Limited Resurrection of the Born Approximation

Abstract

I t is shown that the ordinary Born approximation for pn and pp charge-exchange scattering correctly accounts for (1) the shape of the forward peak for 0 5 (-t)Sw2/2 a t P L =~ GeV/c, and (2) the energy dependence of the cross sections a t t=O in the energy range PL=2-8 GeV/c. This result is analogous to the %yell-kn0~r.n success of the electric Born approximation in T+ photoproduction. I t is then shown that the simplest interpretation of this surprising result within the framework of Regge-pole theory is in terms of the fixed poles which are allowed by unitarity in hadronic amplitudes a t certain nonsense points of right signature. Finally, it is shown how such a fixed pole a t a nonsense point of one helicity amplitude affects another amplitude for which the corresponding point is sense.'

Manifestation of the pion pole in p → n charge-exchange scattering

“…The Born approximation predicts therefore a narrow dip in the forward direction, rather than the observed spike. Taking into account also the u-channel 0 exchange gives the correct cross-section value at t = 0, but still fails to reproduce the measured t-dependence [5]. Agreement with the data can be obtained only assuming destructive i n terference between the pion-and some`background'-term [6].…”