The goal of this project is to examine in greater depth nuclear mass formula fits (taking known nuclear data and fitting it to certain equations and determining the equation's parameters using a data modeling program) and apply these fits to an infinite nuclear matter model. So far, the main focus has been on nuclear energies and their applications to mass formulae that are derived from the liquid droplet model of the atom. The purpose of this is to shed light on current problems that exist in our knowledge of the nucleus and the behavior of protons and neutrons within it. Some questions that need to be answered are: 1) what is the relationship between mass formula parameters and the type of mass formula used, 2) do the parameters depend in any significant way on the data one uses to fit (should binding energies be used alone or do Fermi energies or other types of empirical data need be included or excluded), 3) are there ways to eliminate shell or pairing effects and 4) can other simple improvements be made to traditional formulae or the liquid droplet model of the atom itself. The reasons for exploring and attempting to answer these questions are that nuclear mass formulas can be extremely useful in aiding physicists' understanding various types of nuclei in the most extreme cases, such as in neutron stars. Also, fits using old and perhaps outdated formulas are providing nuclear densities that do not agree with experimental electron scattering data. This is one of the main problems that currently exists and will be the focus of the discussion in the first part of the project. Thus, an accurate nuclear mass formula has many astronomical and astrophysical ramifications.
As stated, one of the main problems under investigation here is that the nuclear densities that are obtained using current nuclear mass formulas with fitted parameters do not agree with those obtained by electron scattering data. This is known as the r0 paradox. Thus, one of the immediate goals in our research right now will be to focus on this problem and on the coulomb energy that we suspect is the cause.
A new method has been proposed by Dr. Lakshamidhar Sapathy, in his paper "How to go from finite to infinite nuclear matter," to resolve this paradox and attempt to find nuclear densities, using mass formulas, that correlate with the scattering data. Sapathy's new method involves using proton and neutron Fermi energies along with binding energies in the fitting process. Also, with the implementation of the Hugenholtz-Van Hove theorem, certain parameters are isolated in the method. Dr. Lattimer and I decided to first test Sapathy's method before attempting to alter the nature of the liquid droplet model or the physics behind it. Basically, we attempted to recreate the results Sapathy obtained. However, the parameters that we received revealed that the problem of the nuclear density was still left unsolved. The parameters from the old formulas that we used to fit were very similar to the ones we obtained by fitting with Sapathy's method. The coulomb parameter value from the old equation was .69 while Sapathy's method gave us a value of .71. Neither of these numbers solves the density issue. Thus, a new method of parameterization of the coulomb energy and of nuclear mass formulas in general is needed. For this, Dr. Lattimer and I plan to find new methods of fitting and incorporate proton density information from electron scattering data. This work was supported with funding from the Simons Foundation.