Effect of break-up channels on (d,pn) coincidence cross section in post form break-up theories

Abstract

The effect of deuteron break-up channels on the (d, pn) coincidence cross section as calculated within the framework of the post-form distorted-wave Born-approximation (DWBA) has been investigated. Expressions for the T-matrix for this reaction are derived in the post-form theory taking explicitly into account the coupling of break-up channels on the elastic deuteron channel. In this derivation the correction to the post-form DWBA T-matrix arising from coupling to the break-up channels are well separated from the latter, thus making it easier to visualize the effect of coupling clearly. Formulas are also derived for an alternate post-form T-matrix. It is shown that the final channel wave function to be used in this T-matrix does not correspond to the optical potential describing the deuteron-target elastic scattering. This makes the usefulness of the alternate post-form theories based on such potentials questionable. Numerical applications to ⁵¹V(d, pn) and ¹¹⁸Sn(d, pn) reactions at E_d=56 MeV show that the effect of coupling to break-up channels on the post-form DWBA (d, pn) cross section is not very significant. This is due to the fact that in this theory dominant contributions to these reactions come from the larger partial waves, in particular grazing partial waves and beyond.