Abstract
This work presents analytical and numerical results for the position-
and momentum-space information entropies, of the
1s2-state of helium-like ions, using different
interaction potentials. The potentials that we used are the Yukawa
potential (YP), and the exponential-cosine-screened Coulomb potential
(ECSCP). The investigated studies allow us to relate the position-space
information with the momentum-space information of Shannon and Fisher,
as well as Shannon entropy power, and the Fisher-Shannon information
product, through different famous relations. The calculation is done
using the one-electron charge density of entangled two-parameter wave
function. On one hand, the results that are presented for ten members in
the helium isoelectronic sequence demonstrate with precision the effect
of correlation on bare charge distributions. On the other hand, it leads
to some very important results for both the correlated and uncorrelated
values of the informatic entropies. Analytical formula for the
momentum-space information entropies are given. The effect of the
nuclear charge and the screening parameter on the information
expressions has been studied for both potentials. Detailed computational
and numerical values and characteristics of these information
quantities, as a function of the screening parameter, are reported here
for the first time. New inequality has been proposed with Fisher’s total
value to measure the correlation of two electrons.