Surrogate Reactions Research Articles

Surrogate Reactions Research at JAEA/Tokyo Tech

The research activities at JAEA and Tokyo Tech. in the development of a surrogate method based on multi-nucleon transfer reactions induced by (mainly) heavy-ion projectiles are presented. This project consists of 3 parts: the development of an apparatus to measure (1) fission cross sections and (2) neutron capture cross sections, and (3) the development of the underlying theoretical framework. Equipment has already been developed and preliminary experiments carried out to validate the methods and to provide new data. At the same time, theories to describe the surrogate reaction processes were constructed and conditions for the surrogate ratio method to derive the correct neutron-induced cross sections were investigated.

Determining the239Np(n,f)cross section using the surrogate ratio method

Background: Neutron-induced fission cross-section data are needed in various fields of applied and basic nuclear science. However, cross sections of short-lived nuclei are difficult to measure directly due to experimental constraints.Purpose: The first experimental determination of the neutron-induced fission cross section of ${}^{239}$Np at nonthermal energies was performed. This minor actinide is the waiting point to ${}^{240}$Pu production in a nuclear reactor.Method: The surrogate ratio method was employed to indirectly deduce the ${}^{239}\text{Np}(n,f)$ cross section. The surrogate reactions used were ${}^{236}\text{U}{(}^{3}\text{He},p)$ and ${}^{238}\text{U}{(}^{3}\text{He},p)$ with the reference cross section given by the well-known ${}^{237}\text{Np}(n,f)$ cross section. The ratio of observed fission reactions resulting from the two formed compound nuclei, ${}^{238}$Np and ${}^{240}$Np, was multiplied by the directly measured ${}^{237}\text{Np}(n,f)$ cross section to determine the ${}^{239}\text{Np}(n,f)$ cross section.Results: The ${}^{239}\text{Np}(n,f)$ cross section was determined with an uncertainty ranging between 4$%$ and 30$%$ over the energy range of 0.5--20 MeV. The resulting cross section agrees closest with the JENDL-4.0 evaluation.Conclusions: The measured cross section falls in between the existing evaluations, but it does not match any evaluation exactly (with JENDL-4.0 being the closest match); hence reactor codes relying on existing evaluations may under- or overestimate the amount of ${}^{240}$Pu produced during fuel burnup. The measurement helps constrain nuclear structure parameters used in the evaluations.

Measurement of the entry-spin distribution imparted to the high excitation continuum region of gadolinium nuclei via (p,d) and (p,t) reactions

Over the last several years, the surrogate reaction technique has been successfully employed to extract ($n,\phantom{\rule{-0.16em}{0ex}}f$) and ($n,\phantom{\rule{-0.16em}{0ex}}\ensuremath{\gamma}$) cross sections in the actinide region to a precision of $\ensuremath{\sim}$5$%$ and $\ensuremath{\sim}$20$%$, respectively. However, attempts to apply the technique in the rare earth region have shown large (factors of 2--3) discrepancies between the directly measured ($n,\phantom{\rule{-0.16em}{0ex}}\ensuremath{\gamma}$) and extracted surrogate cross sections. One possible origin of this discrepancy lies in differences between the initial spin-parity population distribution in the neutron induced and surrogate reactions. To address this issue, the angular momentum transfer to the high excitation energy quasicontinuum region in Gd nuclei has been investigated. The ($p,\phantom{\rule{-0.16em}{0ex}}d$) and ($p,\phantom{\rule{-0.16em}{0ex}}t$) reactions on ${}^{154,158}$Gd at a beam energy of 25 MeV were utilized. Assuming a single dominant angular momentum transfer component, the measured angular distribution for the ($p,\phantom{\rule{-0.16em}{0ex}}d$) reactions is well reproduced by distorted-wave Born approximation (DWBA) calculations for $\ensuremath{\Delta}L=4$ $\ensuremath{\hbar}$ transfer, whereas the ($p,\phantom{\rule{-0.16em}{0ex}}t$) reactions are better characterized by $\ensuremath{\Delta}L=5$ $\ensuremath{\hbar}$. A linear combination of DWBA calculations, weighted according to a distribution of $L$ transfers (peaking around $\ensuremath{\Delta}L=4$--5 $\ensuremath{\hbar}$), is in excellent agreement with the experimental angular distributions.

Study of the surrogate-reaction method applied to neutron-induced capture cross sections

Gamma-decay probabilities of 173Yb and 176Lu have been measured using the surrogate reactions 174Yb(3He,αγ)173Yb* and 174Yb(3He,pγ)176Lu*, respectively. For the first time, the gamma-decay probabilities have been obtained with two independent experimental methods based on the use of C6D6 scintillators and Germanium detectors. Our results for the radiative-capture cross sections are several times higher than the corresponding neutron-induced data. To explain these differences, we have used our gamma-decay probabilities to extract rather direct information on the spin distributions populated in the transfer reactions used. They are about two times wider and the mean values are 3 to 4 ℏ higher than the ones populated in the neutron-induced reactions. As a consequence, in the transfer reactions neutron emission to the ground and first excited states of the residual nucleus is strongly suppressed and gamma-decay is considerably enhanced.

Compound-nuclear reaction cross sections from surrogate measurements

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 $(n,f)$ 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 rare-isotope 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.

Neutron-capture cross sections from indirect measurements

Cross sections for compound-nuclear reactions reactions play an important role in models of astrophysical environments and simulations of the nuclear fuel cycle. Providing reliable cross section data remains a formidable task, and direct measurements have to be complemented by theoretical predictions and indirect methods. The surrogate nuclear reactions method provides an indirect approach for determining cross sections for reactions on unstable isotopes, which are di cult or impossible to measure otherwise. Current implementations of the method provide useful cross sections for (n,f) reactions, but need to be improved upon for applications to capture reactions.

Spin-dependent observables in surrogate reactions

Observables emitted from various spin states in compound U nuclei are investigated to validate usefulness of the surrogate reaction method. It was found that energy spectrum of cascading $\gamma$-rays and their multiplicities, spectrum of evaporated neutrons, and mass-distribution of fission fragments show clear dependence on the spin of decaying nuclei. The present results indicate that they can be used to infer populated spin distributions which significantly affect the decay branching ratio of the compound system produced by the surrogate reactions.

Nuclear reactions for astrophysics and other applications

Cross sections for compound-nuclear reactions are required for many applications. The surrogate nuclear reactions method provides an indirect approach for determining cross sections for reactions on unstable isotopes, which are difficult or impossible to measure otherwise. Current implementations of the method provide useful cross sections for (n,f) reactions, but need to be improved upon for applications to capture reactions.

Surrogate Approaches for Neutron Capture

The prospects for obtaining neutron capture cross sections indirectly from surrogate measurements are discussed. The surrogate reactions approach has been successfully employed to determine (n,f) cross sections from observed fission decays of compound nuclei created with the help of light-ion inelastic scattering or transfer reactions. The challenges encountered in applications of the method to capture reactions are considered. Case studies are presented that shed light on the accuracy to be expected from this approach, and ideas for improving the resulting cross sections are discussed.

Dynamical model of surrogate reactions

A new dynamical model is developed to describe the whole process of surrogate reactions; transfer of several nucleons at an initial stage, thermal equilibration of residues leading to washing out of shell effects and decay of populated compound nuclei are treated in a unified framework. Multi-dimensional Langevin equations are employed to describe time-evolution of collective coordinates with a time-dependent potential energy surface corresponding to different stages of surrogate reactions. The new model is capable of calculating spin distributions of the compound nuclei, one of the most important quantity in the surrogate technique. Furthermore, various observables of surrogate reactions can be calculated, e.g., energy and angular distribution of ejectile, and mass distributions of fission fragments. These features are important to assess validity of the proposed model itself, to understand mechanisms of the surrogate reactions and to determine unknown parameters of the model. It is found that spin distributions of compound nuclei produced in $^{18}$O+$^{238}$U $\rightarrow ^{16}$O+$^{240*}$U and $^{18}$O+$^{236}$U $\rightarrow ^{16}$O+$^{238*}$U reactions are equivalent and much less than 10$\hbar$, therefore satisfy conditions proposed by Chiba and Iwamoto (PRC 81, 044604(2010)) if they are used as a pair in the surrogate ratio method.

Verification of the surrogate ratio method

Effects of difference in the spin and parity distributions for the surrogate and neutron-induced reactions are investigated. Without assuming specific (schematic) spin-parity distributions, it was found that the surrogate ratio method can be employed to determine neutron fission and capture cross sections if 1) weak Weisskopf-Ewing condition (defined in this paper) is satisfied, 2) there exist two surrogate reactions whose spin-parity distributions of the decaying nuclei are almost equivalent, and 3) difference of the representative spin values between the neutron-induced and surrogate reactions is no much larger than 10 $\hbar$. If these conditions are satisfied, we need not to know the spin-parity distributions populated by the surrogate method. Instead, we should just select a pair of surrogate reactions which will populate the similar spin-parity distributions, using targets having similar structure and reactions having the similar reaction mechanisms. Achievable accuracy is estimated to be around 5 and 10 % for fission and capture channels, respectively, for nuclei of the Uranium region. The surrogate absolute method, on the contrary, can be marginally applicable to determination of fission cross sections. However, there will be little hope to apply this method for capture cross section measurements unless the spin-parity distributions in the neutron-induced and surrogate reactions are fairly close to each other or the difference can be corrected theoretically. The surrogate ratio method was shown also to be a robust method in the presence of breakup reactions, again, without assuming specific breakup reaction mechanisms.

Measurement ofγ-emission branching ratios forGd154,156,158compound nuclei: Tests of surrogate nuclear reaction approximations for(n,γ) cross sections

The surrogate nuclear reaction method can be used to determine neutron-induced reaction cross sections from measured decay properties of a compound nucleus created using a different reaction and calculated formation cross sections. The reliability of $(n,\ensuremath{\gamma})$ cross sections determined using the Weisskopf-Ewing and ratio approximations are explored for the $^{155,157}\mathrm{Gd}$$(n,\ensuremath{\gamma})$ reactions. Enriched gadolinium targets were bombarded with 22-MeV protons and $\ensuremath{\gamma}$ rays were detected in coincidence with scattered protons using the Silicon Telescope Array for Reaction Studies/Livermore-Berkeley Array for Collaborative Experiments (STARS/LiBerACE) silicon and germanium detector arrays. The $\ensuremath{\gamma}$-emission probabilities for the $^{154,156,158}\mathrm{Gd}$ compound nuclei were measured at excitation energies up to 12 MeV. It is found that the approximations yield results that deviate from directly measured $^{155,157}\mathrm{Gd}$$(n,\ensuremath{\gamma})$ cross sections at low energies. To extract reliable cross sections, a more sophisticated analysis should be developed that takes into account angular-momentum differences between the neutron-induced and surrogate reactions.

Cross sections for neutron capture from surrogate measurements: An examination of Weisskopf-Ewing and ratio approximations

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, gamma) 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,gamma) 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.

Compound-nuclear reaction cross sections via surrogate reactions

The surrogate reaction method is an indirect technique for determining cross sections for nuclear reactions that proceed through a well-defined compound nucleus. In this method, the same compound nucleus is produced by an alternate (“surrogate”) reaction and its decay products measured. The assumptions underlying the method are examined for the special case of 235 U( n , f ).