Analytic inhomogeneous electron liquid and its density for model spin-compensated two-electron atomic ions with Coulomb confinement: an exact nonrelativistic Hamiltonian

Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

“…Second, it is possible to probe the correlation effect by examining the behavior of Shannon entropies under different confinement conditions [41]. Third, Amovilli, Howard and March have systematically investigated the electron density expression for He-like ion sequence with a modified interparticle interaction [42][43][44]. Therefore, it is possible to examine the behavior of Shannon entropies for these systems.…”

Approaching the s-wave model ground state energy of He-like atomic ions: results from a model Hamiltonian

“…comes from Amovilli et al [3] source paper. The functional H is rather simple and it has an absolute minimum for Z greater than a critical value smaller than 1.…”

“…Amovilli, Howard and March (AHM) [3] proposed a new model Hamiltonian by adding to the Temkin s-wave Hamiltonian an electron-electron contact type interaction of the form δ(r 1 − r 2 ). The resulting problem is now analytically solvable.…”

Recent progress in low-order density matrix theory of inhomogeneous electron liquids by exact solution of two- and four-electron model atoms

“…Here, we stress the potential of the two-electron Hamiltonian for a model atomic ion with V ext (r) = −Ze 2 /r, but with an interaction modified from u(r 12 ) = e 2 /r 12 . While this involves the angle θ between vectors r 1 and r 2 , Amovilli, Howard, and March [21] have proposed u involving only scalar r 1 , r 2 , and no angle θ. The first part of the two term u(r 1 , r 2 ) form is due to Temkin [22], while the second involves the addition of the δ-function δ(r 1 − r 2 ).…”