Revised calculation of four-particle harmonic-oscillator transformation brackets matrix

Abstract

In this article we present a new, considerably enhanced and more rapid method for calculation of the matrix of four-particle harmonic-oscillator transformation brackets (4HOB). The new method is an improved version of 4HOB matrix calculations which facilitates the matrix calculation by finding the eigenvectors of the 4HOB matrix explicitly. Using this idea the new Fortran code for fast and 4HOB matrix calculation is presented. The calculation time decreases more than a few hundred times for large matrices. As many problems of nuclear and hadron physics structure are modeled on the harmonic oscillator (HO) basis our presented method can be useful for large-scale nuclear structure and many-particle identical fermion systems calculations. Program summaryTitle of program: HOTB_MCatalogue identifier: AEFQ_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v3_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License version 3No. of lines in distributed program, including test data, etc.: 2149No. of bytes in distributed program, including test data, etc.: 17576Distribution format: tar.gzProgramming language: Fortran 90.Computer: Any computer with Fortran 90 compiler.Operating system: Windows, Linux, FreeBSD, True64 Unix.RAM: Up to a few Gigabytes (see Tables 1 and 2 included in the distribution package)Classification: 17.16, 17.17.Catalogue identifier of previous version: AEFQ_v2_0Journal reference of previous version: Comput. Phys. Comm. 182(2011)1377Does the new version supersede the previous version?: YesNature of problem: Calculation of the matrix of the 4HOB in a more effective way, which allows us to calculate the matrix of the brackets up to a few hundred times more rapidly than in a previous version.Solution method: The method is based on compact expressions of 4HOB, presented in [1] and its simplifications presented in this paper.Reasons for new version: We facilitated the calculation of the 4HOB, based on the method presented in the section ’Theoretical aspects’. The new program version gives shorter calculation times for the 4HOBSummary of revisions: New subroutines for calculation of the matrix of the 4HOB. For theoretical issues of revision see the section ’Theoretical aspects’.Restrictions: The 4HOB matrices up to e=28.Running time: Depends on the dimension of the 4HOB matrix (see Tables 1 and 2 included in the distribution file).