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

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

1999-07-24

arxiv.org/abs/nucl-th/9907097v1

Phys.Rev.Lett. 84 (2000) 5484

Physics

Nuclear Physics

Nuclear Theory

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

Scientific paper

10.1103/PhysRevLett.84.5484

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.

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