Unreliability of the autocorrelation function as evidence for Ericson fluctuations

Abstract

In a recent combined experimental and theoretical paper for the total photoionization cross section of helium up to the single-ionization threshold ${I}_{13}$, we had shown that Ericson fluctuations were absent, although the Ericson regime had already been reached. In the present paper, we study the autocorrelation functions of the total photoionization cross section below ${I}_{9}\text{--}{I}_{13}$ and find that these are essentially identical to that of an artificial spectrum with Ericson fluctuations. Consequently, we have to conclude that the autocorrelation function alone---although its Lorentzian-like shape for small displacements $\ensuremath{\varepsilon}$ has been used by some authors---is a necessary but is not a sufficient proof for the existence of Ericson fluctuations. In the present case of He, the absence of Ericson fluctuations is a consequence of a strong hierarchy between the transitions belonging to different series with approximate quantum numbers that still exist in this region; this causes the spectra to be dominated by the principal series.