The adiabatic expansion and Wannier's ionization threshold law

Abstract

A new formal derivation of Wannier's ionization threshold law is given within the framework of the hyperspherical adiabatic expansion method. A standard linearization of the potential energy surface near the unstable configuration of the electron pair is performed to derive the adiabatic potential energy and the interchannel coupling matrix. The Bogoliubov transformation is exploited to solve the coupled-channel equations to order 1/R32/. The derivation gives an insight to the nature of the interchannel couplings, and allows one to identify essential elements necessary for numerically reproducing the cross section near the ionization threshold. The number of adiabatic channels needed to obtain the Wannier exponent up to three significant figures is found to be two.