Investigation of the Ground and Excited States of the 3H and 4He Nuclei by Using the Methods of Group Theory

TL;DR

This paper employs group theory and shell model methods to analyze the ground and excited states of triton and helium nuclei, providing detailed wave functions, energies, and physical properties with convergence analysis.

Contribution

It introduces a group theory-based approach combined with shell model calculations to study nuclear states, extending the basis to N=30 for improved accuracy.

Findings

Calculated energies and wave functions for triton and helium nuclei.

Determined probabilities of S, P, D states and physical properties like radius and magnetic moment.

Demonstrated convergence of results with extended basis size.

Abstract

The method of group theory is applied to investigate the ground and the excited states of the triton and helium nuclei by using the translation invariant shell model with basis functions corresponding to even number of quanta of excitations in the range 0 less than or equal to N less than or equal to 20. Accordingly, the ground and first excited state wave functions and energies, the S, P and D state probabilities, the root mean square radius and the magnetic dipole moment of triton have been investigated. Also, the energies and wave functions of the ground and the even parity excited states and the root mean square radius of helium have been investigated. Two residual two body interactions together with two three nucleon interactions have been used in the calculations. Moreover, the convergence of calculations has been examined by extrapolating the results with N less than or equals to 20 step by step to reach N equals to 30 for the two nuclei.