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Constraining capture cross sections using proton inelastic scattering as a surrogate reaction

Aaina Thapa, Jutta Escher, Emanuel Chimanski, Oliver Gorton, Marc Dupuis, Eun Jin In, Shuya Ota, Sophie Péru, Walid Younes

TL;DR

The paper tackles the challenge of obtaining neutron-capture cross sections for unstable nuclei by developing a surrogate-reaction framework using proton inelastic scattering to infer Hauser-Feshbach decay probabilities. It introduces new theory tools to extract $^{89}$Zr$(n,\gamma)$ and $^{89}$Y$(p,\gamma)$ cross sections from $^{90}$Zr$(p,p'\gamma)$ surrogate data, including (i) a calculation of the spin-parity population $F_{p,p'}^{CN}(E_{ex}, J, \pi)$ from one- and two-step processes and (ii) a Markov Chain Monte Carlo (MCMC) inference of nuclear level density (NLD) and gamma-ray strength functions (GSF), with Porter-Thomas fluctuations accounted for. Applying the method to the surrogate data yields constrained $\Gamma_\gamma$ and $D_0$, and cross sections for $^{89}$Y$(p,\gamma)$ and $^{89}$Zr$(n,\gamma)$ that agree with evaluated libraries where available and provide new predictions otherwise; the results are sensitive to the low-energy behavior of the $M1$ strength and to the proton optical-model potential. By quantifying these uncertainties and incorporating two-step surrogate pathways, the approach reduces Hauser-Feshbach uncertainties in regions of low level density and near shell closures, enabling more reliable predictions for exotic isotopes.

Abstract

The surrogate reaction method is an alternative to direct measurements of compound nuclear reaction cross sections. We introduce theory tools for extracting capture cross sections from experiments that use proton inelastic scattering as a surrogate reaction mechanism. This makes it possible to constrain compound nucleus decay models which are typically the largest source of uncertainty in capture cross section calculations. This letter describes the theory developments that were used to simultaneously infer $^{89}$Y$(p,γ)$ and $^{89}$Zr$(n,γ)$ cross sections from $^{90}$Zr$(p,p'γ)$ surrogate measurements.

Constraining capture cross sections using proton inelastic scattering as a surrogate reaction

TL;DR

The paper tackles the challenge of obtaining neutron-capture cross sections for unstable nuclei by developing a surrogate-reaction framework using proton inelastic scattering to infer Hauser-Feshbach decay probabilities. It introduces new theory tools to extract Zr and Y cross sections from Zr surrogate data, including (i) a calculation of the spin-parity population from one- and two-step processes and (ii) a Markov Chain Monte Carlo (MCMC) inference of nuclear level density (NLD) and gamma-ray strength functions (GSF), with Porter-Thomas fluctuations accounted for. Applying the method to the surrogate data yields constrained and , and cross sections for Y and Zr that agree with evaluated libraries where available and provide new predictions otherwise; the results are sensitive to the low-energy behavior of the strength and to the proton optical-model potential. By quantifying these uncertainties and incorporating two-step surrogate pathways, the approach reduces Hauser-Feshbach uncertainties in regions of low level density and near shell closures, enabling more reliable predictions for exotic isotopes.

Abstract

The surrogate reaction method is an alternative to direct measurements of compound nuclear reaction cross sections. We introduce theory tools for extracting capture cross sections from experiments that use proton inelastic scattering as a surrogate reaction mechanism. This makes it possible to constrain compound nucleus decay models which are typically the largest source of uncertainty in capture cross section calculations. This letter describes the theory developments that were used to simultaneously infer Y and Zr cross sections from Zr surrogate measurements.

Paper Structure

This paper contains 6 sections, 3 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Surrogate Reaction Theory
  3. Calculating the spin-parity population $F_{p,p'}^{\rm{CN}} (E_{\rm{ex}}, J, \pi)$
  4. Constraining the nuclear level density (NLD) and the $\gamma$-ray strength functions (GSF)
  5. Results
  6. Summary and Outlook

Figures (4)

  • Figure 1: The spin-parity population, $F_{p,p'}^{\rm{CN}} (E_{\rm{ex}}, J, \pi)$, from both one-step inelastic scattering (solid bars) and two-step $(p,d)(d,p')$ process (hatched bars). It shows that the 1- states are most likely to be populated in the $^{90}$Zr nucleus near $S_n$, followed by the $3-$ and $5-$ states. The angular momentum quantum number for the excited states is shown on $x$-axis and the $y$-axis gives the probability of populating a particular $J,\pi$ state at 12 MeV excitation energy in $^{90}$Zr.
  • Figure 2: Comparison between modeled and measured coincidence probabilities, $P_{p'\gamma} (E_{\rm{ex}})$, as a function of the excitation energy, $E_{\rm{ex}}$, for discrete transition in $^{90}$Zr (indicated on each subplot). The black curve is the median, dark grey and light grey are the $68\%$ and 98% confidence bands of the MCMC posterior, respectively. The vertical dashed-line marks the neutron separation energy $S_n$ for $^{90}$Zr and the horizontal dotted line shows the excitation energy range for which fitting is performed in the MCMC run.
  • Figure 3: (a) The $E$1 $+ M$1 GSFs obtained from the MCMC fit to the surrogate data (black curve with 68% and 98% grey uncertainty bands) compared to data from references netterdon-2015Fedorets_2013PDR-2008GS-1979. (b) Proton capture cross sections obtained from the surrogate fit with 68% and 98% light brown and peach bands, respectively. The brown (black) solid curve and bands were obtained with the models described in section \ref{['fit']}. The black curve (along with the dark grey 68% and light grey 98% uncertainty bands) is the result of a fit without including an M1 upbend in fitting NLD and GSF to the surrogate data. Dots show experimental data from references netterdon-2015Y89pg-2Y89pg-3.
  • Figure 4: The brown (black) curve shows our extracted $^{89}$Zr$(n,\gamma)$ cross section. The light brown (dark grey) and peach (dim grey) shaded areas give the 68% and 98% confidence bands based on the MCMC posterior from fitting to the surrogate data with (without) an upbend in the M1-strength function included. Our results are compared to the nuclear data evaluations JENDL-5.0 (dashed-dotted) JENDL5, JEFF-3.3 (dotted) JEFF3 and TENDL-astro-2023 (dashed) TENDL-2023.