On the theory of nuclear heavy-ion direct transfer reactions

We review the distorted-wave approach to direct transfer reactions and draw attention to some of the shortcomings of current theories. We show that a reformulated form of the distorted-wave Born approximation (DWBA) for transfer can lead to important simplifications of the theory, which are valid for nuclear heavy-ion induced reactions at energies ? 10 MeV/nucleon. In particular, in the semiclassical limit, it leads to a new and simple formula for the transfer t-matrix which includes all the essential physics while offering several important advantages over standard “full-recoil finite-range” DWBA. One such advantage is that the new formula is more transparent in that it is amenable to interpretation and analytical manipulation. At high-energy it is shown to reduce to one earlier deduced using eikonal-DWBA.The conditions for the validity of the new theory are discussed in detail. They are shown to be generally well satisfied for small-mass transfer between heavy-ions at energies at or above those which particularly favour transfer (? 10 MeV/nucleon for transfer of valence nucleons). The restriction to small mass is not due to any recoil approximation; in fact, it is only a necessary restriction at certain energies. The theory treats recoil exactly.Consideration of the optimum dynamical conditions for transfer leads to a set of matching conditions. The presence of hitherto neglected absorption, arising from dynamical effects of poor matching, is suggested and qualitatively discussed. Conditions under which such absorption may be neglected are derived. Results of numerical calculations are presented showing that the theory is capable of good agreement with standard full-recoil finite-range DWBA, and that it is capable of giving at least as good an account of experimental data for nucleon-transfer between heavy-ions at energies ～10 MeV/nucleon.