Determination of energy spectra by using proper quantization rule of woods-saxon potential

Abstract

In this study, the energy spectra of Schrodinger equation for non-zero l values considering Woods Saxon potential (WSP) iscalculated using proper quantization rule, then the binding energies (BE) of random light nuclei is obtained and the optimizedpotential parameters such as potential depth (V0) and surface thickness (a) are found. In order to calculate the energy levels of thenuclei with WSP, the PQR method was used, which has not been considered before. In quantum mechanics, the exact solution ofenergy systems, momentum, and quantum states can be found using the proper quantization rule(PQR) method.Using the Matlabcalculation program, we have achieved numerical values of the energy spectrum for random light nuclei and compared the resultwith the experimental Nuclear Data Center (NDC) values. In addition, we found potential depth and surface thickness for four lightnuclei. Correlations between the light nuclei show the facts about the nuclear structure characteristics, origin, and energies of thesenuclei. Pearson’s correlation coefficient is accepted as the most common correlation coefficient. According to the values of Pearsoncorrelation coefficients, it is observed that there is a significant positive correlation between the nucleons examined. Finally, weplot the E-V0-a diagrams for those values to optimize and provide the appropriate coefficients. It is shown that there is a goodagreement between the results of this work and experimental values.