Semi-classical, Microscopic Approach to the Liquid Drop Model --- A Possible Way of the Description of Heavy Ion Reactions

Z Sosin,J Kallunkathariyil

doi:10.5506/aphyspolb.45.925

Abstract

An isospin and spin dependent form of the equation of state for nuclear matter is presented. This form is used for the description of nucleon interaction in a new dynamic model. Preliminary calculations show that the new approach makes possible predicting the alpha structures appearing in the case of the ground state even-even nuclei.

Highlights

Nuclei are close to 55 orders of magnitude lighter than a typical neutron star, it seems that the state of the material comprising of the above two objects can be determined by the same equation, which is the equation of the state (EOS) of nuclear matter
We arrived at these conclusions using semiclassical, microscopic version of the liquid drop model in which dynamics is governed by EOS
Preliminary results show that the Microscopic LDM model (MLDM) model is able to reproduce the basic properties of atomic nuclei

Summary

Introduction

Nuclei are close to 55 orders of magnitude lighter than a typical neutron star, it seems that the state of the material comprising of the above two objects can be determined by the same equation, which is the equation of the state (EOS) of nuclear matter. Such models typically assume one body dissipation and no compression of the nuclear matter In such an approach the volume energy together with energies which are corrections related to a not equal number of protons and neutrons and a non-zero spin of the system may be treated as the 0th term of the expansion of the energy density function (given by EOS). All the aforementioned types of energy are functional expressed by integrals determined by the distribution of nuclear matter Since these densities are here uniquely determined by the position and other parameters of wave packets (spin, isospin and variance), the description can be interpreted as the Microscopic LDM model (MLDM). The expectation which is in line with a mean field theory (e.g. with the Skyrme-Hartree-Fock model) determine the zero energy density in case where density of matter tends to zero (it is in contrast with some other models like, for instance, an idealized alpha-mater picture [4])

For the saturation density we require:

An equation of state given by the third-degree polynomials

Application of the proposed EOS form to the MLDM calculations

The MLDM calculations for describing the ground state properties of nuclei

Conclusions