Quantum Corrections to the Semiclassical Quantization of the SU(3) Shell Model

TL;DR

This paper develops a semi-quantum approach with quantum corrections for the SU(3) shell model, providing analytical energy level formulas and testing their numerical accuracy against traditional semiclassical methods.

Contribution

It introduces a novel semi-quantal formula with quantum corrections for the SU(3) shell model energy levels using canonical perturbation theory and Einstein--Brillowin--Keller quantization.

Findings

Quantum corrections improve energy level accuracy.

Analytical formulas match numerical results closely.

Method enhances semiclassical quantization precision.

Abstract

We apply the canonical perturbation theory to the semi--quantal hamiltonian of the SU(3) shell model. Then, we use the Einstein--Brillowin--Keller quantization rule to obtain an analytical semi--quantal formula for the energy levels, which is the usual semi--classical one plus quantum corrections. Finally, a test on the numerical accuracy of the semiclassical approximation and of its quantum corrections is performed.