Surrogate Reaction Method Research Articles

Improving nuclear data evaluations with predictive reaction theory and indirect measurements

Nuclear reaction data required for astrophysics and applications is incomplete, as not all nuclear reactions can be measured or reliably predicted. Neutron-induced reactions involving unstable targets are particularly challenging, but often critical for simulations. In response to this need, indirect approaches, such as the surrogate reaction method, have been developed. Nuclear theory is key to extract reliable cross sections from such indirect measurements. We describe ongoing efforts to expand the theoretical capabilities that enable surrogate reaction measurements. We focus on microscopic predictions for charged-particle inelastic scattering, uncertainty-quantified optical nucleon-nucleus models, and neural-network enhanced parameter inference.

Indirect measurements of neutron-induced reaction cross sections at storage rings

Neutron-induced reaction cross sections of unstable nuclei are essential for understanding the synthesis of heavy elements in stars. However, their measurement is very difficult due to the radioactivity of the targets involved. We propose to circumvent this problem by using for the first time the surrogate reaction method in inverse kinematics at heavy-ion storage rings. In this contribution, we describe the developments we have done to perform surrogate-reaction studies at the storage rings of GSI/FAIR. In particular, we present the first results of the proof of principle experiment, which we conducted recently at the Experimental Storage Ring (ESR).

Testing the Extended SRM against the 238U(3He,4He)237U* surrogate probabilities

Since its introduction in the seventies’, the so-called surrogate-reaction method (SRM) has motivated the development and improvement of theories in connection to direct reactions. A recent work by Bouland and Noguère, Phys. Rev. C 102, 054608 (2020), has shown that the inclusion of experimental probabilities in the neutron cross section evaluation process can be better achieved using tools resulting from the efforts made over the two last decades. In particular, the authors have put forward a new prescription, named after the SRM as extended SRM (ESRM), to convert, with reasonable confidence, probabilities measured in direct reactions to pseudo-experimental neutron-induced reaction cross sections. Applied to the 174Yb(3He,py)176Lu* transfer reaction, the ESRM has demonstrated much more precision than the early use of the SRM. In addition to the ‘direct’ analysis of reaction probabilities measured in direct reactions using the right modeling as developed in Phys. Rev. C 100, 064611 (2019), it is worth to try converting the measured probabilities in pseudo experimental neutron-induced cross sections for neutron reactor data applications. In the present paper, first results, before conversion, are shown by applying the two ESRM equations to a fissile isotope.

Preparation of PbSe targets for [formula omitted]Se neutron capture cross section studies

A methodology for the production of PbSe targets for 79Se neutron capture cross section studies is presented. PbSe material was synthesized by direct reaction of its constituents at high temperature, and characterized by X-ray diffraction. Thin PbSe targets, produced for cross section experiments with the surrogate reaction method, were obtained by applying a physical vapor deposition technique, and their morphology and composition were analyzed by X-ray fluorescence, Scanning Electron Microscopy, and Energy dispersive X-ray spectroscopy. Pb79Se targets produced for cross section measurements with the Time of Flight method were characterized by γ-ray spectroscopy. Finally, a procedure for the recovery of Se from PbSe is suggested. The purity of the retrieved Se was determined with Inductively Coupled Plasma Optical Emission Spectroscopy.

Investigation of Weisskopf-Ewing approximation for the determination of ( n,p ) cross sections using the surrogate reaction technique

The present study explores the limitations of the surrogate reaction method for determining the $(n,p)$ cross sections for the target nuclei in the mass region $A\ensuremath{\approx}50$ for the neutron energies 1--20 MeV. In the past few years there have been several experimental attempts for determining the $(n,p)$ and $(n,xp)$ cross sections using the surrogate reaction method. But this method has not been benchmarked with the experimentally well-known $(n,p)$ cross sections. The surrogate reaction method with Weisskopf-Ewing approximation may help in providing good constraints for the cross-section data, but this approximation has not been validated yet for $(n,p)$ reactions. In this paper, we have examined the validity of the Weisskopf-Ewing approximation for the $(n,p)$ reactions and also check the sensitivity of the surrogate reaction results with respect to the compound nucleus spin distribution. We have simulated the cross sections obtained through the surrogate reaction method for $n+^{48}\mathrm{Ti}, n+^{53}\mathrm{Cr}, n+^{56}\mathrm{Fe}$, and $n+^{59}\mathrm{Co}$ reactions for the different schematic spin distributions of the compound nucleus and studied the effect of assuming the validity of the Weisskopf-Ewing approximation. It has been observed that the proton decay probabilities of the compound nucleus for the $(n,p)$ channel are strongly spin dependent, therefore the Weisskopf-Ewing approximation is violated. We have also observed that the cross sections obtained using the Weisskopf-Ewing approximation show clear dependence on the spin distribution of the compound nucleus. It has also been observed that, due to the large pre-equilibrium contributions in the $(n,p)$ reactions at higher neutron energies, the use of the surrogate reaction method for the neutron energies greater than $\ensuremath{\approx}15$ MeV may not be suitable. It is concluded that the surrogate reaction method relying solely on the Weisskopf-Ewing approximation is not sufficient for determining the $(n,p)$ cross sections for the target nuclei in mass range $A\ensuremath{\approx}50$ and further development and exploration of the surrogate technique is required.

Reconciling surrogate-reaction probabilities and neutron-induced cross sections

Since its inception, the so-called surrogate-reaction method (SRM) has motivated the development and improvement of theories in connection to direct reactions. This paper reassesses some of the developments carried out in previous decades to deal with the representation of direct reaction probability data. It is believed that the experimental probabilities assimilation in the neutron cross section evaluation process can be better estimated using tools resulting from the efforts made over the years. This paper provides a new perspective on this issue both in terms of fission and $\ensuremath{\gamma}$-ray emission probabilities. In addition to the ``natural'' assimilation path that considers analyzing probabilities jointly with cross sections to extract nuclei structural properties, this article puts forward a prescription to convert, with a good level of confidence, measured direct-reaction induced probabilities to pseudoexperimental neutron-induced cross sections. This approach is named after the SRM as extended SRM (ESRM).

Indirect measurements of neutron cross-secti at heavy-ion storage rings

Cross sections for neutron-induced reactions of short-lived nuclei are essential for nuclear astrophysics since these reactions in the stars are responsible for the production of most heavy elements in the universe. These reactions are also key in applied domains like energy production and medicine. Nevertheless, neutron-induced cross-section measurements can be extremely challenging or even impossible to perform due to the radioactivity of the targets involved. Indirect measurements through the surrogate-reaction method can help to overcome these difficulties.The surrogate-reaction method relies on the use of an alternative reaction that will lead to the formation of the same excited nucleus as in the neutron-induced reaction of interest. The decay probabilities (for fission, neutron and gamma-ray emission) of the nucleus produced via the surrogate reaction allow one to constrain models and the prediction of the desired neutron cross sections.We propose to perform surrogate reaction measurements in inverse kinematics at heavy-ion storage rings, in particular at the CRYRING@ESR of the GSI/FAIR facility. We present the conceptual idea of the most promising setup to measure for the first time simultaneously the fission, neutron and gamma-ray emission probabilities. The results of the first simulations considering the 238U(d,d’) reaction are shown, as well as new technical developments that are being carried out towards this set-up.

Simultaneous Determination of Neutron-Induced Fission and Radiative Capture Cross Sections from Decay Probabilities Obtained with a Surrogate Reaction.

Reliable neutron-induced-reaction cross sections of unstable nuclei are essential for nuclear astrophysics and applications but their direct measurement is often impossible. The surrogate-reaction method is one of the most promising alternatives to access these cross sections. In this work, we successfully applied the surrogate-reaction method to infer for the first time both the neutron-induced fission and radiative capture cross sections of ^{239}Pu in a consistent manner from a single measurement. This was achieved by combining simultaneously measured fission and γ-emission probabilities for the ^{240}Pu(^{4}He,^{4}He^{'}) surrogate reaction with a calculation of the angular-momentum and parity distributions populated in this reaction. While other experiments measure the probabilities for some selected γ-ray transitions, we measure the γ-emission probability. This enlarges the applicability of the surrogate-reaction method.

Exploitation of surrogate reaction method for deriving proton induced fission cross sections of short lived actinides

In this article we have explored the possibility of measuring the proton induced fission cross sections using surrogate reaction method. To establish the validity of the surrogate method, we have derived the cross sections for 240Pu(p, f), 234Th(p, f), 236U(p, f) and 233Th(p, f) reactions using the derived cross section data of 240Am(n, f), 234Pa(n, f), 236Np(n, f) and 233Pa(n, f) reactions, which were measured by the surrogate ratio method. To extract the data, we have used the independence hypothesis of compound nucleus formation and derived a relation between proton and neutron induced fission cross sections of the consecutive isobars. The validity of the Weisskopf–Ewing approximation has been studied in detail. This study successfully confirms that the surrogate ratio method can be used to derive (p, f) cross sections of the short lived actinides. It is also concluded that a common surrogate reaction can be used for the determination of (n, f) and (p, f) cross sections for the consecutive isobars.

Measurement of (n, f) and (n, xn) cross sections with surrogate reaction method

Surrogate reaction method is an important approach to overcome the difficulties meet in the direct measurement of neutron induced nuclear reaction. The current existing surrogate reactions generally employ the peripheral reactions such as inelastic excitation and transfer reaction where the involved angular momenta are much larger than the neutron capture reaction, which causes a difficulty in theoretical correction of spin of compound nucleus. We proposed to use capture reaction of light charged particle as the surrogate reaction, thus the spin distributions of compound nucleus in two reactions are quite similar and therefore the spin correction is not strongly desired. Based on this idea, the 239Pu(n, f) and (n, 2n) cross sections were successfully extracted by using 236U(α,, f) and (α, 2n) reactions as the surrogate reactions. The well coincidence of the present results with the data of ENDFB7 within the error bars shows the reliability of the proposed surrogate capture reaction method.

Monte Carlo simulation of γ and fission transfer reactions using extended ℛ-matrix theory

This paper comes back on the accuracy of the surrogate-reaction method (SRM) historically used for neutron-induced average partial cross sections inference from measured surrogate-reaction probabilities. The SRM level of performance is examined in relation to a reasonably accurate reference calculation performed with the 𝒜𝒱𝒳𝒮ℱ-ℒ𝒩𝒢 code [1] through a challenging test case : the 240Pu* compound system. This paper argues on some ingredients of the reference calculation [2] and returns some hints about the failure now well-known of the neutron-induced γ average cross section inference. It shows also that in some special cases, the SRM can be poorly accurate also in terms of neutron-induced fission average cross section inference.

Incorporating a two-step mechanism into calculations of (p,t) reactions used to populate compound nucleus spin-parity distributions in support of surrogate measurements

The surrogate reaction method may be used to determine the cross section for neutron-induced reactions not accessible through standard experimental techniques by creating the same compound nucleus which the desired reaction would pass through, but via a different entrance channel. A variety of direct reactions have been employed in order to generate the required compound nuclei for surrogate studies. In this work, a previously developed (p,t) reaction model has been extended to incorporate a two-step reaction mechanism, which takes the form of sequential neutron transfer. This updated model is applied to the 92Zr(p,t)90Zr reaction and is found to modify the strengths of the previously predicted populated levels. It is planned that this improved (p,t) model will be used to attempt to constrain cross section predictions for a number of (n,γ) reactions in future, as well as provide a possible comparison against other surrogate studies utilising different direct reactions such as (p,d).

Reexamining fission-probability data using R -matrix Monte Carlo simulations: Beyond the surrogate-reaction method

This article describes an original approach to analyze simultaneously cross sections and surrogate data measurements using efficient Monte Carlo extended $\mathcal{R}$-matrix theory algorithm based on unique set of nuclear structure parameters. The alternative analytical path based on the manifold Hauser-Feshbach equation was intensively used in this work to gauge the errors carried by the surrogate-reaction method commonly taken to predict neutron-induced cross sections from observed partial decay probabilities. Present paper emphasizes in particular a dedicated way to treat direct reaction entrance and prior decay excited nucleus outgoing channels widths correlations. Present smart theoretical foundation brought the opportunity to apply successfully our method to both fission-probability data and directly measured neutron cross sections according to Pu fissile isotopes; namely the $^{237, 238, 240, 242~and~244}$Pu$^*$ nuclei. This new capability opens genuine perspectives in matter of 'evaluation process' from foreseen fission- and $\gamma$-decay probabilities simultaneously measured as derived data will become available.

Determining the average prompt-fission-neutron multiplicity forPu239(n,f)via aPu240(α,α′f)surrogate reaction

The average prompt-fission-neutron multiplicity $\bar{\nu}$ is of significance in the areas of nuclear theory, nuclear nonproliferation, and nuclear energy. In this work, the surrogate-reaction method has been used for the first time to indirectly determine $\bar{\nu}$ for $^{239}$Pu($n$,$f$) via $^{240}$Pu($\alpha$,$\alpha^{\prime}f$) reactions. A $^{240}$Pu target was bombarded with a beam of 53.9-MeV $\alpha$ particles. Scattered $\alpha$ particles, fission products, and neutrons were measured with the NeutronSTARS detector array. Values of $\bar{\nu}$ were obtained for a continuous range of equivalent incident neutron energies between 0.25--26.25~MeV, and the results agree well with direct neutron measurements.

Monte Carlo simulation of γ and fission transfer-induced probabilities using extended 𝓡-matrix theory: Application to the 237U∗ system

This paper deals with simultaneous neutron-induced average partial cross sections and surrogate-like probability simulations over several excitation and de-excitation channels of the compound nucleus. Present calculations, based on one-dimensional fission barrier extended 𝓡-matrix theory using Monte Carlo samplings of both first and second well resonance parameters, avoid the surrogate-reaction method historically taken for surrogate data analyses that proved to be very poor in terms of extrapolated neutron-induced capture cross sections. Present theoretical approach is portrayed and subsequent results can be compared for the first time with experimental γ-decay probabilities; thanks to brand new simultaneous 238 U(3 He,4 Heγ) and 238 U(3 He,4 He f) surrogate measurements. Future integration of our strategy in standard neutron cross section data evaluation remains tied to the developments made in terms of direct reaction population probability calculations.

Investigation of the surrogate-reaction method via the simultaneous measurement of gamma-emission and fission probabilities

We present the results of two experiments where we have measured for the first time simultaneously the fission and gamma-decay probabilities induced by different surrogate reactions. In particular, we have investigated the 238 U(d,p), 238 U( 3 He,t) and 238 U( 3 He, 4 He) reactions as surrogates for the neutron-induced n + 238 U, n + 237 Np and n + 236 U reactions, respectively. In the region where gamma emission, neutron emission and fission compete, our results for the fission probabilities agree fairly well with the neutron-induced data, whereas our gamma-decay probabilities are significantly higher than the neutron-induced data. The interpretation of these results is not obvious and is discussed within the framework of the statistical model with preliminary results for calculated spin-parity distributions populated in surrogate reactions. We also present future plans for surrogate-reaction studies in inverse kinematics with radioactive-ion beams at storage rings.

Application of the EXtrapolated Efficiency Method (EXEM) to infer the gamma-cascade detection efficiency in the actinide region

The study of transfer-induced gamma-decay probabilities is very useful for understanding the surrogate-reaction method and, more generally, for constraining statistical-model calculations. One of the main difficulties in the measurement of gamma-decay probabilities is the determination of the gamma-cascade detection efficiency. In Boutoux et al. (2013) [10] we developed the EXtrapolated Efficiency Method (EXEM), a new method to measure this quantity. In this work, we have applied, for the first time, the EXEM to infer the gamma-cascade detection efficiency in the actinide region. In particular, we have considered the 238U(d,p)239U and 238U(3He,d)239Np reactions. We have performed Hauser–Feshbach calculations to interpret our results and to verify the hypothesis on which the EXEM is based. The determination of fission and gamma-decay probabilities of 239Np below the neutron separation energy allowed us to validate the EXEM.

Measurement ofFe55(n,p)cross sections by the surrogate-reaction method for fusion technology applications

Measurement of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Fe</mml:mi><mml:mprescripts /><mml:none /><mml:mn>55</mml:mn></mml:mmultiscripts><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mo>)</mml:mo></mml:math>cross sections by the surrogate-reaction method for fusion technology applications

Calculations of Compound Nucleus Spin-Parity Distributions Populated via the (p,t) Reaction in Support of Surrogate Neutron Capture Measurements

The surrogate reaction method may be used to determine the cross section for neutron induced reactions not accessible through standard experimental techniques. This is achieved by creating the same compound nucleus as would be expected in the desired reaction, but through a different incident channel, generally a direct transfer reaction. So far, the surrogate technique has been applied with reasonable success to determine the fission cross section for a number of actinides, but has been less successful when applied to other reactions, e.g. neutron capture, due to a ‘spin-parity mismatch’. This mismatch, between the spin and parity distributions of the excited levels of the compound nucleus populated in the desired and surrogate channels, leads to differing decay probabilities and hence reduces the validity of using the surrogate method to infer the cross section in the desired channel. A greater theoretical understanding of the expected distribution of levels excited in both the desired and surrogate channels is therefore required in order to attempt to address this mismatch and allow the method to be utilised with greater confidence. Two neutron transfer reactions, e.g. (p,t), which allow the technique to be utilised for isotopes further removed from the line of stability, are the subject of this study. Results are presented for the calculated distribution of compound nucleus states populated in 90Zr, via the 90Zr(p,t)90Zr reaction, and are compared against measured data at an incident proton energy of 28.56 MeV.

Development of a measurement system for the determination of ([formula omitted]) cross-sections using multi-nucleon transfer reactions

We have installed a new experimental apparatus to measure γ-rays from highly excited states populated by the multi-nucleon transfer reactions with heavy-ion projectiles to determine the (n, γ) cross-sections by means of the surrogate reaction method. An apparatus consists of two anti-Compton LaBr3(Ce) spectrometers to measure the γ-rays and a Si ΔE–E detector system to detect outgoing projectile-like particles. Reactions of 153-MeV 18O beams with 155Gd and 157Gd targets were used to study the performance of apparatus. By using the LaBr3(Ce) scintillators with relatively large volume (101.6mm in diameter and 127mm in length), we have successfully measured γ-rays from the compound nuclei, which have excitation energy above neutron separation energy, populated by 155Gd(18O, 16O)157Gd and 157Gd(18O, 16O)159Gd two-neutron transfer reactions. To measure in-beam γ-rays through heavy-ion-induced transfer reaction, it is important to assign the reaction channel clearly, since the cross-sections of the transfer reactions are much smaller than those of competing reactions such as Coulomb excitation and fusion reactions. The Si ΔE–E detector system was used to separate outgoing particles. The present study has demonstrated high capability of apparatus to measure the de-excitation γ-rays in the compound nuclei produced by the multi-nucleon transfer reactions for determination of the (n, γ) cross-sections by using the surrogate reaction method.