Data-adaptive unfolding of nuclear excitation spectra: a time-series approach

Abstract

A common problem in the statistical characterization of the excitation spectrum of quantum systems is the adequate separation of global system-dependent properties from the local fluctuations that are universal. In this process, called unfolding, the functional form to describe the global behaviour is often imposed externally on the data and can introduce arbitrarities in the statistical results. In this contribution, we show that a quantum excitation spectrum can readily be interpreted as a time series, before any previous unfolding. An advantage of the time-series approach is that specialized methods such as Singular Spectrum Analysis (SSA) can be used to perform the unfolding procedure in a data-adaptive way. We will show how SSA separates the components that describe the global properties from the components that describe the local fluctuations. The partial variances, associated with the fluctuations, follow a definite power law that distinguishes between soft and rigid excitation spectra. The data-adaptive fluctuation and trend components can be used to reconstruct customary fluctuation measures without ambiguities or artifacts introduced by an arbitrary unfolding, and also define the global level density of the excitation spectrum. The method is applied to nuclear shell-model calculations for 48Ca, using a realistic force and Two-Body Random Ensemble (TBRE) interactions. We show that the statistical results are very robust against a variation in the parameters of the SSA method.