Analytic Evaluation of Four-Particle Integrals with Complex Parameters
V.S.Zotev, T.K.Rebane
TL;DR
This paper extends an analytic method for four-particle integrals to complex parameters, introducing a numerical branch tracking technique that enables high-precision solutions for Coulomb four-body problems.
Contribution
It generalizes the Fromm and Hill method to complex parameters and develops a numerical branch tracking procedure for improved accuracy.
Findings
High precision variational solutions achieved
Method demonstrates high efficiency and versatility
Applicable to Coulomb four-body problems
Abstract
The method for analytic evaluation of four-particle integrals, proposed by Fromm and Hill, is generalized to include complex exponential parameters. An original procedure of numerical branch tracking for multiple valued functions is developed. It allows high precision variational solution of the Coulomb four-body problem in a basis of exponential-trigonometric functions of interparticle separations. Numerical results demonstrate high efficiency and versatility of the new method.
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