Shannon information entropy sum of the confined hydrogenic atom under the influence of an electric field

In this work, we present the effects of an external electric field on the Shannon entropy sum of a spherically confined hydrogenic atom. The confinement considered is of the impenetrable hard wall type. The electric field modifies the spectrum of the confined hydrogenic system, which results in avoided crossings among the energy levels of the system, with strong competition between the Coulombic and hard wall potential. The results presented indicate that the electric field is a strong candidate to modify information theoretic measures. In addition, we examine the effects of field strength, nuclear charge and hard walls on the minima/maxima structure of the entropic sum. Shannon entropy sum, $$S_t$$ , versus confinement radius, $$R_c$$ , of the 2p level of confined hydrogenic atoms, with field strength $$\epsilon = 0$$ (black), $$\epsilon = 0.001$$ (red), $$\epsilon = 0.01$$ (green) and $$\epsilon = 0.05$$ (blue). The intensity of the field modifies the structure in $$S_t$$ .