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The Shell Model, the Renormalization Group and the Two-Body Interaction

B. K. Jennings
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Abstract

The no-core shell model and the effective interaction $V_{{\rm low} k}$ 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 $V_{{\rm low} k}$ 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 $V_{{\rm low} k}$. 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.

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B. K. Jennings. 2005-04-25. The Shell Model, the Renormalization Group and the Two-Body Interaction. https://doi.org/10.1209/epl%2Fi2005-10222-0

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