Energy and lifetime of resonant states with real basis sets

TL;DR

This paper introduces a new formula for calculating the lifetime of resonant states using real basis-set expansion techniques, avoiding the need for density of states estimation.

Contribution

It presents a novel probabilistic approach to determine resonance lifetimes with real basis sets, simplifying previous methods.

Findings

Accurate calculation of $s$ and $p$ resonant-state energies.

Effective estimation of resonance lifetimes without density of states.

Method validated through illustrative examples.

Abstract

Using a probabilistic interpretation of resonant states, we propose a formula useful to calculate the lifetime of a resonance using square-integrable real basis-set expansion techniques. Our approach does not require an estimation of the density of states. The method is illustrated with calculations of $s$ and $p$ resonant-state energies and lifetimes.