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Many Body Methods and Effective Field Theory

Thomas Schaefer·Chung-Wen Kao·Stephen R. Cotanch
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Abstract

In the framework of pionless nucleon-nucleon effective field theory we study different approximation schemes for the nuclear many body problem. We consider, in particular, ladder diagrams constructed from particle-particle, hole-hole, and particle-hole pairs. We focus on the problem of finding a suitable starting point for perturbative calculations near the unitary limit (k_Fa)->infinity and (k_Fr)-> 0, where k_F is the Fermi momentum, a is the scattering length and r is the effective range. We try to clarify the relationship between different classes of diagrams and the large g and large D approximations, where g is the fermion degeneracy and D is the number of space time dimensions. In the large D limit we find that the energy per particle in the strongly interacting system is 1/2 the result for free fermions.

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Thomas Schaefer, Chung-Wen Kao, Stephen R. Cotanch. 2005-08-05. Many Body Methods and Effective Field Theory. https://doi.org/10.1016/j.nuclphysa.2005.08.006

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