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- W2020030167 abstract "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 u1 and u2 and derive a new turning point ρ+. Since u1 is well behaved at infinity, there exists only the singularity in u2 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." @default.
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- W2020030167 date "2006-08-23" @default.
- W2020030167 modified "2023-09-24" @default.
- W2020030167 title "Semiclassical treatment of Wannier's theory when the exponent diverges" @default.
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- W2020030167 doi "https://doi.org/10.1088/0953-4075/39/17/019" @default.
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