⁶ GCFPs of E_x=1. The time for all 5.5×10⁷ GCFPs of E_x=2 was about 53 hours. For this number of particles, the calculation time of both E_x=0 and E_x=1 with CompMode = 1 and 4 is nearly the same, when no other processes are running. The case of E_x=2 could not be calculated with CompMode = 4, because the RAM memory was insufficient. In general, the latter CompMode requires a longer computation time, although the resulting files are smaller in size. The program parGCFP puts virtually no time overhead. Its parallel version speeds-up the calculation. However, the results need to be collected from several files created for each configuration.

References:

[1] J. Levinsonas, Works of Lithuanian SSR Academy of Sciences 4 (1957) 17.

[2] A. Deveikis, A. Bončkus, R. Kalinauskas, Lithuanian Phys. J. 41 (2001) 3.

[3] A. Deveikis, R.K. Kalinauskas, B.R. Barrett, Ann. Phys. 296 (2002) 287.

[4] A. Deveikis, Comput. Phys. Comm. 173 (2005) 186. (CPC Catalogue ID. ADWI_v1_0)