A statistical model of heavy nuclei

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1971

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Abstract

The density distribution of nucleons, the range of the Yukawa force and the strength of mesic charge of heavy nuclei are investigated in the context of a statistical model. It is assumed that nucleons in a heavy nucleus are in equilibrium with the Fermi gas pressure balancing mechanical forces. From the conditions of equilibrium, a set of nonlinear differential equations is obtained which are solved by numerical methods. It is shown that proper values of densities of nucleons at the center of a nucleus, the range of the Yukawa force and the strength of mesic charge can be chosen so that the calculation of the mass number and the number of protons yield nuclear parameters consistent with experimental results. The evidence of neutron excess in the surface of a heavy nucleus is investigated from this model. The energy per particle is calculated and compared with experimental results. It is shown also how the four parameters of this model, the densities of neutrons and protons at the center, range of the nuclear force and the strength of mesic charge change with the various values of the mass number and the atomic number. This model also gives us a value of the nuclear radius which is roughly in agreement with that predicted by various scattering experiments.

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