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The Shell Model, the Renormalization Group and the Two-Body Interaction
The no-core shell model and the effective interaction can
both be derived using the Lee-Suzuki projection operator formalism. The main
difference between the two is the choice of basis states that define the model
space. The effective interaction can also be derived using
the renormalization group. That renormalization group derivation can be
extended in a straight forward manner to also include the no-core shell model.
In the nuclear matter limit the no-core shell model effective interaction in
the two-body approximation reduces identically to . The same
considerations apply to the Bloch-Horowitz version of the shell model and the
renormalization group treatment of two-body scattering by Birse, McGovern and
Richardson
Projection Operator Formalisms and the Nuclear Shell Model
The shell model solve the nuclear many-body problem in a restricted model
space and takes into account the restricted nature of the space by using
effective interactions and operators. In this paper two different methods for
generating the effective interactions are considered. One is based on a partial
solution of the Schrodinger equation (Bloch-Horowitz or the Feshbach projection
formalism) and other on linear algebra (Lee-Suzuki). The two methods are
derived in a parallel manner so that the difference and similarities become
apparent. The connections with the renormalization group are also pointed out.Comment: 4 pages, no figure
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