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Shannon entropy in position ($S_{\rvec}$) and momentum ($S_{\pvec}$) spaces,along with their sum ($S_t$) are presented for unit-normalized densities of He,Li$^+$ and Be$^{2+}$ ions, spatially confined at the center of an impenetrablespherical enclosure defined by a radius $r_c$. Both ground as well as someselected low-lying singly excited states, \emph{viz.,} 1sns (n $=$ 2-4) $^3$S,1snp (n $=$ 2-3) $^3$P, 1s3d $^3$D are considered within a density functionalmethodology that makes use of a work-function-based exchange potential alongwith two correlation potentials (local Wigner-type parametrized functional aswell as the more involved non-linear gradient- and Laplacian-dependentLee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved usingan optimal spatial discretization scheme via the generalized pseudospectral(GPS) method. A detailed systematic analysis of the confined system (relativeto corresponding free system) has been performed for these quantities withrespect to $r_c$ in tabular and graphical forms, \emph{with and without}electron correlation. Due to compression, the pattern of entropy inaforementioned states gets characterized by various crossovers at intermediateand lower $r_c$ regions. The impact of electron correlation is more pronouncedin weaker confinement limit, and appears to decay with rise in confinementstrength. The exchange-only results are quite good to provide a decentqualitative discussion. The lower-bounds provided by entropic uncertaintyrelation holds good in all cases. Several other new interesting features areobserved.

Shannon entropy in confined He-like ions within a density functional formalism