New methods for old Coulomb few-body problems



Coulomb problems involving three or four particles can advantageously be described using wavefunctions that explicitly involve all the interparticle distances. In what is known as the Hylleraas method, a set of Slater-type orbitals for the electrons of an atom is augmented by linear (or in some cases higher powers) of the interelectron separation(s). An alternative approach, of particular value when all the particles have comparable masses, is to use a wavefunction containing exponentials in all the interparticle distances. This “exponential ansatz” is straightforward to implement when there are three particles but has only recently been implemented for four-body systems. Integral evaluation is reviewed for both the exponential ansatz and the Hylleraas method, the treatment of general angular symmetry is discussed, and kinetic-energy matrix elements are examined and related to simpler integrals. Some illustrative results for the positronium molecule (e+ee+e) are included. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004