Threshold behaviour of the ionization cross section in positron atom collisions

The behaviour of the ionization cross section in positron-atom collisions is analysed near the threshold energies by using two forms of the final-state wavefunction which are obtained in the three-body formalism of Faddeev and Vainshtein approximation. It is found that, while the first-order Faddeev wavefunction yields the threshold cross section ∼εsup(3/2), same as that given by the Born approximation, the Vainshtein approximation predicts a law ∼εsup(1/2)∫sub(0)sup(1)f(x)exp(-g(x)/√ε)dx, where f(x) and g(x) are analytic functions of x. (author). 7 refs