Establishing a theory for deuteron-induced surrogate reactions

Background: Deuteron-induced reactions serve as surrogates for neutron capture into compound states. Although these reactions are of great applicability, no theoretical efforts have been invested in this direction over the last decade.

Purpose: The goal of this work is to establish on firm grounds a theory for deuteron-induced neutron-capture reactions. This includes formulating elastic and inelastic breakup in a consistent manner.

Method: We describe this process both in post- and prior-form distorted wave Born approximation following previous works and discuss the differences in the formulation. While the convergence issues arising in the post formulation can be overcome in the prior formulation, in this case one still needs to take into account additional terms due to nonorthogonality.

Results: We apply our method to the ${}^{93}\mathrm{Nb}(d,p)X$ at $E_d=15$ and 25 MeV and are able to obtain a good description of the data. We look at the various partial wave contributions, as well as elastic versus inelastic contributions. We also connect our formulation with transfer to neutron bound states.

Conclusions: Our calculations demonstrate that the nonorthogonality term arising in the prior formulation is significant and is at the heart of the long-standing controversy between the post and the prior formulations of the theory. We also show that the cross sections for these reactions are angular-momentum dependent and therefore the commonly used Weisskopf limit is inadequate. Finally, we make important predictions for the relative contributions of elastic breakup and nonelastic breakup and call for elastic-breakup measurements to further constrain our model.

Figure 1

Definition of coordinates used in our formulations.

Figure 2

Energy distributions of the detected proton for ${}^{93}\mathrm{Nb}(d,p)$ at (a) 15 MeV and (b) $25.5$ MeV: total cross sections (solid line), elastic breakup (EB, dot-dashed line), and inelastic breakup (NEB, dashed line). The arrows indicate the position of the neutron emission threshold. Data are from Ref. [16].

Figure 3

Energy distributions for ${}^{93}\mathrm{Nb}(d,p)$ at (a) 15 MeV and (b) $25.5$ MeV: partial wave decomposition.

Figure 4

Energy distributions for ${}^{93}\mathrm{Nb}(d,p)$ at 15 MeV below the neutron threshold for those partial waves that have bound states: (a) strength of the imaginary potential $W=0.5\text{MeV}$. and (b) strength of the imaginary potential $W=3.0$ MeV.

Figure 5

Effect of the nonorthogonality and cross terms in the cross sections: (a) energy distribution for ${}^{93}\mathrm{Nb}(d,p)$ at $25.5$ MeV for an angle $\theta ={10}^{\circ }$ and (b) angular distributions for both $E_n=-3$ MeV and $E_n=5$ MeV.