Difference between the Density Distribution of Neutrons and Protons in Atomic Nuclei

Abstract

IN a former communication¹ I calculated the energy and distribution of nucleon density of atomic nuclei by Ritz's method in the first approximation, assuming Yukawa forces between the nucleons. In the energy expression of the nucleus, in addition to the exchange energy and kinetic zero-point Fermi energy of the nucleons, we have also taken into account the kinetic energy correction of Weizsäcker, the electrostatic Coulomb energy of protons and the Coulomb exchange energy of protons arising from the Coulomb interaction of protons. In the first approximation for the neutron density ρ_n and the proton density ρ_p, functions of Gaussian type have been set up in the following form: where r is the distance from the centre of the nucleus, r₀ is the Compton wave-length of the π-mesons divided by 2π, ${\text{ρ}}_{n_{\text{0}}}$ and ${\text{ρ}}_{p_{\text{0}}}$ are normalizing factors and a denotes a variational parameter to be determined from the minimization of the energy.