  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.
