First experimental constraint on the ${}^{191}\mathrm{Os}(n,\gamma )$ reaction rate relevant to $s$-process nucleosynthesis

The nuclear level density and $\gamma$-decay strength of ${}^{192}\mathrm{Os}$ have been extracted using particle-$\gamma$ coincidence data from the ${}^{192}\mathrm{Os}(\alpha ,{\alpha }^{\prime }\gamma ){}^{192}\mathrm{Os}$ reaction by means of the Oslo method. The level density is found to be a rather smooth function of excitation energy, approximately following the constant temperature model. The $\gamma$-decay strength is compared to photoneutron cross-section data above the neutron separation energy, and to $E1$ and $M1$ strengths for nuclei in this mass region derived from primary transitions following neutron capture. Our results are in good agreement with these previous data and draw a consistent picture of the $\gamma$-strength function in the range $E_{\gamma }\approx 1.5–6\mathrm{MeV}$. Using the measured nuclear level density and $\gamma$-decay strength as input to the nuclear-reaction code talys, we provide the first experimentally constrained Maxwellian-averaged cross section (MACS) for the ${}^{191}\mathrm{Os}(n,\gamma ){}^{192}\mathrm{Os}$ reaction relevant to $s$-process nucleosynthesis. The systematic uncertainties introduced by the normalization procedure of the level density and $\gamma$-strength function were investigated and propagated to the calculated Maxwellian-averaged cross section. The obtained result of the Maxwellian-averaged cross section at $k_{B}T=30\mathrm{keV}$, ${\langle \sigma \rangle }_{n,\gamma }=1134\pm 375\mathrm{mb}$, is in very good agreement with the theoretical estimate provided by the KADoNiS project, giving experimental support to the adopted KADoNiS value. Good agreement is also found with MACS values obtained from other libraries, such as TENDL-2017, ENDF/B-VII.0, and JEFF.

Figure 1

A section of the chart of nuclides indicating the $s$-process path with arrows. The stable (unstable) isotopes are displayed in black (blue), and a few rounded off half-lives adapted from [14] are presented in the vicinity of ${}^{192}\mathrm{Os}$ and ${}^{186}\mathrm{W}$. The red arrows suggest the $s$-process path given the activation of the ${}^{185}\mathrm{W}$ and ${}^{191}\mathrm{Os}$ branch points.

Figure 2

Excitation energy $E_x$ versus $\gamma$ energy $E_{\gamma }$ for ${}^{192}\mathrm{Os}$: (a) the original, (b) unfolded, and (c) first-generation matrices. The number of counts are represented by the color scale and the bin widths (see the text) are 32 and 80 keV for the $x$ and $y$ axes, respectively. In (a) and (b) the diagonal line $E_x=E_{\gamma }$ is displayed in red, and in (c) the black solid lines represent the limits included in the ${\chi }^2$-minimization method. Note that the bin values below the diagonal in (a) fluctuate around zero with counts $<10$. Before unfolding, all data points in the region below the diagonal plus the resolution of the NaI(Tl) detector $\delta E_{\gamma }$, i.e., counts below the line $E_x=E_{\gamma }+\delta E_{\gamma }$, were set to zero.

Figure 3

The level density at the separation energy $\rho \left(S_n\right)$ plotted against the neutron separation energy $S_n$. The mass numbers $A$ are annotated next to the data points. The values are calculated from evaluated experimental $D_0$ values (RIPL-3 [48], Mughabghab [49]) using spin cutoff parameters according to EB05/06 [47].

Figure 4

The scaling factor $b$ versus the ${\chi }^2$ value found by using evaluated experimental values from Mughabghab et al. (S.F.M.) [49] (green); see the text. The red line represents ${\chi }_{\min }^2+1$, and the blue lines present the $b$ values corresponding to $0.6{\rho }_{th}\left(S_n\right)$ and $1.4{\rho }_{th}\left(S_n\right)$.

Figure 5

The level density versus excitation energy for the Oslo data (black). The CT interpolation between the data and $\rho \left(S_n\right)$ (blue) is indicated by a red line in addition to the known levels (light blue).

Figure 6

The average radiative widths $\langle {\mathrm{\Gamma }}_{\gamma 0}\rangle$ at $S_n$ plotted against mass number $A$ for osmium (squares), tungsten (circles), rhenium (diamond), and iridium (cross). The data are collected from RIPL-3 [48], Mughabghab et al. [49] (S.F.M.), and the n_TOF Collaboration [52]. See the text for information on the linear regressions.

Figure 7

The $\gamma$-strength function (black) versus $\gamma$-ray energy obtained using the recommended $\langle {\mathrm{\Gamma }}_{\gamma 0}\rangle$ value at $S_n$. In addition, $(\gamma ,n)$ data (colors) from [53, 54] are presented. Systematic errors from the normalization procedure are not included.

Figure 8

The level density versus excitation energy for the Oslo data (black). The Oslo method errors combined with the systematic error estimate of the normalization parameters are presented as the light-blue colored band.

Figure 9

The $\gamma$-strength function (black) versus $\gamma$-ray energy for the Oslo data (black). The Oslo method errors combined with the systematic error estimate of the normalization parameters are presented as the light-blue colored band.

Figure 10

The $\gamma$-strength function versus $\gamma$-ray energy together with strength values of osmium (diamond), iridium (star), tungsten (circle), platinum (downward triangle), and gold (upward triangle) from Kopecky et al. [38] and Capote et al. [48]. The $E1$ (blue line) and $M1$ strengths (pink line) are estimated using a fit to the points shown in (a) and (b), respectively. The colored band represent the systematic and statistical uncertainties obtained in Sec. 3c.

Figure 11

The Maxwellian-averaged $(n,\gamma )$ cross section versus energy $k_{B}T$ at the stellar temperature $T$. The systematic and statistical uncertainties (blue band) of the recommended MACS for the ${}^{191}\mathrm{Os}(n,\gamma ){}^{192}\mathrm{Os}$ reaction are presented as the colored band. Values from a talys calculation done with default input is displayed in addition to several theoretical and evaluated libraries: the KADoNiS library [20], TENDL-2017 [62], ENDF/B-VII.0 [23], JEFF-3.0/A [24], JEFF-3.2 [24], and non-smoker [69].