Three Families of Integrals Which Arise in Some Three-Body Problems

摘要

Three families of integrals that arise in the three-body problem with Coulomb pair potentials are examined. Two of the families are definite integrals on a single variable where the integrands are products of two Coulomb Sturmian functions. The third family is a triple integral where the integrands are products of four Coulomb Sturmian functions and two Legendre polynomials. Closed-form expressions are derived for all the integrals, except for one subset of the most general triple integral. An outline of the procedure necessary to obtain a closed expression for this subset is given. (Author)