Wave functions and two-electron probability distributions of the Hooke's-law atom and helium

Darragh P. O'Neill, Peter M. W. Gill
2003 Physical Review A. Atomic, Molecular, and Optical Physics  
The Hooke's-law atom ͑hookium͒ provides an exactly soluble model for a two-electron atom in which the nuclear-electron Coulombic attraction has been replaced by a harmonic one. Starting from the known exact position-space wave function for the ground state of hookium, we present the momentum-space wave function. We also look at the intracules, two-electron probability distributions, for hookium in position, momentum, and phase space. These are compared with the Hartree-Fock results and the
more » ... esults and the Coulomb holes ͑the difference between the exact and Hartree-Fock intracules͒ in position, momentum, and phase space are examined. We then compare these results with analogous results for the ground state of helium using a simple, explicitly correlated wave function.
doi:10.1103/physreva.68.022505 fatcat:7byyfcrxz5dyvkk74n4avnoepa