New experimental constraint on the ${}^{185}\mathrm{W}(n,\gamma ){}^{186}\mathrm{W}$ cross section

In this work, we present new data on the ${}^{182,183,184}\mathrm{W}(\gamma ,n$) cross sections, utilizing a quasi-monochromatic photon beam produced at the NewSUBARU synchrotron radiation facility. Further, we have extracted the nuclear level density and $\gamma$-ray strength function of ${}^{186}\mathrm{W}$ from data on the ${}^{186}\mathrm{W}(\alpha ,{\alpha }^{\prime }\gamma ){}^{186}\mathrm{W}$ reaction measured at the Oslo Cyclotron Laboratory. Combining previous measurements on the ${}^{186}\mathrm{W}(\gamma ,n$) cross section with our new ${}^{182,183,184}\mathrm{W}(\gamma ,n$) and ($\alpha ,{\alpha }^{\prime }\gamma ){}^{186}\mathrm{W}$ data sets, we have deduced the ${}^{186}\mathrm{W}\gamma$-ray strength function in the range of $1<E_{\gamma }<6$ MeV and $7<E_{\gamma }<14$ MeV. Our data are used to extract the level density and $\gamma$-ray strength functions needed as input to the nuclear-reaction code talys, providing an indirect, experimental constraint for the ${}^{185}\mathrm{W}(n,\gamma ){}^{186}\mathrm{W}$ cross section and reaction rate. Compared to the recommended Maxwellian-averaged cross section (MACS) in the KADoNiS-1.0 database, our results are on average lower for the relevant energy range $k_{B}T\in [5,100]$ keV, and we provide a smaller uncertainty for the MACS. The theoretical values of Bao et al. [At. Data Nucl. Data Tables 76, 70 (2000)] and the cross section experimentally constrained on photoneutron data of Sonnabend et al. [Astrophys. J. 583, 506 (2003)] are significantly higher than our result. The lower value by Mohr et al. [Phys. Rev. C 69, 032801(R) (2004)] is in very good agreement with our deduced MACS. Our new results provide an improved uncertainty estimate for the ($n,\gamma ){}^{186}\mathrm{W}$ reaction rate, which is one important ingredient in simulations for investigating the neutron density and the ${}^{186,187}\mathrm{Os}$ production in the $s$ process.

Figure 1

Schematic illustration of the nuclear chart in the W-Re-Os region. The black arrows indicate $(n,\gamma )$ reactions on stable or near-stable isotopes, the blue dashed arrows show the possible $(n,\gamma )$ branch on the long-lived W, Re, and Os isotopes, while the pink arrows display the ${\beta }^{-}$ decay branch.

Figure 2

A schematic illustration of the experimental set up at NewSUBARU used in the ($\gamma ,n$) cross-section measurements.

Figure 3

The simulated energy profiles for the $\gamma$ beams used. The distributions (integrated over all $E_{\gamma }$) are normalized to unity.

Figure 4

Monochromatic cross sections of ${}^{182,183,184}\mathrm{W}$. The error bars contain statistical uncertainties from the number of detected neutrons, the uncertainty in the efficiency of the neutron detector and the uncertainly in the pile-up method used to determine the integrated $\gamma$ flux on target.

Figure 5

Cross sections of ${}^{182,183,184}\mathrm{W}$ obtained after deconvolution. Also shown are cross sections of ${}^{182,184}\mathrm{W}$ from Goryachev et al. [35].

Figure 6

(a) Particle-identification spectrum for one of the front strips at ${130}^{\circ }$ with its corresponding back detector ($\mathrm{\Delta }E\text{−}E$ banana plot); (b) a zoom on the $\alpha$-particle banana with the qkinz calculations used for calibration (crosses).

Figure 7

Excitation-energy vs. $\gamma$-ray energy matrices of ${}^{186}\mathrm{W}$. (a) Background-subtracted data; (b) unfolded $\gamma$-ray spectra; (c) first-generation $\gamma$-ray spectra. The lines indicate the limits set for the further analysis.

Figure 8

Experimental first-generation spectra (black crosses) compared to the predicted ones using the extracted level density and $\gamma$-transmission coefficient (blue line) for various excitation-energy bins (224-keV wide).

Figure 9

Normalized level density of ${}^{186}\mathrm{W}$. The discrete levels [57] are binned with the same bin size as our data (224 keV/channel). The dashed line shows the CT-model interpolation between our data and $\rho \left(S_n\right)$. The black error bars represent statistical uncertainties from the experiment and systematic errors connected to the unfolding procedure and the first-generation method. The blue band includes also systematic errors from the normalization procedure (see text).

Figure 10

$\gamma$-ray transmission coefficient of ${}^{186}\mathrm{W}$ before normalization. The arrows indicate the fit regions used for determining the extrapolations (see text). The gray data points are not considered further in the analysis due to very low statistics in the first-generation matrix for these $\gamma$ energies.

Figure 11

$\alpha$-ray strength function of ${}^{186}\mathrm{W}$. The black error bars represent statistical uncertainties from the experiment and systematic errors connected to the unfolding procedure and the first-generation method. The blue band includes also systematic errors from the normalization procedure (see text).

Figure 12

Comparison of the level-density data from this work with models included in the talys code (see text).

Figure 13

(a) Comparison of $\gamma$-strength data from this work with data from the literature (Berman et al. [80], Mohr et al. [9], and Kopecky et al. [81]), and to models included in the talys code (see text); (b) fit to the $\gamma$-ray strength function data of ${}^{186}\mathrm{W}$ and the ${}^{184}\mathrm{W}$ data of Kopecky et al. [81]) (see text).

Figure 14

Maxwellian-averaged cross section for the ${}^{185}\mathrm{W}(n,\gamma$) reaction. The shaded band indicates the present data-constrained MACS. The thick, azure dashed-dotted line shows the talys result using default input, the thin, azure dashed lines show the talys MACS when varying the level-density models, and the thin, cyan lines show the variation due to different $\gamma$-strength models. The dotted line shows the deviation from the default when using the optical-model potential of Bauge et al. [91].

Figure 15

Reaction rate for the ${}^{185}\mathrm{W}(n,\gamma$) reaction. The shaded band indicates the present data-constrained result. See also the caption of Fig. 14.