Analysis of Compton profile through information theory in H-like atoms inside impenetrable sphere

TL;DR

This paper constructs and analyzes the Compton profile of a hydrogen atom confined inside an impenetrable sphere, using information theory measures to characterize the effects of confinement on the atom's momentum distribution.

Contribution

It introduces a novel analytical and numerical framework for studying the Compton profile of confined H-like atoms using information theory measures.

Findings

Confinement broadens the Compton profile.

Information measures reveal how confinement affects energy dissipation.

Opposite trends in free and confined systems for certain parameters.

Abstract

Confinement of atoms inside various cavities has been studied for nearly eight decades. However, the Compton profile for such systems has not yet been investigated. Here we construct the Compton profile (CP) for a H atom radially confined inside a \emph{hard} spherical enclosure, as well as in \emph{free condition}. Some exact analytical relations for the CP's of circular or nodeless states of free atom is presented. By means of a scaling idea, this has been further extended to the study of an H-like atom trapped inside an impenetrable cavity. The accuracy of these constructed CP has been confirmed by computing various momentum moments. Apart from that, several information theoretical measures, like Shannon entropy ($S$) and Onicescu energy ($E$) have been exploited to characterize these profiles. Exact closed form expressions are derived for $S$ and $E$ using the ground state CP in free H-like atoms. A detailed study reveals that, increase in confinement inhibits the rate of dissipation of kinetic energy. At a fixed $\ell$, this rate diminishes with rise in $n$. However, at a certain $n$, this rate accelerates with progress in $\ell$. A similar analysis on the respective free counterpart displays an exactly opposite trend as that in confined system. However, in both free and confined environments, CP generally gets broadened with rise in $Z$. Representative calculations are done numerically for low-lying states of the confined systems, taking two forms of position-space wave functions: (a) exact (b) highly accurate eigenfunctions through a generalized pseudospectral method. In essence, CPs are reported for confined H atom (and isoelectronic series) and investigated adopting an information-theoretic framework.