Hyperradial expansion in the quantum-mechanical three- and four-body problems

Behavior of the wave function Psi and of the basis functions ]R/sub n/(rho)] in the space of the hyperradius rho in the method of expansion of Psi in the hyperspherical basis is investigated. Convergence properties of the expansion of the hyperradial amplitudes Psi in ]R/sub n/(rho)] are obtained. Two new sets of ]R/sub n/(rho)], convenient for practical applications in problems of discrete and continuous spectra, are proposed. Ways to improve the methods of solving three- and four-body problems with the use of the hyperspherical or oscillator basis expansions are suggested. The cause of the poor convergence of these expansions for the S' component of Psi in the problem of the bound state of three nucleons is determined, and a simple way to eliminate it is indicated