Shannon Information Entropy in Position Space for Two-Electron Atomic Systems

TL;DR

This paper explores the use of Shannon entropy in position space to analyze electron correlation effects in two-electron atomic systems, extending previous entropic measures like linear and von Neumann entropy.

Contribution

It introduces Shannon entropy as a new entropic measure for quantum correlation analysis in two-electron systems, including systems near the ionization threshold.

Findings

Shannon entropy varies with nuclear charge and electron correlation.

Results include systems like positronium negative ion and hydrogen negative ion.

Provides insights into correlation effects in systems close to ionization threshold.

Abstract

Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited states in helium-like systems. In this work, we adopt another entropic measure, Shannon entropy, to probe the nature of correlation effects. Besides the results of the Shannon entropy in coordinate space for the singlet ground states of helium-like systems including positronium negative ion, hydrogen negative ion, helium atom, and lithium positive ion, we also show results for systems with nucleus charge around the ionization threshold.