Low-Lying S-States of Two-Electron Systems

Abstract

The energies of the low-lying bound S-states of some two-electron systems (treating them as three-body systems) like negatively charged hydrogen, neutral helium, positively charged-lithium, beryllium, carbon, oxygen, neon, argon and negatively charged muonium and exotic positronium ions have been calculated employing hyperspherical harmonics expansion method. The matrix elements of two-body interactions involve Raynal–Revai coefficients which are particularly essential for the numerical solution of three-body Schrődinger equation when the two-body potentials are other from Coulomb or harmonic. The technique has been applied for to two-electron ions 1H− (Z = 1) to 40Ar16+ (Z = 18), negatively charged-muonium Mu− and exotic positronium ion Ps−(e+e−e−) considering purely Coulomb interaction. The available computer facility restricted reliable calculations up to 28 partial waves (i.e. Km = 28) and energies for higher Km have been obtained by applying an extrapolation scheme suggested by Schneider.