2 research outputs found
Perturbative Effective Theory in an Oscillator Basis?
The effective interaction/operator problem in nuclear physics is believed to
be highly nonperturbative, requiring extended high-momentum spaces for accurate
solution. We trace this to difficulties that arise at both short and long
distances when the included space is defined in terms of a basis of harmonic
oscillator Slater determinants. We show, in the simplest case of the deuteron,
that both difficulties can be circumvented, yielding highly perturbative
results in the potential even for modest (~6hw) included spaces.Comment: 10 pages, 4 figure
Beyond the Shell Model: The Canonical Nuclear Many-Body Problem as an Effective Theory
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 He, to contrast a rigorous effective theory with the shell
model, thereby illustrating several of the uncontrolled approximations in the
latter.Comment: Revtex; two columns; four pages; two figures; submitted to Phys. Rev.
Let