Final-State Spectrum of $^3$He after $\beta^-$ Decay of Tritium Anions T$^-$

TL;DR

This study calculates the final electronic state distribution of helium-3 after beta decay of tritium anions, using advanced quantum methods to understand the decay process and continuum states.

Contribution

It introduces a full configuration-interaction approach combined with the sudden approximation to accurately compute the spectrum and continuum transition probabilities.

Findings

Transition probability converges at high energies to an analytical model.

Wavefunctions obtained via full configuration-interaction method.

Continuum states are effectively described using complex scaling.

Abstract

The final-state spectrum of $\beta$ decaying tritium anions T$^-$ was calculated. The wavefunctions describing the initial T$^-$ ground state and the final $^3$He states were obtained by the full configuration-interaction method. The transition probability was calculated within the sudden approximation. The transition probability into the electronic continuum is extracted from the complex-scaled resolvent and is shown to converge for very high-energies to an approximate analytical model probability distribution.