Counter terms for low momentum nucleon–nucleon interactions

Abstract

There is much current interest in treating low energy nuclear physics using the renormalization group (RG) and effective field theory (EFT). Inspired by this RG-EFT approach, we study a low-momentum nucleon–nucleon (NN) interaction, V low- k , obtained by integrating out the fast modes down to the scale Λ∼2 fm −1. Since NN experiments can only determine the effective interaction in this low momentum region, our chief purpose is to find such an interaction for complex nuclei whose typical momenta lie below this scale. In this paper we find that V low- k can be highly satisfactorily accounted for by the counter terms corresponding to a short range effective interaction. The coefficients C n of the power series expansion ∑ C n q n for the counter terms have been accurately determined, and results derived from several meson-exchange NN interaction models are compared. The counter terms are found to be important only for the S, P and D partial waves. Scaling behavior of the counter terms is studied. Finally we discuss the use of these methods for computing shell model matrix elements.