Low-momentum NN interactions and all-order summation of ring diagrams of symmetric nuclear matter

Details Low-momentum NN interactions and all-order summation of ring diagrams of symmetric nuclear matter Low-momentum NN interactions and all-order summation of ring diagrams of symmetric nuclear matter

2009-04-07

arxiv.org/abs/0904.1139v1

Phys.Rev.C79:054004,2009

Physics

Nuclear Physics

Nuclear Theory

8 pages, 7 figures

Scientific paper

10.1103/PhysRevC.79.054004

We study the equation of state for symmetric nuclear matter using a ring-diagram approach in which the particle-particle hole-hole ($pphh$) ring diagrams within a momentum model space of decimation scale $\Lambda$ are summed to all orders. The calculation is carried out using the renormalized low-momentum nucleon-nucleon (NN) interaction $V_{low-k}$, which is obtained from a bare NN potential by integrating out the high-momentum components beyond $\Lambda$. The bare NN potentials of CD-Bonn, Nijmegen and Idaho have been employed. The choice of $\Lambda$ and its influence on the single particle spectrum are discussed. Ring-diagram correlations at intermediate momenta ($k\simeq$ 2 fm$^{-1}$) are found to be particularly important for nuclear saturation, suggesting the necessity of using a sufficiently large decimation scale so that the above momentum region is not integrated out. Using $V_{low-k}$ with $\Lambda \sim 3$ fm$^{-1}$, we perform a ring-diagram computation with the above potentials, which all yield saturation energies $E/A$ and Fermi momenta $k_F^{(0)}$ considerably larger than the empirical values. On the other hand, similar computations with the medium-dependent Brown-Rho scaled NN potentials give satisfactory results of $E/A \simeq -15$ MeV and $k_F^{(0)}\simeq 1.4$ fm$^{-1}$. The effect of this medium dependence is well reproduced by an empirical 3-body force of the Skyrme type.

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