Three-body problem in the ground-state representation

V. M. Vinogradov

T. K. Lim

An exact solution is obtained for a model three-body system in which the particles interact through pairwise, harmonic oscillator, and spin-dependent potentials, the solution being achieved by a simple transformation to an appropriate coordinate system. In particular, it is shown that the S-state wave functions of the ground state of the triton span the two-dimensional representation of the symmetric group S3, are orthogonal, and resemble closely the Irving wave forms found so successful in variational calculations.

Eugene P. Gross

Behnam Farid

The conventional many-body perturbation theory suffers from three major ills: (i) some terms in the perturbation series may be unbounded; (ii) the series as a whole may not have a limit and (iii) despite convergence,the calculated limit may be false ('bogus' convergence). In renormalizable field theories, as the name indicates, problem (i) can be bypassed. Problems (ii) and (iii) remain. Here we demonstrate that these two problems can also be resolved, by choosing an appropriate Kohn-Sham Hamiltonian as the 'unperturbed' Hamiltonian. For this to be possible, some pertinent ground-state densities must be pure-state non-interacting v-representable. We illustrate our findings by means of two examples.

Wu-Yi Hsiang

S. Fluegge, W. Pieper