Ground state for two-electron and electron-muon three-body atomic systems

Abstract

In this article, the angular correlated configuration interaction method previously introduced by some of the authors is extended to three-body atomic systems with general masses. A recently proposed angularly correlated basis set is used to construct ground state wave functions which: (i) satisfy exactly Kato cusp conditions atthe two-body coalescence points; (ii) have only linear coefficients; and (iii) show a fast convergency rate for the energy. The efficiency of the construction is illustrated by the study of the negatively charged hydrogen-like systems (∞H-, T-, D-, 1H-, and Mu-), neutral helium-like systems (e-e- ∞He +2,e-e- 4He+2, e -e- 3He+2, e-μ - ∞He+2, e-μ -4He+2, and e-μ- 3He+2), and positively charged lithium-like systems (e-e- ∞Li+3,e -e- 7Li+3, e-e - 6Li+3, e-μ- ∞Li+3, e-μ- 7Li+3, and e-μ- 6Li+3). The ground state energies and other mean values are compared with those given in the literature, when available. Wave functions with a moderate number of (20 maximum) linear coefficients are given explicitly; they are sufficiently simple and accurate to be used in practical calculations of atomic collision in which multidimensional integrations are involved.