Fisher information and Shannon entropy calculations for two-electron systems

Fisher information is calculated for the ground state of He-isoelectronic series, in position ((r) over right arrow) space. The results are given and discussed as a function of the nuclear charge (Z) and the screening parameter (lambda) in the case study of Yukawa potential. Simple and explicit one-, two-, and three-correlated terms of Hylleraas wave function are used to focus on extracting the most characteristic physical features of the results. The numerical values of Fisher information are given in 1-and 2-electron charge densities, and their ratio of 2-to 1-electron densities results are defined and analyzed. To enable a comparison with others, the Fisher-Shannon information products, which measure the electron-electron correlation strength, are calculated in 1-electron density. The calculations of Fisher information, the ratio, and the Shannon-information products for two-electron systems in the presence of Yukawa potential are carried out for the first time in this study.