Evaluation of a general three-denominator Lewis integral

Abstract
An integral of the type. ∫ dq (q^2 +μ^2 _0 )^(l+1)(|q-q_1 |^2 +μ^2 _1 )^(m+1)(|q-q_2 |^2 +μ^2 _2 )^(n+1). is expressed by contour integration as a sum of two finite series for any finite values of l, m, n, thus avoiding parametric differentiation of a complicated closed form expression with respect to μ_0 , μ_1 , μ_2 . This integral is frequently encountered in studies of atomic, molecular, nuclear and plasma physics.

Title of program: LEWIS
Catalogue Id: ADCO_v1_0

Nature of problem
Structural and collisional studies in atomic, molecular and nuclear physics often encounter a certain type of 3-denominator integrals in the course of the calculations [1]. These integrals (called here general Lewis integrals [2]) appear naturally whenever two or more centres of force are present and relative coordinates of the interacting particles are involved. We derive a closed analytic form for these integrals and demonstrate by a few examples the usefulness of the results.

Versions of this program held in the CPC repository in Mendeley Data
ADCO_v1_0; LEWIS; 10.1016/0010-4655(95)00121-4

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要：该类型积分的表达式为 ∫ dq (q^2 +μ^2_0 )^(l+1)(|q-q_1 |^2 +μ^2_1 )^(m+1)(|q-q_2 |^2 +μ^2_2 )^(n+1)，通过轮廓积分表示为两个有限级数的和，适用于 l, m, n 为任意有限值的情况，从而避免了针对 μ_0, μ_1, μ_2 的复杂封闭形式的参数微分。此类积分在原子、分子、核和等离子体物理的研究中频繁出现。

程序名称：LEWIS
目录编号：ADCO_v1_0

问题性质：在原子、分子和核物理的结构和碰撞研究中，计算过程中常会遇到一种特定类型的三个分母的积分[1]。这些积分（在此称为通用 Lewis 积分[2]）在存在两个或更多力的中心以及涉及相互作用粒子的相对坐标时自然出现。我们推导出这些积分的封闭解析形式，并通过几个示例展示了结果的有用性。

Mendeley 数据库中 CPC 存档的此程序版本：ADCO_v1_0; LEWIS; 10.1016/0010-4655(95)00121-4

该程序已从贝尔法斯特女王大学（1969-2019）的 CPC 程序库中导入。