Elsevier

Nuclear Physics A

Volume 158, Issue 1, 7 December 1970, Pages 1-42
Nuclear Physics A

Nuclear saturation and the smoothness of nucleon-nucleon potentials

https://doi.org/10.1016/0375-9474(70)90047-3Get rights and content

Abstract

The two-nucleon and nuclear matter problems are solved by matrix inversion in momentum space. Direct matrix inversion of the Lippman-Schwinger and Brueckner equations is shown to be useful for general nuclear potentials including ones that are local, nonlocal, weak, strong, central, or noncentral. This flexibility is employed to study the relationship between nuclear saturation and the smoothness of the two-nucleon interaction.

Five potentials are considered that give approximately equivalent phase shifts but differ in their smoothness. Two examples of smooth potentials with very weak nonlocal tensor terms are given. The potentials are classified according to their smoothness by calculating the wave function defect and the wound integral for each case.

The binding energy of nuclear matter is calculated for each potential using the effective mass and angle-averaged Pauli operator approximations. A self-consistent hole spectrum and a free particle spectrum are used.

A systematic dependence of saturation on the smoothness of the two-nucleon interaction is found. Only strong potentials with strong tensor terms yield correct saturation, whereas very smooth potentials produce overbinding and large equilibrium densities.

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