Cross sections for neutron-induced reactions from surrogate data: Reexamining the Weisskopf-Ewing approximation for ( n , n ' ) and ( n , 2 n ) reactions
Background: Modeling nuclear reaction networks for nuclear science applications and for simulations of astrophysical environments relies on cross section data for a vast number of reactions, many of which have never been measured. Cross sections for neutron-induced reactions on unstable nuclei are particularly scarce, since they are the most difficult to measure. Consequently, we must rely on theoretical predictions or indirect measurements to obtain the requisite reaction data. For compound nuclear reactions, the surrogate reaction method can be used to determine many cross sections of interest. Purpose: Earlier work has demonstrated that cross sections for neutron-induced fission and radiative neutron capture can be determined from a combination of surrogate reaction data and theory. For the fission case, it was shown that the Weisskopf-Ewing approximation, which significantly simplifies the implementation of the surrogate method, can be employed. Capture cross sections cannot be obtained, and require a detailed description of the surrogate reaction process. Here, we examine the validity of the Weisskopf-Ewing approximation for determining unknown (n, n') and (n, 2n) cross sections from surrogate data. Methods: Using statistical reaction calculations with realistic parametrizations, we investigate first whether the assumptions underlying the Weisskopf-Ewing approximation are valid for (n, n') and (n, 2n) reactions on representative target nuclei. We then produce simulated surrogate reaction data and assess the impact of applying the Weisskopf-Ewing approximation when extracting (n, n') and (n, 2n) cross sections in situations where the approximation is not strictly justified. Results: We find that peak cross sections can be estimated using the Weisskopf-Ewing approximation, but the shape of the (n, n') and (n, 2n) cross sections, especially for low neutron energies, cannot be reliably determined without accounting for the angular-momentum differences between the neutron-induced and surrogate reaction. Conclusions: To obtain reliable (n, n') and (n, 2n) cross sections from surrogate reaction data, a detailed description of the surrogate reaction mechanisms is required. To do so for the compound-nucleus energies and decay channels relevant to these reactions, it becomes necessary to extend current modeling capabilities.