‘tripleint_cc’: A program for 2-centre variational leptonic Coulomb potential matrix elements using Hylleraas-type trial functions, with a performance optimization study

Abstract We present a program used to calculate intricate three-particle integrals for variational calculations of solutions to the leptonic Schrödinger equation with two nuclear centres in which inter-leptonic distances (electron-electron and positron-electron) are included directly in the trial functions. The program has been used so far in calculations of He - over(H, ̄) interactions and positron H _2 scattering, however the precisely define... Title of program: tripleint.cc Catalogue Id: AEEV_v1_0 Nature of problem The 'tripleint.cc' code evaluates three-particle integrals needed in certain variational (in particular: Rayleigh-Ritz and generalized-Kohn) matrix elements for solution of the Schrödinger equation with two fixed centres (the solutions may then be used in subsequent dynamic nuclear calculations). Specifically the integrals are defined by equation (16) in the main text and contain terms proportional to r ik × r jk /r ij , i ≠j , i ≠ k , j ≠ k , with r ij the distance between leptons i and j. The ... Versions of this program held in the CPC repository in Mendeley Data AEEV_v1_0; tripleint.cc; 10.1016/j.cpc.2009.07.008 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要 我们介绍一款用于计算复杂三粒子积分的程序，该程序用于含两个核中心的轻子薛定谔方程（leptonic Schrödinger equation）解的变分计算，其中轻子间距离（电子-电子与正电子-电子距离）被直接纳入试探波函数。截至目前，该程序已被应用于反氢与氦的相互作用计算以及正电子与氢分子散射的计算，但完整定义尚待完善…… 程序名称：tripleint.cc 目录编号：AEEV_v1_0 问题本质 `tripleint.cc`代码可计算特定变分（尤其是瑞利-里兹（Rayleigh-Ritz）与广义科恩（generalized-Kohn））矩阵元所需的三粒子积分，用于求解双固定中心薛定谔方程，所得解可用于后续核动力学计算。具体而言，这些积分由正文式(16)定义，其中包含与$r_{ik} imes r_{jk}/r_{ij}$成正比的项，其中$i eq j, i eq k, j eq k$，$r_{ij}$为轻子$i$与$j$之间的距离。…… 存放在Mendeley数据的CPC程序库中的本程序版本：AEEV_v1_0; tripleint.cc; 10.1016/j.cpc.2009.07.008 本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2019年）