Nuclear matter properties, phenomenological theory of clustering at the nuclear surface, and symmetry energy

Abstract

We present a phenomenological theory of nuclei that incorporates clustering at the nuclear surface in a general form. The theory explains the recently extracted large symmetry energy by Natowitz et al., at low densities of nuclear matter and is fully consistent with the static properties of nuclei. In a phenomenological way, clusters of all sizes and shapes along with medium modifications are included. Symmetric nuclear matter properties are discussed in detail. Arguments are given that lead to an equation of state of nuclear matter consistent with clustering in the low-density region. We also discuss properties of asymmetric nuclear matter. Because of clustering, an interesting interpretation of the equation of state of asymmetric nuclear matter emerges. As a framework, an extended version of Thomas-Fermi theory is adopted for nuclei which also contain phenomenological pairing and Wigner contributions. This theory connects the nuclear matter equation of state, which incorporates clustering at low densities, with clustering in nuclei at the nuclear surface. Calculations are performed for various equations of state of nuclear matter. We consider measured binding energies of 2149 nuclei for $N$, $Z$ \ensuremath{\geqslant} 8. The importance of the quartic term in symmetry energy is demonstrated at and below the saturation density of nuclear matter. It is shown that it is largely related to the use of, ab initio, a realistic equation of state of neutron matter, particularly the contribution arising from the three neutron interactions and somewhat to clustering. Reasons for these are discussed. Because of clustering the neutron skin thickness in nuclei is found to reduce significantly. The developed theory predicts situations and regimes to be explored both theoretically and experimentally.