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 the scale ~2fm^{-1}. Since NN experiments can only determine the effective interaction in the 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 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*k^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 for the S, P, and D partial waves. Scaling behavior of the counter terms is also studied, and we discuss the use of these methods for computing shell model matrix elements.

8 pages, 5 figures, substantially revised procedure, content, and references

References in corpus (21)

• An accurate nucleon-nucleon potential with charge-independence breaking
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Construction of high-quality Nucleon-Nucleon potential models
• Chiral Dynamics in Nucleons and Nuclei
• Effective Field Theory for Few-Nucleon Systems
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Nuclear forces from chiral Lagrangians using the method of unitary transformation II: The two-nucleon system
• Effective Field Theory of Nuclear Forces
• Low momentum nucleon-nucleon potential and shell model effective interactions
• Low momentum nucleon-nucleon potential and shell model effective interactions
• On the Manifestation of Chiral Symmetry in Nuclei and Dense Nuclear Matter
• Low momentum nucleon-nucleon potentials with half-on-shell T-matrix equivalence
• Effective theory for the two-nucleon system
• Low Momentum Nucleon-Nucleon Interaction and Fermi Liquid Theory
• Beyond the Shell Model: The Canonical Nuclear Many-Body Problem as an Effective Theory
• Building light nuclei from neutrons, protons, and pions
• Chiral NN model and Ay puzzle
• Realistic shell-model calculations for proton particle-neutron hole nuclei around 132Sn
• Microscopic Nuclear Structure Based upon a Chiral NN Potential
• Effective Field Theory For Nuclei: Confronting Fundamental Questions in Astrophysics

Cited by in corpus (15)

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• Symmetries of the Similarity Renormalization Group for Nuclear Forces
• Implicit vs Explicit Renormalization and Effective Interactions
• Low momentum shell model effective interactions with all-order core polarizations
• Unitarity potentials and neutron matter at the unitary limit
• Incorporating Brueckner-Hartree-Fock correlations in the Density Matrix Expansion approach
• Local Projections of Low-Momentum Potentials
• Spin-orbit coupling in nuclei and realistic nucleon-nucleon potentials
• Introduction to low-momentum effective interactions with Brown-Rho scaling and three-nucleon forces
• Low-momentum nucleon-nucleon interaction and shell-model calculations
• Implicit and explicit renormalization: two complementary views of effective interactions
• $NN$ scattering in ${}^3{S}_1{-}^3{D}_1$ channels of EFT ($/\pi$)