# Predicting Atomic Decay Rates Using an Informational-Entropic Approach

## TL;DR

This paper introduces a novel informational-entropic measure called configurational entropy (CE) to predict spontaneous decay rates of hydrogen atom states, achieving high accuracy without traditional calculations.

## Contribution

The study demonstrates that configurational entropy can effectively predict atomic decay rates, providing a new approach that bypasses traditional dipole matrix element computations.

## Key findings

- CE correlates with decay rates across quantum states
- The method predicts decay rates with less than 3.7% error up to n=20
- A scaling law links CE to n-averaged decay rates

## Abstract

We show that a newly proposed Shannon-like entropic measure of shape complexity applicable to spatially-localized or periodic mathematical functions known as configurational entropy (CE) can be used as a predictor of spontaneous decay rates for one-electron atoms. The CE is constructed from the Fourier transform of the atomic probability density. For the hydrogen atom with degenerate states labeled with the principal quantum number n, we obtain a scaling law relating the n-averaged decay rates to the respective CE. The scaling law allows us to predict the n-averaged decay rate without relying on the traditional computation of dipole matrix elements. We tested the predictive power of our approach up to n=20, obtaining an accuracy better than 3.7% within our numerical precision, as compared to spontaneous decay tables listed in the literature.