The decay widths, the decay constants, and the branching fractions of a resonant state

TL;DR

This paper develops a theoretical framework for calculating decay widths, decay constants, and branching fractions of resonant states, linking these quantities to measurable experimental data.

Contribution

It introduces a comprehensive formalism for decay properties of resonant states, including differential and partial decay widths, and relates decay constants to observable quantities.

Findings

Derived expressions for decay widths resembling Golden Rule formulas

Defined dimensionless decay constants and related them to experimental measurements

Provided a unified approach for analyzing decay processes of resonant states

Abstract

We introduce the differential and the total decay widths of a resonant (Gamow) state decaying into a continuum of stable states. When the resonance has several decay modes, we introduce the corresponding partial decay widths and branching fractions. In the approximation that the resonance is sharp, the expressions for the differential, partial and total decay widths of a resonant state bear a close resemblance with the Golden Rule. In such approximation, the branching fractions of a resonant state are the same as the standard branching fractions obtained by way of the Golden Rule. We also introduce dimensionless decay constants along with their associated differential decay constants, and we express experimentally measurable quantities such as the branching fractions and the energy distributions of decay events in terms of those dimensionless decay constants.