Europhys. Lett.
Volume 72, Number 2, October 2005
Page(s) 216 - 220
Section Nuclear physics
Published online 09 September 2005
Europhys. Lett., 72 (2), pp. 216-220 (2005)
DOI: 10.1209/epl/i2005-10222-0

The shell model, the renormalization group and the two-body interaction

B. K. Jennings

TRIUMF - 4004 Wesbrook Mall, Vancouver, BC, Canada, V6T 2A3

received 27 July 2005; accepted in final form 16 August 2005
published online 9 September 2005

The no-core shell model and the effective interaction $V_{\ab{low}\
k}$ 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 $V_{\ab{low}\
k}$ can also be derived using the renormalization group. That renormalization group derivation can be extended in a straightforward 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 $V_{\ab{low}\
k}$. 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.

21.60.Cs - Shell model.
21.30.Fe - Forces in hadronic systems and effective interactions.

© EDP Sciences 2005