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.
ASJC Scopus subject areas
- Physical and Theoretical Chemistry
- Atomic and Molecular Physics, and Optics