The four-particle harmonic-oscillator brackets: Compact expressions and updated Fortran program

We present a new version of the four-particle harmonic-oscillator transformation brackets (4HOB) calculation program, where marginal cases of mass-ratio parameters d=0d=0, d→∞d→∞ and d1=0d1=0, which cannot be calculated in previous version, are presented. The simplified 4HOB calculation formulas for these cases are given.Program summaryProgram title: HOTBCatalogue identifier: AEFQ_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFQ_v2_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 3998No. of bytes in distributed program, including test data, etc.: 65 088Distribution format: tar.gzProgramming language: Fortran 90Computer: Any computer with FORTRAN 90 compilerOperating system: Windows, Linux, FreeBSD, True64 UnixRAM: 8 MBClassification: 17.17Catalogue identifier of previous version: AEFQ_v1_0Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 420Does the new version supersede the previous version?: YesNature of problem:   Calculation of the four-particle harmonic-oscillator transformation brackets for cases of mass-ratio parameters d=0d=0, d→∞d→∞ and d1=0d1=0.Solution method: The method is based on compact expressions of the four-particle harmonics oscillator brackets, presented in [1] and its simplifications presented in this paper.Reasons for new version:   We simplified the four-particle harmonic-oscillator transformation brackets expressions in cases d=0d=0, d→∞d→∞ and d1=0d1=0. It gives shorter calculation times and the possibility of calculating the four-particle harmonics oscillator brackets in these cases, which was not possible in the previous version of the program.Summary of revisions:   New subroutines for the calculation of the harmonic-oscillator transformation brackets in cases d=0d=0, d→∞d→∞ and d1=0d1=0. In case d=0d=0 subroutine HOB4_d_0(e1, l1, e2, l2, l12, e3, l3, e1s, l1s, e2s, l2s, l12s, e3s, l3s, l)   is used. In this case e2′=e2′ and l2=l2′. In case d→∞d→∞ subroutine HOB4_d_infinity(e1, l1, e2, l2, l12, e3, l3, e1s, l1s, e2s, l2s, l12s, e3s, l3s, l)   is used. In this case e1=e1′ and l1=l1′. In case d1=0d1=0 subroutine HOB4_d1_0(e1, l1, e2, l2, l12, e3, l3, e1s, l1s, e2s, l2s, l12s, e3s, l3s, l) is used. For theoretical issues of the revision see section ‘Theoretical aspects’.Restrictions:   The four-particle harmonic-oscillator transformation brackets up to e=28e=28.Running time: Less than one second for the single harmonic-oscillator transformation bracket.References:[1] D. Germanas, S. Mickevičius, R.K. Kalinauskas, Calculation of four-particle harmonic-oscillator transformation brackets, Computer Physics Communications 181 (2010) 420-425.