The bateman method and algebraic solution of the three-nucleon integral equations

Abstract

By using a separable expansion for the two-particle t-matrix the problem of three particles with pair interaction is reduced to a set of one-dimensional integral equations. By a subsequent separable representation of the kernels of such integral equations (based on the Bateman method) the three-body problem is reduced to the solution of algebraic equations. Results are presented for the three-particle binding energies and scattering length in the case of identical zero-spin particles and for the triton binding energy and n-d scattering lengths. Comparisons are made between two separable approximations for the two-particle t-matrix, namely, between the unitary pole approximation and the Hilbert-Schmidt one.