Novel methods for determining effective interactions for the nuclear shell model

Abstract

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. 7

Nonperturbative renormalization of the neutrinoless double-βoperator inp-shell nuclei

“…One alternative, known as the Contractor Renormalization (CORE) mapping [24], is to make the small-space ground state |0 proportional to P |0 , the projection of the full ground state, and then construct the other |k from the set P |k through Graham-Schmidt orthogonalization. But in fact any unitary transformation of the |k 's generated by the Lee-Suzuki procedure defines a valid mapping.…”

Nonperturbative renormalization of the neutrinoless double-beta operator in p-shell nuclei

“…This prescription seems particularly appropriate for a comprehensive description of the spectrum, but in double-beta decay we are not equally interested in all states. One alternative, known as the Contractor Renormalization (CORE) mapping [24] is to make the smallspace ground state | 0 proportional P |0 , the projection of the full ground state, and then construct the other | k from the set P |k through Graham-Schmidt orthogonalization. But in fact any unitary transformation of the | k 's generated by the Lee-Suzuki procedure defines a valid mapping.…”

Study of the spectral properties of spin ladders in different representations via a renormalization procedure

“…The procedure consists of an algorithm which implements a step by step reduction of the size of Hilbert space by means of a projection technique. It relies on the renormalization concept following in spirit former work based on this concept [10,11,12]. Since the reduction procedure does not act in ordinary or momentum space but in Hilbert space, it is universal in the sense that it works for any kind of many-body quantum system.…”