Three-body systems with Coulomb interaction. Bound and quasi-bound S-states

A simple Mathematica (versions 7-9) code for computing S-state energies and wave functions of three-particles systems is presented. The relevant systems include two-electron atoms, molecular electronic ions and mesomolecular exotic species. In addition to the bound S-states the code enables one to compute the positions and widths of the lowest resonance, quasi-bound, states. The elegant technique derived from the classical papers of Pekeris is applied. The basis functions are composed of Laguerre functions. The method is based on the perimetric coordinates and specific properties of the Laguerre polynomials. A direct solution of the generalized eigenvalues and eigenvectors problem is used, distinct from Pekeris' works. The complex scaling method is applied for calculating the resonance states. The resultant wave functions have a simple analytical form, that enables calculation of expectation values of arbitrary physical operators without any difficulties. Only one mathematical parameter characterizing the basis size is required in the input. The other input parameters are of the physical nature.