Angular Symmetry and Hylleraas Coordinates in Four-Body Problems

摘要: Abstract The most accurate studies of few-body Coulomb systems have used wavefunctions forms that are simple in Hylleraas coordinates (those explicitly include all the interparticle distances). In wavefunction has been constructed from Slater-type orbitals about a single center (relative to which other particles at positions r i ) by adjoining each orbital product polynomial distances j . Matrix elements then usually evaluated expanding terms This type is not ideal for “nonadiabatic” comparable (finite) mass; preferable alternative use exponentials coordinates. It practical usual expansion methods exponential wavefunctions, and this paper considers issues arising when four-body treated directly states general angular symmetry. two problems here (1) convenient compact expression kinetic energy eigenstates, (2) integrations matrix elements. Both these differ their well-known counterparts formulations, part because orthogonal coordinates, angles independent variables.