Fisher information of two-electron systems

Abstract

We present a theoretical model to compute numbers for position- and momentum-space Fisher information ( $ I_{\rho}$ and $ I_{\gamma}$ of correlated two-electron systems. The numbers for the first five members of the helium iso-electronic sequence indicate that i) values of $ I_{\rho}$ increase with the atomic number Z while those of $ I_{\gamma}$ decrease, and, ii) the effect of correlation reduces (increases) the bare values of $ I_{\rho}(I_{\gamma})$ . The observed behavior of Fisher information in i) and ii) is opposite to that exhibited by Shannon information entropy, presumably because in describing disorder in the probability distribution, the former is convex while the latter is concave. The information measures of Fisher and of Shannon have also been found to share some common properties, the origin of which is purely physical rather than statistical.