Quantum information-theoretical analysis on the two-photon transitions in hydrogen isoelectronic ions under plasma confinement

Quantum information-theoretical measure in terms of Shannon and Fisher entropy in conjugate position and momentum spaces provides important information about the localization/delocalization patterns of the inter-atomic charge density under arbitrary confining environments. In this article, we have attempted to employ such measures to the ground, excited, and the virtual states arising out of two-photon transitions (\(1s\rightarrow nl\); \(n=2-4\), \(l=0,2\)) of weakly coupled classical plasma embedded H iso-electronic ions (nuclear charge, \(Z = 2 - 5\)). The wavefunction for the said states is essentially a linear combination of the Slater-type orbitals, the coefficients of which are generated from a fourth-order time-dependent perturbation theory within the variational framework. A complementary nature has been noted in the Shannon and Fisher measures versus the plasma screening parameter plot in the conjugate spaces. A novel scaling law has been proposed to replicate the variation of the Shannon and Fisher entropy w.r.t. Z for the virtual as well as real 2p states of free and plasma confined ions.