Resonance enhancement of neutrinoless double electron capture

TL;DR

This paper explores the resonant enhancement of neutrinoless double electron capture in nearly degenerate atoms, proposing a framework for detecting this rare process through electromagnetic de-excitation, and predicts potential half-lives around 10^22 years.

Contribution

It introduces a theoretical formalism for resonant neutrinoless double electron capture involving atomic oscillations and mass degeneracy, highlighting conditions for experimental detection.

Findings

Resonant enhancement can significantly increase transition probabilities.

Predicted half-lives could be as low as 10^22 years for certain candidates.

Precision atomic mass measurements are crucial for accurate predictions.

Abstract

The process of neutrinoless double electron capture ($0\nu$ECEC) is revisited for those cases where the two participating atoms are nearly degenerate in mass. The theoretical framework is the formalism of an oscillation of two atoms with different total lepton number (and parity), one of which can be in an excited state so that mass degeneracy is realized. In such a case and assuming light Majorana neutrinos, the two atoms will be in a mixed configuration with respect to the weak interaction. A resonant enhancement of transitions between such pairs of atoms will occur, which could be detected by the subsequent electromagnetic de-excitation of the excited state of the daughter atom and nucleus. Available data of atomic masses, as well as nuclear and atomic excitations are used to select the most likely candidates for such resonant $0\nu$ECEC transitions. Assuming an effective mass for the Majorana neutrino of 1 eV, some half-lives are predicted to be as low as $10^{22}$ years in the unitary limit. It is argued that, in order to obtain more accurate predictions for the $0\nu$ECEC half-lives, precision mass measurements of the atoms involved are necessary, which can readily be accomplished by today's high precision Penning traps. Further advancements also require a better understanding of high-lying excited states of the final nuclei (i.e. excitation energy, angular momentum and parity) and the calculation of the nuclear matrix elements.