Improved ${}^{95}\mathrm{Mo}$ neutron resonance parameters and astrophysical reaction rates

Background: Improved ${}^{95}\mathrm{Mo}$ neutron resonance parameters and reaction rates are important for nuclear astrophysics, testing nuclear models, and nuclear criticality safety. However, despite many previous neutron-capture and total cross-section measurements on this nuclide, there still is much room for improvement as well as several discrepancies. For example, there are very few firm resonance spin and parity assignments; average resonance parameters are available only for each parity, the currently recommended astrophysical reaction rate results in disagreements between stellar models and meteoric isotopic anomalies, and there are substantial disagreements in the neutron-capture cross section at low energies important for nuclear criticality safety.

Purpose: To obtain an improved set of neutron resonance parameters and astrophysical reaction rates for ${}^{95}\mathrm{Mo}$.

Method: High-resolution neutron-capture and transmission data were measured at the Oak Ridge Electron Linear Accelerator (ORELA) using highly isotopically enriched ${}^{95}\mathrm{Mo}$ samples. The neutron-capture apparatus, data reduction, and analysis were improved so that information contained in the $\gamma$-ray cascade following neutron capture were used to assign resonance $J^{\pi }$ values. Following this, simultaneous analysis of the new neutron-capture and transmission data was used to obtain resonance energies, gamma widths, and neutron widths and their uncertainties to a maximum energy of 10 keV. Accurate neutron-capture cross sections also were obtained for the unresolved resonance region to a maximum energy of 500 keV and, together with the new resonance parameters, used to calculate the astrophysical reaction rates in the temperature range from 5 to 30 keV.

Results: A vastly improved set of ${}^{95}\mathrm{Mo}$ neutron resonance parameters and an astrophysical reaction rate accurate to about 3% were obtained. Firm $J^{\pi }$ assignments were determined for 261 of the 314 observed resonances. This is a very large improvement over the previously published 32 firm $J^{\pi }$ assignments for 108 resonances. Also, the number of resonances having both firm $J^{\pi }$ assignments and ${\mathrm{\Gamma }}_{\gamma }$ values was increased by almost a factor of 24—from 11 to 261. Neutron- and total-radiation-width distributions and average resonance spacings, average total radiation widths, and neutron strength functions were obtained for the six different $s$- and $p$-wave possibilities. Parameters for the lowest $s$-wave resonance, which is most important for criticality benchmarks, were obtained with high accuracy.

Conclusions: Simple modification of the neutron-capture apparatus and expansion and improvement of data analysis techniques led to a large increase in firm $J^{\pi }$ assignments for ${}^{95}\mathrm{Mo}$ neutron resonances. The resulting astrophysical reaction rate is 20%–30% larger than the currently recommended rate at $s$-process temperatures, which should lead to better agreement between stellar models and meteoric isotopic anomalies. The neutron-capture cross section at low energies is substantially larger than recommended in the latest evaluation, which is problematical for criticality benchmarks. The average resonance spacing as a function of spin and parity is significantly different from current models. The total-radiation-width distributions are significantly broader than predicted by theory and show significant departures from the expected Gaussian shapes.

Figure 1

Singles:singles ratios ($J_1$) vs coincidences:coincidences ($J_2$) for all observed resonances (open blue circles with one-standard-deviation error bars), firm positive-parity resonances (solid green circles), and firm negative-parity resonances (red X's) for PH gates optimizing the separation of (previous firmly assigned) spin-2 and -3 resonances. A linear transformation was applied to the $J$ values in this figure as well as Figs. 2 and 3 so that the groups are centered at integer values between 1 and 4. See text for further details.

Figure 2

Singles:singles ratios ($J_1$) vs singles:coincidences ($J_3$) for all observed resonances (open blue circles with one-standard-deviation error bars), firm positive-parity resonances (solid green circles), and firm negative-parity resonances (red X's) for PH gates optimizing the separation of (previous firmly assigned) spin-2 and -3 resonances.

Figure 3

Weighted averages of the three spin indexes are shown as histograms for all resonances (solid blue), firm positive-parity resonances (dashed green), and firm negative-parity resonances (dot-dashed red).

Figure 4

Weighted averages of the three spin indexes vs weighted averages of the three parity indexes for all spin-2 and -3 resonances assigned firm parity. A linear transformation was applied to the spin index so that the groups are centered at 2 and 3. Similarly, a linear transformation was applied to the parity index so that the groups were centered at -1 and 1. See text for details.

Figure 5

⁹⁵Mo neutron transmissions (bottom) and capture cross sections (top) from 1.0 to 1.07 keV. Data are shown as solid blue circles with one-standard-deviation error bars, sammy R-matrix fits as red curves, and ENDF/B-VIII.0 [18] as dot-dash green curves.

Figure 6

⁹⁵Mo neutron transmissions (bottom) and capture cross sections (top) from 1.65 to 1.80 keV. Data are shown as solid blue circles with one-standard-deviation error bars, sammy R-matrix fits as red curves, and ENDF/B-VIII.0 [18] as dot-dash green curves.

Figure 7

⁹⁵Mo($n,\alpha$) cross sections [47] from 10 to 5.2 keV (the highest energy fitted in this work for this cross section). Data are shown as open blue circles with one-standard-deviation error bars and sammy R-matrix fits as red curves.

Figure 8

Cumulative ${\mathrm{\Gamma }}_{\gamma }$ distributions for resonances of each $J^{\pi }$. Data from the present work are shown as open blue circles with one-standard-deviation error bars. Solid curves depict Gaussian distributions resulting from a ML analysis of the data using the method of Ref. [51]. See text for details.

Figure 9

Reduced ${}^{95}\mathrm{Mo}(n,\gamma )$ cross sections averaged over coarse energy bins. Results from this work are shown as open blue circles (calculated via numerical integration) and green X's (calculated from the resonance parameters). Results from previous work [25, 53, 54] are shown as solid red diamonds, magenta crosses, and open black diamonds, respectively. One-standard-deviation statistical uncertainties are smaller than the size of the symbols for this work. Error bars depict statistical (total) uncertainties for Ref. [54] ([25]). No uncertainties were reported for Ref. [53].

Figure 10

Ratios of ${}^{95}\mathrm{Mo}(n,\gamma )$ astrophysical reaction rates. Ratios of this work to Refs. [25, 54, 59] are shown as solid blue circles, red X's, and green diamonds, respectively. Error bars depict one-standard-deviation uncertainties. The data points for Refs. [25, 59] have been offset slightly in temperature for clarity.

Figure 11

Reduced neutron widths ($g{\mathrm{\Gamma }}_n^0=g{\mathrm{\Gamma }}_n/\sqrt{E_n}$) vs $E_n$ for all resonances fitted in this work. Firm $s$- and $p$-wave resonances are shown as solid blue circles and solid red boxes, respectively, and tentative $s$- and $p$-wave resonances as open blue circles and open red boxes, respectively. An energy-dependent threshold used to guard against systematic errors due to missed small resonances and many of the resonances of uncertain parity are shown as the solid black curve. See text for details.

Figure 12

Nuclear level densities, calculated from the average resonance spacings in Table 3, for negative (solid blue circles) and positive (open red circles) parity. The solid green curve depicts a least-squares fit to the data, from which a spin-cutoff parameter of $\sigma =3.75\pm 0.94$ was extracted. Also shown are the level densities at Sn predicted by five nuclear-level-density models in talys 1.8. Note that talys 1.8 model-5-level densities have been divided by 4.0. See text for details.

Figure 13

Capture kernels for the 44.67-eV resonance from this and previous [22, 32, 33, 35, 36] work (solid blue circles with one-standard-deviation error bars) are compared to the most recent evaluated value [18] (solid red line).