Double-bound equivalent of the three-body Coulomb double-continuum wave function
L. U. ANCARANI AND G. GASANEO
PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS
American Physical Society
Año: 2007 vol. 75 p. 1 - 13
In cross-section calculations of electron or photon double ionization processes of two-electron atoms, it isdesirable to have a symmetric description of initial and final states. In this contribution, we search the doublybound analog, for S states, of the well-known and widely used three-body Coulomb C3 double-continuumwave function. This is performed with two alternative approaches: through an analytic continuation of the C3continuum and through a C3 approach of the Hylleraas equation for S bound states. The double-boundanalog consists of the product of two Coulomb bound states one for each electron-nucleus interactionmultiplied by a Coulomb distortion factor which describes the electron-electron correlation. Our result differsfrom Pluvinages wave function which is commonly misbelieved to be the bound counterpart of the C3 doublecontinuum. With a rigorous treatment of the analytic continuation of the distortion factor, the double-boundequivalent of the C3 model is also found. Though the purpose is not to obtain good two-electron bound states,the found bound wave functions are tested, in the case of helium, through various local and mean quantitieswhich probe different regions of the configuration space, in particular those close to the two-particle coalescencepoints.