Low Energy Scattering by a Compound System: Positrons on Hydrogen (Classic Reprint)

Excerpt from Low Energy Scattering by a Compound System: Positrons on Hydrogen

The formalism, developed by Kato, which gives upper and lower bounds on the phase shift for the scattering of a particle from a center of force is shown to have useful applications when the scatterer is a compound system. In particular, the problem of low energy positron scattering from, atomic hydrogen, with zero total orbital angular momentum, is studied. It is shown that at zero energy the ordinary variational calculation, which ignores second order contributions, provides a bound on the scattering length, from which a bound on the cross section is deduced. For non-zero energies a bound on the phase shift may similarly be obtained, but for a fictitious problem with cut-off potentials. If the energy is sufficiently small (less than 3 e.v., say) the error thus incurred is expected to be negligibly small. Numerical calculations performed at k = 0 and ka = 0.2 lead to the result that the effects of polarization are large enough to cause the positron to be on the whole attracted to the hydrogen atom.

It is shown, independently of the Kato formalism, that in general a bound on the scattering length may be obtained from the ordinary variational calculation provided no composite bound state exists for the system.

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