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 phenomenological way clusters of all sizes, 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 incorporate clustering at low densities, with clustering in nuclei at the nuclear surface. Calculations are performed for various equation of state of nuclear matter. We consider measured binding energies of 2149 nuclei for N, Z ≥ 8. The importance of 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, realistic equation of state of neutron matter, particularly the contribution arising from the three neutron interaction and somewhat to clustering.Reasons for these are discussed. Because of clustering the neutron skin thickness in nuclei is found to reduce significantly. Theory predicts new situations and regimes to be explored both theoretically and experimentally. *

The many facets of the (non-relativistic) Nuclear Equation of State

“…where ρ = ρ ρ 0 , ǭf is the average fermi energy, A 1 , B 1 , σ, c 1 and c 2 are the parameters to be determined in order to reproduce some properties of INM. The assumed form for the energy per particle in equation ( 33) is for guidance only and many different forms can be found in the literature [10,58,75,123,124,125,126,172,173,174]. It is a simple expansion to second order in m χ , and higher order terms might be added once more constraints to the NEOS are determined.…”

Symmetry Energy and Surface Clustering in Nuclei; Probing the Asymmetric Nuclear Matter

“…We explain this assumption through a proof by contradiction and inference. The proof is demonstrated in Usmani et al [3].…”

Nucleation and cluster formation in low-density nucleonic matter: A mechanism for ternary fission

“…Thus quantitative analyses of the data on skin thicknesses may require that the correlations which lead to the cluster formation be included. This could have an effect on analyses presently being carried out to extract information on the slope of the symmetry potential near normal density, for example [41].…”