Nuclear reaction cross sections are important for a variety of applications in the areas of astrophysics, nuclear energy, and national security. When these cross sections cannot be measured directly or predicted reliably, it becomes necessary to develop indirect methods for determining the relevant reaction rates. The surrogate nuclear reactions approach is such an indirect method. First used in the 1970s for estimating ðn; fÞ cross sections, the method has recently been recognized as a potentially powerful tool for a wide range of applications that involve compound-nuclear reactions. The method is expected to become an important focus of inverse-kinematics experiments at rareisotope facilities. The present paper reviews the current status of the surrogate approach. Experimental techniques employed and theoretical descriptions of the reaction mechanisms involved are presented and representative cross section measurements are discussed.

The validity of the Surrogate Ratio method for determining (n,f) cross sections for actinide nuclei is examined. This method relates the ratio of two compound-nucleus reaction cross sections to a ratio of coincidence events from two measurements in which the same compound nuclei are formed via a direct reaction. With certain assumptions, the method allows one of the cross sections to be inferred if the other is known. We develop a nuclear reaction-model simulation to investigate whether the assumptions underlying the Ratio approach are valid and employ these simulations to assess whether the cross sections obtained indirectly by applying a Ratio analysis agree with the expected results. In particular, we simulate Surrogate experiments that allow us to determine fission cross sections for selected actinide nuclei. The nuclei studied, 233 U and 235 U, are very similar to those considered in recent Surrogate experiments. We find that in favorable cases the Ratio method provides useful estimates of the desired cross sections, and we discuss some of the limitations of the approach.

Indirect methods play an important role in the determination of nuclear reaction cross sections that are hard to measure directly. In this paper we investigate the feasibility of using the so-called surrogate method to extract neutron-capture cross sections for low energy compound-nuclear reactions in spherical and near-spherical nuclei. We present the surrogate method and develop a statistical nuclear-reaction simulation to explore different approaches to utilize surrogate reaction data. We assess the success of each approach by comparing the extracted cross sections with a predetermined benchmark. In particular, we employ regional systematics of nuclear properties in the 34 ≤ Z ≤ 46 region to calculate (n, γ) cross sections for a series of Zr isotopes, and to simulate a surrogate experiment and the extraction of the desired cross section. We identify one particular approach that may provide very useful estimates of the cross section, and we discuss some of the limitations of the method. General recommendations for future (surrogate) experiments are also given.PACS numbers: 24.10. 24.60.Dr, 25.40.Lw, 98.80.Ft

Motivated by the renewed interest in the surrogate nuclear reactions approach, an indirect method for determining compound-nuclear reaction cross sections, the prospects for determining (n,γ) cross sections for deformed rare-earth and actinide nuclei are investigated. A nuclear-reaction model is employed to simulate physical quantities that are typically measured in surrogate experiments and used to assess the validity of the Weisskopf-Ewing and ratio approximations, which are typically employed in the analysis of surrogate reactions. The expected accuracy of (n,γ) cross sections extracted from typical surrogate measurements is discussed and limitations of the approximate methods are illustrated. Suggestions for moving beyond presently-employed approximations are made.

We present an account of the current status of the theoretical treatment of inclusive (d, p) reactions in the breakup-fusion formalism, pointing to some applications and making the connection with current experimental capabilities. Three independent implementations of the reaction formalism have been recently developed, making use of different numerical strategies. The codes also originally relied on two different but equivalent representations, namely the prior (Udagawa-Tamura, UT) and the post (Ichimura-Austern-Vincent, IAV) representations. The different implementations have been benchmarked, and then applied to the Ca isotopic chain. The neutron-Ca propagator is described in the Dispersive Optical Model (DOM) framework, and the interplay between elastic breakup (EB) and non-elastic breakup (NEB) is studied for three Ca isotopes at two different bombarding energies. The accuracy of the description of different reaction observables is assessed by comparing with experimental data of (d, p) on 40,48 Ca. We discuss the predictions of the model for the extreme case of an isotope ( 60 Ca) currently unavailable experimentally, though possibly available in future facilities (nominally within production reach at FRIB). We explore the use of (d, p) reactions as surrogates for (n, γ) processes, by using the formalism to describe the compound nucleus formation in a (d, pγ) reaction as a function of excitation energy, spin, and parity. The subsequent decay is then computed within a Hauser-Feshbach formalism. Comparisons between the (d, pγ) and (n, γ) induced gamma decay spectra are discussed to inform efforts to infer neutron captures from (d, pγ) reactions. Finally, we identify areas of opportunity for future developments, and discuss a possible path toward a predictive reaction theory.

Background: One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are the cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not feasible, indirect methods, e.g., (d,p) reactions, should be used. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. While there exist several separable representations for the nucleon-nucleon interaction, the optical potential between a neutron (proton) and a nucleus is not readily available in separable form. The purpose of this paper is to introduce a separable representation for complex phenomenological optical potentials of Woods-Saxon type. Results: Starting from a global optical potential, a separable representation thereof is introduced based on the Ernst-Shakin-Thaler (EST) scheme. This scheme is generalized to non-Hermitian potentials. Applications to n + 48 Ca, n + 132 Sn, and n + 208 Pb are investigated for energies from 0 to 50 MeV and the quality of the representation is examined. Conclusions: We find a good description of the on-shell t matrix for all systems with rank up to 5. The required rank depends inversely on the angular momentum. The resulting separable interaction exhibits a different off-shell behavior compared to the original potential, reducing the high-momentum contributions.

No abstract

A fermion realization of the nuclear Sp(6,R) model, which complements the traditional bosonic representation, is developed. A recursive process is presented in which symplectic matrix elements of arbitrary one-body fermion operators between states of excitation Nប and NЈប in the same or in different symplectic bands are related back to valence shell matrix elements, which can be evaluated by standard shell model techniques. Matrix elements so determined may be used to calculate observables such as electron scattering form factors which carry detailed structural information on nuclear wave functions.