Finite-element calculations for the three-body Coulomb problem with two equal masses

Abstract

An accurate numerical finite-element method (FEM) solution of the three-body Coulomb problem with two equal masses is presented. The application of the FEM to systems with mass ratios ranging from 1836 to 1/1836 yields upper bounds for energy eigenvalues to a precision in the range of ${10}^{\mathrm{\ensuremath{-}}11}$--${10}^{\mathrm{\ensuremath{-}}9}$ a.u. Expectation values for different operators are computed and discussed. \textcopyright{} 1996 The American Physical Society.