Inelastic Electron-Scattering Form Factors in 19F: A Shell-Model Investigation of Positive and Negative Parities

Abstract

We present a comprehensive shell-model study of 19F focusing on inelastic longitudinal and transverse electron-scattering form factors, excitation energies, and electromagnetic transition strengths for both positive- and negative-parity states. The calculations are carried out within the zbm model space using the ZBMI effective interaction, providing a consistent and unified description of nuclear structure and configuration mixing for both parities. The novelty of this work lies in performing a controlled and systematic comparison of different single-particle radial wave functions-Skyrme (Sk29), Woods-Saxon (WS3), and harmonic oscillator (HT)-within the same shell-model framework. This approach allows isolating the role of radial structure in determining electromagnetic observables without introducing additional model-dependent uncertainties. The electromagnetic matrix elements are calculated using radial wave functions generated from different mean-field potentials, enabling a detailed investigation of their impact on the calculated observables. In particular, the sensitivity of form factors to variations in radial behavior is examined over a wide range of momentum transfer. The calculated excitation energies and transition strengths show reasonable agreement with experimental data, confirming the reliability of the adopted interaction and model space. The results reveal a pronounced dependence of inelastic electron-scattering form factors on the choice of radial potential, especially at intermediate and high momentum transfer, where differences in radial tails and nodal structure significantly affect both the magnitude and diffraction patterns. The Skyrme-based radial wave functions provide a more consistent overall description compared to Woods-Saxon and harmonic oscillator potentials. All calculations are performed using the NuShellX@MSU code within a unified computational framework to ensure consistency, reproducibility, and a direct comparison between different potentials and parities.