Elastic and inelastic electron-nucleus scattering form factors of some light nuclei:Na23,Mg25,Al27, andCa41

Abstract

Nuclear structure (energy levels, elastic and inelastic electron-nucleus scattering, and transition probability) of $^{23}\mathrm{Na}$, $^{25}\mathrm{Mg}$, $^{27}\mathrm{Al}$, and $^{41}\mathrm{Ca}$ nuclei have been studied using shell-model calculations. A set of two-body interactions are used in this paper. The universal $sd$ of the Wildenthal interaction in the proton-neutron formalism, universal $sd$-shell interaction A, universal $sd$-shell interaction B, and GXFP1 interaction for the $fp$ shell is used with the nucleon-nucleon realistic interaction Michigan three-range Yakawa as a two-body interaction for core-polarization calculations. Two shell-model codes, cpm3y and nushell for Windows, have been used to calculate the results. The wave functions of radial single-particle matrix elements have been calculated with harmonic-oscillator and Woods-Saxon potentials. The level schemes are compared with the experimental data up to 5.776, 5.251, and 4.51 MeV for $^{23}\mathrm{Na}$, $^{25}\mathrm{Mg}$, and $^{27}\mathrm{Mg}$, respectively. Very good agreements are obtained for all nuclei in this study. Results from electron scattering form-factor calculations have shown that the core-polarization effects are essential to obtain a reasonable description of the data with no adjustable parameters.