A. INTRODUCTION

The calculation of cross sections for one- or several-nucleon transfer reactions involves the evaluation of multidimensional integrals. This is complicated by the fact that the integrands consist of products of wave functions and a potential that depends on a number of vector coordinates. However, only several of them are the independent variables of integration. For light-ion reactions such as (d, p) reactions (Chapter 7) and (t, p) reactions (Chapter 15), the direct reaction causing the transition is often approximated by a zero-range potential. This is partially justified by the small size of the light nucleus (the deuteron or triton in the examples cited) in comparison with the size of the other nuclei. (Remember that direct reactions are dominantly surface reactions). In addition, the de Broglie wavelength associated with the relative motion is not small compared to the neglected distance (range of the potential). For a deuteron of say 10 MeV, it is

where m is the reduced mass of the deuteron and c=197 MeV fm. As a consequence, the reaction does not have a great sensitivity to distances of this order. The zero-range assumption results in a great simplification; the arguments of the distorted waves become proportional to each other [see (15.13)], and the DWBA integrals reduce to an integration over a single vector coordinate, for which the angle integrals can be done in closed form. There then remains a one-dimensional integral (or rather a sum of such), which must be performed numerically because in general...