Discontinuity of Shannon information entropy for two-electron atoms

Atomic Shannon information entropies are computed using Hyllerass-type basis functions for the helium isoelectronic series. As one varies the nuclear charge Z for the two-electron atoms, finite size scaling analysis shows that the system exhibits a critical point of the ground state energy at λc=1/Zc=1.0971+/-0.0005 with a critical exponent α=1, E(λ)∼(λ-λc)α. At the critical point, the ground state energy becomes degenerate with the hydrogenic threshold. The Shannon information entropy develops a step-like discontinuity at λc. Further analysis indicates that the entropy as a function of λ is proportional to the first derivative of the energy with respect to λ. The critical exponent for the entropy αs=0, S(λ)∼(λ-λc)αs