Novel Methods for Determining Effective Interactions for the Nuclear Shell Model

The Contractor Renormalization (CORE) method is applied in combination with modern effective-theory techniques to the nuclear many-body problem. A one-dimensional--yet ``realistic''--nucleon-nucleon potential is introduced to test these novel ideas. It is found that the magnitude of ``model-space'' (CORE) corrections diminishes considerably when an effective potential that eliminates the hard-momentum components of the potential is first introduced. As a result, accurate predictions for the ground-state energy of the there-body system are made with relatively little computational effort when both techniques are used in a complementary fashion.Comment: 14 pages, 5 figures and 2 tabl

Renormalisation and fixed points in Hilbert Space

The energies of low-lying bound states of a microscopic quantum many-body system of particles can be worked out in a reduced Hilbert space. We present here and test a specific non-perturbative truncation procedure. We also show that real exceptional points which may be present in the spectrum can be identified as fixed points of coupling constants in the truncation procedure.Comment: 4 pages, 1 tabl