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

Abstract

We present a new version of the four-particle harmonic-oscillator transformation brackets (4HOB) calculation program, where marginal cases of mass-ratio parameters d = 0 , d → ∞ and d 1 = 0 , which cannot be calculated in previous version, are presented. The simplified 4HOB calculation formulas for these cases are given. Program summary Program title: HOTB Catalogue identifier: AEFQ_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v2_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3998 No. of bytes in distributed program, including test data, etc.: 65 088 Distribution format: tar.gz Programming language: Fortran 90 Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix RAM: 8 MB Classification: 17.17 Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 420 Does the new version supersede the previous version?: Yes Nature of problem: Calculation of the four-particle harmonic-oscillator transformation brackets for cases of mass-ratio parameters d = 0 , d → ∞ and d 1 = 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 = 0 , d → ∞ and d 1 = 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 = 0 , d → ∞ and d 1 = 0 . In case d = 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 e 2 ′ = e 2 ′ and l 2 = l 2 ′ . In case 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 e 1 = e 1 ′ and l 1 = l 1 ′ . In case d 1 = 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 = 28 . Running time: Less than one second for the single harmonic-oscillator transformation bracket.