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Extraction of neutron-capture cross sections on $^{92}$Zr using the charge-exchange Oslo method

N. D. Pathirana, R. G. T. Zegers, B. Gao, A. Spyrou, A. C. Larsen, H. Berg, D. Bazin, H. L. Crawford, A. Gade, P. Gastis, T. Ginter, C. J. Guess, M. Guttormsen, S. Noji, B. Longfellow, J. Pereira, L. A. Riley, D. Weisshaar, J. C. Zamora

TL;DR

This work introduces and validates the charge-exchange Oslo method, extending the Oslo technique to intermediate-energy CE reactions to extract nuclear level densities and γ-ray strength functions. By applying it to the $^{93}$Nb($t$,$^{3}$He) reaction populating $^{93}$Zr, the authors obtain ρ and the γSF, including a low-energy $M1$ upbend, and then infer the indirect cross section for $^{92}$Zr($n$,$γ$)$^{93}$Zr. The results show good agreement with direct measurements at low neutron energies and yield Maxwellian-averaged cross sections consistent within uncertainties at higher temperatures, though the upbend substantially affects the low-energy capture cross section. The study demonstrates a powerful, simultaneous probe of ($n$,$γ$) cross sections and Gamow-Teller strengths, with potential extensions to inverse-kinematics reactions on unstable nuclei for astrophysical applications.

Abstract

The $^{93}$Nb($t$,$^{3}$He) reaction at 115 MeV/u was studied to demonstrate that nuclear level densities and $γ$-ray strength functions can be extracted from charge-exchange reactions at intermediate energies using the Oslo technique. The matrix of excitation energy in $^{93}$Zr, reconstructed from the ($t$,$^{3}$He) reaction, versus the energy of $γ$ rays emitted by the excited $^{93}$Zr nuclei, was obtained in an experiment with the S800 Spectrograph operated in coincidence with the GRETINA $γ$-ray detector. The extracted level density and $γ$-ray strength function obtained by applying the Oslo method to this matrix were used to estimate the $^{92}$Zr($n$,$γ$)$^{93}$Zr cross section by combining the new results with other experimental data and theoretical calculations for $E$1 and $M$1 strength functions at higher energies. Good agreement with direct measurements of the $^{92}$Zr($n$,$γ$)$^{93}$Zr cross section was found. The contribution from the upbend in the extracted $γ$-ray strength function was important to achieve the consistency as the neutron-capture cross section without this contribution is significantly below the direct measurements otherwise. Since charge-exchange reactions at intermediate energies have long been used for extracting Gamow-Teller strengths, the successful demonstration of the charge-exchange Oslo method enables experiments in which ($n$,$γ$) cross sections and Gamow-Teller strengths can be measured simultaneously, which is of benefit for astrophysical studies.

Extraction of neutron-capture cross sections on $^{92}$Zr using the charge-exchange Oslo method

TL;DR

This work introduces and validates the charge-exchange Oslo method, extending the Oslo technique to intermediate-energy CE reactions to extract nuclear level densities and γ-ray strength functions. By applying it to the Nb(,He) reaction populating Zr, the authors obtain ρ and the γSF, including a low-energy upbend, and then infer the indirect cross section for Zr(,)Zr. The results show good agreement with direct measurements at low neutron energies and yield Maxwellian-averaged cross sections consistent within uncertainties at higher temperatures, though the upbend substantially affects the low-energy capture cross section. The study demonstrates a powerful, simultaneous probe of (,) cross sections and Gamow-Teller strengths, with potential extensions to inverse-kinematics reactions on unstable nuclei for astrophysical applications.

Abstract

The Nb(,He) reaction at 115 MeV/u was studied to demonstrate that nuclear level densities and -ray strength functions can be extracted from charge-exchange reactions at intermediate energies using the Oslo technique. The matrix of excitation energy in Zr, reconstructed from the (,He) reaction, versus the energy of rays emitted by the excited Zr nuclei, was obtained in an experiment with the S800 Spectrograph operated in coincidence with the GRETINA -ray detector. The extracted level density and -ray strength function obtained by applying the Oslo method to this matrix were used to estimate the Zr(,)Zr cross section by combining the new results with other experimental data and theoretical calculations for 1 and 1 strength functions at higher energies. Good agreement with direct measurements of the Zr(,)Zr cross section was found. The contribution from the upbend in the extracted -ray strength function was important to achieve the consistency as the neutron-capture cross section without this contribution is significantly below the direct measurements otherwise. Since charge-exchange reactions at intermediate energies have long been used for extracting Gamow-Teller strengths, the successful demonstration of the charge-exchange Oslo method enables experiments in which (,) cross sections and Gamow-Teller strengths can be measured simultaneously, which is of benefit for astrophysical studies.

Paper Structure

This paper contains 7 sections, 13 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Experiment
  3. CE-Oslo Method
  4. Normalization of the NLD and $\gamma$SF
  5. Neutron Capture Cross Sections
  6. Summary and Outlook
  7. Acknowledgements

Figures (5)

  • Figure 1: (a) Experimental $E_{x}$--$E_{\gamma}$ particle-$\gamma$ coincidence raw matrix for the $^{93}$Nb($t$,$^{3}$He$+\gamma$) reaction. The x-axis bin size is 10 keV, while the y-axis bin size is 100 keV. The dashed black line represents the neutron separation energy in $^{93}$Zr. The excitation energy was measured up to $E_{x}(^{93}\mathrm{Zr}) = 30$ MeV as shown in the figure. However, only excitation energies up to 7.2 MeV were included in the CE-Oslo analysis; (b) the GRETINA response function obtained from the UCGRETINA simulation. The x-axis bin size is 10 keV, while the y-axis bin size is 10 keV; (c) the $E_{x}$--$E_{\gamma}$ matrix after unfolding of the detector response. The x-axis bin size is 500 keV, while the y-axis bin size is 500 keV; (d) primary $E_{x}$--$E_{\gamma}$ matrix, which is used in the CE-Oslo method. The x-axis bin size is 500 keV, while the y-axis bin size is 500 keV. The area within the solid red lines indicates the region used for the extraction of the NLD and the $\gamma$SF through the Oslo analysis.
  • Figure 2: The normalized NLD of $^{93}$Zr extracted from the CE-Oslo analysis. Level densities of known discrete levels with spins ranging from $J$ = 3/2 to $J$ = 15/2 are represented by a solid blue line. The lower pair of arrows indicates the region used for normalization. The adjusted NLD for $3/2 \leq J \leq 15/2$ at the $S_{n}$, extracted from neutron resonance data, is indicated with an open square. The NLD fitted to the data using the Constant Temperature model is represented by a dashed black line, with the higher pair of arrows indicating the fitting region. The total uncertainty in the extracted NLD, accounting for both systematic and statistical errors, is illustrated by the cyan shaded area.
  • Figure 3: The normalized CE-Oslo $f(E_{\gamma})$ of $^{93}$Zr (black solid circles) and the photo-absorption $f(E_{\gamma})$ of $^{92,94}$Zr (blue asterisks and purple stars, respectively) from Utsunomiya2008 are plotted. The uncertainty band is indicated in cyan. The dashed blue line, dash-dot green line, and the dotted pink line indicate the contributions from $E$1 de-excitations, $M$1 de-excitations, and the upbend, also assumed to be of $M$1 nature. The first two contributions come from the D1M+QRPA model of goriely2018.
  • Figure 4: The extracted CE-Oslo $^{92}$Zr($n,\gamma$)$^{93}$Zr cross sections are shown in a red solid line. The directly measured $^{92}$Zr$(n,\gamma)^{93}$Zr cross sections, obtained from OHGAMA2005Macklin1963, are included. The total uncertainty, which includes both the systematic and statistical uncertainties, is depicted by the cyan shaded area. The effect of removing the contribution from the upbend component in $f(E_{\gamma})$ to the $^{92}$Zr$(n,\gamma)^{93}$Zr cross sections is shown as a black dashed line.
  • Figure 5: The calculated CE-Oslo $^{92}$Zr($n,\gamma$)$^{93}$Zr Maxwellian averaged cross sections (MACS) are shown in a red solid line. The calculated $^{92}$Zr$(n,\gamma)^{93}$Zr Maxwellian-averaged cross sections, obtained from macklin1967BOLDEMAN1976Bao2000Tagliente2010Tagliente2022, are included. The total uncertainty, which includes both the systematic and statistical uncertainties, is depicted by the cyan shaded area.