Symmetry Energy in the Semi-empirical Mass Formula

Abstract

Symmetry energy in the semi-empirical mass formula appears as a correction term, and it can be explained in the classroom in various ways. One can explain it using the elementary idea that the term is proportional to some power of the difference in the neutron and proton numbers, and the binding energy is maximum when these numbers are equal for a given mass number. Other approaches follow the Fermi gas model that treats the neutrons and protons as degenerate gases inside the nucleus. Using an intuitive approach, it is explained that the symmetry energy originates due to a change in the total kinetic energy of the degenerate nucleons as the neutron number deviates from the proton number in a nucleus of a given mass number. A detailed analytical calculation presents that the total kinetic energy of degenerate nucleons contributes to both the volume and symmetry energy terms and thus reduces the nuclear binding energy. The contribution of the potential energy of the nucleons to the symmetry energy is also discussed in this article. Our calculations estimate the associated coefficient of the symmetry energy term, which is found to be close to the existing value.