完全指数相关四体波函数的递推公式
Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions
摘要：
给出了四体积分的递推公式，其中被积函数由所有粒子间距离r_ij的任意整数次幂（>= -1）乘以一个包含所有r_ij的任意线性组合的指数组成。这些积分是使用Hylleraas基函数所遇到的那些积分的推广，并且包括在Li原子和其他四体系统上进行能量计算所需的所有积分，这些四体系统具有任意量子数的完全指数相关Slater型基。开始递归所需的唯一量是由Fromm和Hill首先计算的基本四体积分，加上一些容易计算的三体“边界”积分。在构造积分集的实际计算的计算劳动是小于当积分是由微分的基本积分相对于其参数得到的显式公式产生。通过使用符号代数程序（MAPLE）来计算数组索引指针并将语法正确的FORTRAN源代码作为输出，从而促进了计算;以这种方式，可以以最小的努力获得无错误的高速评估。可以通过验证积分必须满足的求和规则来检查工作。
英文摘要：
Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary linear combination of all the r_ij. These integrals are generalizations of those encountered using Hylleraas basis functions, and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill, plus some easily evaluated three-body "boundary" integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.
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