Unitary Scheme Model Calculations of the Ground- and Excited-State Characteristics of 3H and 4He

TL;DR

This paper employs group-theoretical methods and the unitary scheme model to calculate ground and excited state properties of 3H and 4He nuclei, including energies, wave functions, radii, and transition cross sections.

Contribution

It introduces a comprehensive calculation framework using basis functions of the unitary scheme model for both even and odd parity states of these nuclei, incorporating modern two- and three-nucleon interactions.

Findings

Calculated energies, wave functions, and radii for 3H and 4He.

Analyzed convergence of nuclear characteristics with basis size.

Provided detailed transition cross sections for gamma absorption.

Abstract

The ground and excited states of the 3H and 4He nuclei are studied in the framework of group-theoretical methods. Basis functions of the unitary scheme model corresponding to even numbers of quanta of excitation in the range from zero to twenty are constructed for the even-parity states of these two nuclei, and bases from one to nineteen are constructed for the odd-parity states of the 4He nucleus. The ground-state and first-excited-state energies and wave functions, the ground S-, P- and D-state probabilities, the root-mean-square radius and the magnetic dipole moment of Triton are calculated. Furthermore, for the 4He nucleus, the spectrum and the wave functions, the ground S-, P- and D-state probabilities, the root-mean-square radius and the total integral cross section of the dipole electric transition accompanying the photoabsorption of gamma quanta by this nucleus are calculated. The GPT and AV8' two-body interactions and the Urbana nine three-nucleon interaction are used in these investigations. Moreover, the convergence of the calculations is examined by incrementally extrapolating the nuclear characteristics calculated for N less than or equal to twenty to N equals thirty.