An l-window formalism for elastic heavy-ion scattering

It is shown that the heavy-ion elastic scattering amplitude may be written as an exact summation over sharp cut-off Coulomb amplitudes with coefficients which are simply the differences of successive nuclear S-matrix elements. Thus in the case of strong absorption the coefficients are non-zero only over a small range of angular momenta, formally making the elastic amplitude similar to those for inelastic scattering and transfer reactions in that it possesses an 'l window'. Some good approximations to the sharp cut-off Coulomb amplitudes are given and these enable us to rederive in a simple way the results obtained by the usual integral techniques for dealing with smooth S matrices. The case of identical spin-zero ions is treated in some detail since here one may have very few terms in the transition region due to the absence of all odd partial waves. In particular, the system 16O+16O is discussed and a qualitative understanding of many of the experimental results and of previous fits to the data is obtained.