Modified Phenomenological Formula for the Ground State Energy of Light Nuclei

Abstract

A modified phenomenological formula for the ground state binding energy in the region of light nuclei is proposed. Since binding energy is proportional to the volume of a nuclide, the new formula contains a volume term proportional to the mass number A and expresses asymmetry energy and coulomb repulsion energy between protons in a much simpler form than the way it is presented in the liquid drop model. The formula is used to calculate nuclear binding energy using three terms only, namely mass number A, neutron number, N and atomic number, Z. The correspondence with the conventional Liquid drop model and with the experimental results ishighly satisfactory for light nuclei. Considering a set of 60 light nuclei for 𝐴≤55, the formula yields root mean square deviation of 0.541 MeV, with respect to experimental values. This is better than conventional Liquid drop model which gives a root mean square deviation of 3.485 MeV over the same range of nuclei.The value of 𝑓is comparatively smaller for even-odd nuclei when compared to the corresponding even-even nuclei. Thus even-even nuclei are more strongly bound than odd-odd or even-odd nuclei making them more stable.