Establishing a theory for deuteron-induced surrogate reactions

Abstract

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 non-orthogonality. Results: We apply our method to the 93 Nb(d,p)X at E d =15 MeV 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 non-orthogonality 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 non-elastic breakup, and call for elastic breakup measurements to further constrain our model.

Numerical assessment of post-prior equivalence for inclusive breakup reactions

“…Contrary to the referred results of Udagawa, Tamura, and collaborators, the comparison of these recent calculations with available data has shown very encouraging results. These calculations have been performed using either the original post-form formulation [18,20] or its (in principle) equivalent prior form [19]. However, a consistent comparison between the post and prior results has not been made to our knowledge.…”

Current Status of Nuclear Physics Research

“…A semiclassical model has recently been developed [219]. In fact only in this year three papers have been written and will appear soon published in the journals [220][221][222].…”

Inclusive Breakup Theory of Three-Body Halos

“…These neutron capture reactions on other targets are also important for the study of element formation following supernova explosion through the astrophysical s-process. The general conclusion of [19][20][21]23] was that the Surrogate Method, the extraction of the cross section for the formation and decay of the compound nucleus of the (n + A) subsystem, as well as the total capture cross section (the cross section for the formation of the compound nucleus), is justified as long as the direct part of the cross section is calculated and subtracted from the inclusive breakup total reaction cross section σ (n+A)…”

“…One might consider the inclusive proton spectra in the breakup of 20 Mg + 208 Pb with the formation of 209 Bi, 226 U and 227 Np at different excitation energies. However, 20 Mg presents a very short lifetime and low intensity as a secondary beam.…”

“…Quite recently this theory was applied to the (d,p) reaction [19][20][21]23] as a mean to test the validity of the Surrogate Method [24][25][26], employed to extract neutron capture and fission cross sections of actinide target nuclei, such as 238 U, 232 Th, of importance for the development of next generation fast breeder reactors. These neutron capture reactions on other targets are also important for the study of element formation following supernova explosion through the astrophysical s-process.…”