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 ${}^3\mathrm{He}$, in order to explore the consequences of reformulating the shell model as a controlled effective theory.

• Received 26 July 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.5484