We consider a non-standard application of the Wannier model. A physical example is the single ionization of a hydrogenic beryllium ion with a fully stripped beryllium ion, where the ratio of the charge of the third particle to the charges of the escaping particles is 1/4; we investigate the single ionization by an electron of an atom comprising an electron and a nucleus of charge 1/4. An infinite exponent is obtained suggesting that this process is not tractable within the Wannier model. A modified version of Crothers' uniform semiclassical wavefunction for the outgoing particles has been adopted, since the Wannier exponents and are infinite for an effective charge of Z = 1/4. We use Bessel functions to describe the Peterkop functions u and u and derive a new turning point ?. Since u is well behaved at infinity, there exists only the singularity in u at infinity, thus we employ a one- (rather than two-) dimensional change of dependent variable, ensuring that a uniform solution is obtained that avoids semiclassical breakdown on the Wannier ridge. The regularized final-state asymptotic wavefunction is employed, along with a continuum-distorted-wave approximation for the initial-state wavefunction to obtain total cross sections on an absolute scale. © 2006 IOP Publishing Ltd.
|Number of pages||10|
|Journal||Journal of Physics B: Atomic Molecular and Optical Physics|
|Publication status||Published - 14 Sep 2006|
Condren, D. S., McCann, J., & Crothers, D. (2006). Semiclassical treatment of Wannier's theory when the exponent diverges. Journal of Physics B: Atomic Molecular and Optical Physics, 39(17), 3639-3648. . https://doi.org/10.1088/0953-4075/39/17/019