Allowed $\beta$-decay spectrum with numerical electron wave functions

TL;DR

This paper evaluates the accuracy of numerical electron wave functions in calculating allowed beta-decay spectra, highlighting errors in traditional approximation methods and proposing improved estimation techniques using nuclear data.

Contribution

It introduces a method to accurately compute beta-decay spectra using numerical wave functions and assesses errors in conventional approximations.

Findings

Fermi Function approximations can cause significant errors in spectra simulation.

Numerical wave functions provide more precise beta-decay spectra calculations.

Errors vary with electric charge distributions and nuclear models.

Abstract

Using numerical electron wave functions and state-of-the-art nuclear many-body methods, I evaluate the $\beta$-decay spectra for typical decay channels of spherical nuclei. I check errors brought by various approximations used for deriving the analytical shape factors (the so-called Fermi Function) of allowed decay. I estimate the errors brought by different electric charge distributions and give a way of estimation of $\beta$-spectra with available decay data of specific nuclei. I found that the traditional ways of approximating the electron wave functions by Fermi Function could be a very severe source of error for spectra simulation.