Searching Ground State Properties of 22C, 23Al, and 27P Nuclei Using Whittaker’s Wave Functions

Abstract

In current work, the Whittaker's wave functions were utilized to search the nuclear ground charge distributions, Coulomb form factors and differential cross sections for some stable nuclei (¹²C, ²⁷Al, and ³¹P), besides the density distributions were computed corresponding to them (²²C, ²³Al, and ²⁷P) as well. The Whittaker’s parameters were constrained to produce the available experimental radii. Furthermore, the Whittaker's basis was linked to harmonic-oscillator basis via boundary condition at a specific matching point. For proton-rich nuclei (²²C, ²³Al, and ²⁷P Nuclei) and stable ¹²C, the nuclear shell model in pure configuration was opted. For exotic ²²C, ²³Al and ²⁷P nuclei, the Whittaker’s basis was applied exclusively to the final exotic valence proton, unlike the stable ¹²C, ²⁷Al and ³¹P which the Whittaker’s basis was applied to the last valence proton and neutron. For ²⁷Al and ³¹P, the mixing configuration was employed using sd-shell Bonn A interaction (SDBA) in the sd-shell. In addition to C0 component for ³¹P,  the spin for ²⁷Al is ; there is a C0+C2+C4 component in the empirical Coulomb form factor. The C2 and C4 components were accounted for by applying core-polarization theory within the framework of the Tassie and Bohr-Mottelson models. The model-space contributions to C2+C4 components was calculated using SDBA interaction in the sd-shell. Such approach resulted in very good agreement with experimental measurements.