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\begin{document}

\title{Information entropies calculation for the 1s\textsuperscript{2}-state of
helium-like ions}



\author[1]{Ibraheem Nasser}%
\author[1]{Mostafa Zeama}%
\author[2]{Afaf Abdel-Hady}%
\affil[1]{King Fahd University of Petroleum \& Minerals}%
\affil[2]{ Egyptian Chinese University, Cairo, Egypt}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\begin{abstract}
This work present analytical 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 one-electron charge density of entangled
two-parameter wave function. On one hand, the results that are presented
for fifteen members in the helium iso-electronic 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 informatic expressions has been studied for both potentials.
Detailed computational and numerical values and characteristics of these
quantities are reported here for the first time. New inequality has been
proposed with Fisher's total value to measure the correlation of two
electrons.%
\end{abstract}%



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