Beyond the Shell Model: The Canonical Nuclear Many-Body Problem as an Effective Theory

Abstract

We describe a strategy for attacking the canonical nuclear structure problem ---bound-state properties of a system of point nucleons interacting via a two-body potential---which involves an expansion in the number of particles scattering at high momenta, but is otherwise exact. The required self-consistent solutions of the Bloch-Horowitz equation for effective interactions and operators are obtained by an efficient Green's function method based on the Lanczos algorithm. We carry out this program for the simplest nuclei, d and ${}^3$He, to contrast a rigorous effective theory with the shell model, thereby illustrating several of the uncontrolled approximations in the latter.

Revtex; two columns; four pages; two figures; submitted to Phys. Rev. Lett

References in corpus (2)

• Full $0\hslash \omega$ shell model calculation of the binding energies of the $1f_{7/2}$ nuclei
• Four-nucleon shell-model calculations in a Faddeev-like approach

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