Absorbing Hard Core and Regge Cuts

Abstract

A rigid absorbing core in elastic scattering requires a cut to be associated with a Regge pole. The polarization of the neutron in the n-p charge exchange due to the p-Regge pole and the cut is calculated. The shape of the forward peak m high energy charge exchange differential cross sections as well as its energy dependence was successfully explained by means of a Reggeized p-exchange.l) However, this simple model is incompatible with a nonvanishing polarization of the nucleon as found by Bonamy et aP) A suggestion is made that a cut in the complex angular momentum plane associated with the Pomeranchuk and the p trajectories will account for the phenomenon. S ),4) A singularity in the angular momentum plane other than the p trajectory was also predicted from a sum rule. 5 ) In this note it will be shown that a simple model for high energy scatter­ ing, suggested by the non-shrinking diffraction peaks, requires a cut to be as­ sociated with each Regge pole and that the contribution from the cut can be calculated explicitly. The polarization in 7Cp charge exchange scattering turns out to be of the right order of magnitude. The non-shrinking of the diffraction peaks in elastic scattering suggests that the nucleon, as seen from the projectile pion, behaves as a target of a definite shape which does not change with energy.**) We expect that a geometrical picture will become valid at high energy and the impact parameter concept will make sense. If the pion hits the target, that is, if the impact parameter b is less than the radius R of the target, the pion is absorbed, leading to a thermal equilibrium. This strong absorption is consistent with the dominance of the imaginary part in the elastic scattering amplitude. Coherent scattering can only come from the region b > R.