Adiabatic model of (d, p) reactions with explicitly energy-dependent nonlocal potentials

We have developed an approximate way of dealing with explicit energy dependence of nonlocal nucleon optical potentials as used to predict the (d,p) cross sections within the adiabatic theory. Within this approximation, the nonlocal optical potentials have to be evaluated at an energy shifted from half the incident deuteron energy by the n-p kinetic energy averaged over the range of the n-p interaction and then treated as an energy-independent nonlocal potential. Thus, the evaluation of the distorting potential in the incident channel is reduced to a problem solved in our previous work [N. K. Timofeyuk and R. C. Johnson, Phys. Rev. Lett. 110, 112501 (2013); Phys. Rev. C 87, 064610 (2013)]. We have demonstrated how our new model works for the case of 16O(d,p)17O, 36Ar(d,p)37Ar, and 40Ca(d,p)41Ca reactions and highlighted the need for a detailed understanding of the energy dependence of nonlocal potentials. We have also suggested a simple way of correcting the d-A effective potentials for nonlocality when the underlying energy-dependent nonlocal nucleon potentials are unknown but energy-dependent local phenomenological nucleon potentials are available.