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

The exponential variational expansion is applied to highly accurate computations of the ground states in the Ps(-) and H-infinity(-) ions. The determined variational energies for these systems are -0.262 005 070 232 980 107 7335 and -0.527 751016 544 377 196 5668 au respectively. These energies and corresponding wavefunctions are significantly more accurate than values known from earlier studies. A number of bound state properties are determined for the Ps- ion. The method of scalar coupling for three-body systems is developed. A general analytical expression is derived for the overlap integral between two scalar functions phi (r(32), r(31), r(21)) and psi (r(32), r(31)), written in relative coordinates and one-particle coordinates respectively. The case of bound S(L = 0) states in Coulomb three-body systems is discussed in detail. In this case, explicit analytical formulae for the three-body scalar coupling coefficients have been produced and tested in actual highly accurate calculations for the Ps(-) and H-infinity(-) ions. The approach developed in this work can be applied to a large number of real three-body problems.