Study of Average Characteristic Parameters of Isotopes, Isotones and Isobars by Electron and Proton Scattering

By way of studying the difference of the proton and neutron distributions in isotopes, isotones and isobars, we used the results of theoretical calculations obtained from the scattering of protons and electrons on nuclei. To calculate the differential cross section of proton scattering, an expression was obtained for the distorted-wave formfactor of the nucleus, which, using the mathematical method proposed by us, is expressed through the plane-wave Born formfactor. In addition, using the data for elastic scattering of electrons on nuclei, the average characteristic parameters of C2040a, C2048a, C2452r, C2454r, F2654e, N2858i, N2860i nuclei were determined. In this work, for calculating the differential cross section of the elastic scattering of electrons on spherical nuclei, the Fermi function was chosen as a trial function of the proton density distribution. In the calculations, the pole method was used to solve the Born integral of the target nucleus formfactor. Based on an analysis of the calculations of the differential cross section of the elastic scattering of electrons and the calculations of the differential cross section of the scattering of protons on the same nuclei, the main patterns of behavior of the general characteristics of nuclei, such as the root mean square radius (RMS), diffuseness, and the isotopic and isotonic shifts of parameters, were determined. For the C2048a nucleus, the radial dependence of the nucleon density distribution on the center of the nucleus, as well as the ratio of proton to neutron densities, have been studied. Changes in the distribution of densities of protons and neutrons with the addition of two neutrons to nucleus C2452r as well as changes in the distributions of densities of protons and neutrons when two neutrons are replaced by protons in isobars F2654e−C2454r have been studied. The results of changes in the distribution of densities of protons and neutrons were justified on the basis of the shell model of the nucleus, using characteristic parameters determined for these nuclei from elastic electron scattering. A joint analysis of experimental work on the elastic scattering of electrons and protons on spherical nuclei leads to the conclusion that the distribution patterns of protons and neutrons differ from each other. In particular, this follows from calculations of the RMS of proton, neutron and nucleon distributions.