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arXiv · 0910.3942

Renormalization of the leading-order chiral nucleon-nucleon interaction and bulk properties of nuclear matter

R. Machleidt·P. Liu·D. R. Entem·E. Ruiz Arriola
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Abstract

We renormalize the two-nucleon interaction at leading order (LO) in chiral perturbation theory using the scheme proposed by Nogga, Timmermans, and van Kolck--also known as modified Weinberg counting. With this interaction, we calculate the energy per nucleon of symmetric nuclear matter in the Brueckner pair approximation and obtain a converged, cutoff-independent result that shows saturation, but also substantial underbinding. We find that the renormalized LO interaction is characterized by an extraordinarily strong tensor force (from one-pion exchange), which is the major cause for the lack of binding. The huge tensor force also leads to the unusually large wound integral of 40% in nuclear matter, which implies a very slow convergence of the hole-line or coupled-cluster expansion, rendering this interaction impractical for many-body calculations. In view of the unusual properties of the renormalized LO interaction and in view of the poor convergence of the nuclear many-body problem with this interaction, there is doubt if this interaction and its predictions can serve as a reasonable and efficient starting point that is improved by perturbative corrections.

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R. Machleidt, P. Liu, D. R. Entem, E. Ruiz Arriola. 2010-01-19. Renormalization of the leading-order chiral nucleon-nucleon interaction and bulk properties of nuclear matter. https://doi.org/10.1103/physrevc.81.024001

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