Davidson bases as an appropriate base for the Shell model \\\large 1p- and 1h-nuclei

This study endeavors to develop an improved set of basis functions for nuclear shell-model calculations. The shell model, a well-established approach to understanding nuclear structure, typically employs the harmonic oscillator potential within the mean-field approximation. Given the extensive validation and consistency of harmonic oscillator results with experimental data, we propose a modification by incorporating a centrifugal term that converges toward the Davidson potential. This potential has been extensively studied, and we aim to extract relevant experimental data for the simplest cases in the shell model, namely one-particle and one-hole nuclei. A comprehensive comparison between the Davidson-based results and the harmonic oscillator calculations is presented to demonstrate the effectiveness of the new basis functions.