Exponential variational expansion in relative coordinates and scalar couplingcoefficients for three-body systems

Abstract

The exponential variational expansion is applied to highlyaccurate computations of the ground states in the Ps− and ∞H−ions. The determined variational energies for these systems are−0.262 005 070 232 980 107 7335and −0.527 751 016 544 377 196 5668 aurespectively. These energies and corresponding wavefunctions aresignificantly more accurate than values known from earlier studies. Anumber of bound state properties are determined for the Ps−ion. The method of scalar coupling for three-body systems is developed. A generalanalytical expression is derived for the overlap integral between two scalar functions ϕ(r32, r31, r21) and ψ(r32, r31),written in relative coordinates and one-particle coordinatesrespectively. The case of bound S(L = 0)states in Coulomb three-body systems is discussed in detail. In this case, explicitanalytical formulae for the three-body scalar coupling coefficients have beenproduced and tested in actual highly accurate calculations for the Ps− and ∞H−ions. The approach developed in this work can be applied to a large number ofreal three-body problems.