Reaction Theory Advances For FRIB

Much interest in rare isotopes centers on how they interact with neutrons, in particular concerning their neutron capture rates in many slow and fast processes. Since neutrons do not make a target, we must use indirect methods, and use reaction theory to bridge the gap. Many of these indirect methods are transfer reactions, in which the rare isotope has a neutron or two added or subtracted. Most common is the (d,p) reaction to add one neutron, just as in a capture reaction. The deuteron is {\em itself} weakly bound, however, so I will review recent work on few-body methods to describe deuterons incident on heavy nuclei. When bound neutron states are measured, we can predict direct capture rates for neutrons. Continuum states for the neutron may also be produced in (d,p) reactions. If individual resonances can be distinguished, new theory can describe the transfer cross section in terms of R-matrix parameters for the neutron state. If, however, we have a high level density, then we must use energy averaging, giving a complex optical potential for the neutron. I review the theory of partial fusion needed in this case to describe the competition between breakup and compound-nucleus production. Neutron pickup reactions such as ($^3$He,$\alpha$) and (p,t) are also useful to probe hole states, and do not have competition with direct breakup.