Isospin dependence of ground state properties of A = 20 isobars

The ground state nucleon (neutron and proton) distributions for A = 20 isobars (Z = 6-12) are investigated. For this purpose, the relativistic mean field equations are solved in the coordinate space and also by using the conventional basis expansion method. The pairing is treated in the simple constant gap approximation and also self consistently through the Bogoliubov transformation employing the realistic Gogny D1S interaction as well as the zero range density dependent effective interaction. The comparative study of the results thus obtained indicates the level and the extent of differences in the physical observables like binding energies, sizes, densities, etc. of these nuclei, arising due to the use of these different variants of solving the RMF/RHB equations. Though the results are qualitatively similar, the deviations do appear at a finer level, especially for large T_z (²⁰O and ²⁰N). The calculations also reveal mirror symmetry about T _z = 0 for all physical observables, which is in accordance with the experiment. The calculated nucleon densities are compared with those obtained by using a semi-phenomenological model that incorporates correctly the asymptotic behavior. The reaction cross-sections with these A = 20 isobars as projectiles incident on a ¹²C target at 950 A MeV incident energy, calculated within the Glauber model using the RMF/RHB and model densities agree well with the experiment.