Nuclear $\beta$ spectrum from projected shell model (I): allowed one-to-one transition

TL;DR

This paper introduces a projected shell model (PSM) approach to calculate nuclear $eta$ spectra, emphasizing the importance of nuclear many-body correlations and providing a new tool for high-precision spectral analysis.

Contribution

The paper develops a PSM-based method to compute reduced one-body transition densities for nuclear $eta$ decays, enhancing the accuracy of spectral predictions.

Findings

Calculated $eta$ spectra deviate up to 10% from simple models when using experimental energies.

Spectral sensitivity depends on the accuracy of calculated level energies.

The method can be extended to study forbidden transitions and nuclear resonances.

Abstract

Nuclear $\beta$ spectrum and the corresponding (anti-)neutrino spectrum play important roles in many aspects of nuclear astrophysics, particle physics, nuclear industry and nuclear data. In this work we propose a projected shell model (PSM) to calculate the level energies as well as the reduced one-body transition density (ROBTD) by the Pfaffian algorithm for nuclear $\beta$ decays. The calculated level energies and ROBTD are inputed to the Beta Spectrum Generator (BSG) code to study the high precision $\beta$ spectrum of allowed one-to-one transitions. When experimental level energies are adopted, the calculated $\beta$ spectrum by ROBTD of the PSM deviates from the one by the extreme simple particle evaluation of the BSG by up to $10\%$, reflecting the importance of nuclear many-body correlations. When calculated level energies are adopted, the calculated $\beta$ spectrum shows sensitive dependence on the reliability of calculated level energies. The developed method for ROBTD by the PSM will also be useful for study of the first-forbidden transitions, the isovector spin monopole resonance etc. in a straightforward way.