# Theoretical analysis of the electron bridge process in $^{229}$Th$^{3+}$

## TL;DR

This paper provides a theoretical analysis of the electron bridge process in triply ionized thorium, quantifying how electron excitation can enhance nuclear decay, with detailed calculations including continuum effects and diagram interference.

## Contribution

It introduces a comprehensive theoretical framework for electron bridge enhancement in $^{229}$Th$^{3+}$, including continuum contributions and interference effects, using a B-spline pseudo basis approach.

## Key findings

- Continuum contributions slightly increase the enhancement.
- Interference between Feynman diagrams significantly affects the enhancement.
- The approach accurately models the electron propagator including positive and negative continua.

## Abstract

We investigate the deexcitation of the $^{229}$Th nucleus via the excitation of an electron. Detailed calculations are performed for the enhancement of the nuclear decay width due to this so called electron bridge (EB) compared to the direct photoemission from the nucleus. The results are obtianed for triply ionized thorium by using a B-spline pseudo basis approach to solve the Dirac equation for a local $x_\alpha$ potential. This approach allows for an approximation of the full electron propagator including the positive and negative continuum. We show that the contribution of continua slightly increases the enhancement compared to a propagator calculated by a direct summation over bound states. Moreover we put special emphasis on the interference between the direct and exchange Feynman diagrams that can have a strong influence on the enhancement.