183W
Tungsten is not an active element in nuclear reactors, but, because of its chemical and mechanical properties [1], it is used in many alloys. The interaction of neutrons with tungsten is therefore of importance for reactor physics, in particular for fusion reactors [2], in which tungsten is one of the most exposed materials to high energy neutrons. From a theoretical point of view, a better description of \((\text{n},~x\text{n})\) reactions on tungsten nuclei allows an improvement of models for other key nuclei in reactor fuel. Indeed, tungsten isotopes are deformed like actinides [3], but also easier to describe as they do not present a neutron-induced fission channel (theoretical fission barrier for Tungsten isotopes is around 21 MeV [4]). Still, there are very few measurements available today to test evaluations. Our experimental data [5] will provide an extensive and constraining test to the predictability of models. Figure 4 shows a simplified level scheme for the isotope.
Data for the naturally occurring even-even isotopes (182, 184 and 186) have already been published [6], [5], and [7]. The same setup has been used to record data with a 183W target. The experimental cross-sections for the odd-N isotope will bridge the gap between 182 and 184W by connecting the \((\text{n},~\text{n}')\) and \((\text{n},~2\text{n})\) channel of the three isotopes together. (Note: the \(^\text{184}\text{W}(\text{n},~2\text{n})\) cross section has not yet been analyzed.) Furthermore, because of the unpaired nucleon in 183W, this isotope offers unique insights into nuclear structure, reactions, and forces, and the experimental \((\text{n},~x\text{n}~\gamma)\) cross section will be very valuable to improve our understanding of nuclear reactions and structure.
Figure 4 Simplified level scheme for 183W.
The 5.30 seconds, \(\tfrac{11}{2}^{+}\) isomeric level at 309.5 keV is represented in red, with all transitions below in red too.
The transitions studied in this work are in blue.
For readability, some transitions of low intensity have been ignored.
Level scheme drawn with pylevelscheme [8].
Current knowledge
At the present time (spring 2024), there is only a limited amount of data available on pure neutron induced reactions on 183W (that excludes ratios, …).
In particular, no data is reported in the Exfor database for inelastic scattering \((\text{n},~\text{n}')\) and just a couple of data set exists for partial cross sections in the inelastic channel.
\((\text{n},~2\text{n})\) cross section data
J.Frehaut, et al. [9] measured the \((\text{n},~2\text{n})\) cross section off 183W (along with many other isotopes) in 1974 with neutrons in the range 7 to 15 MeV (Figure 5).
Figure 5 Current experimental data points for \((\text{n},~2\text{n})\) data [9], compared with several evaluations. (Data obtained from Exfor and ENDF.)
The evaluations are overall compatible with experimental data, although there is a spread in model values in the 6 to 12 MeV neutron energy range.
\((\text{n},~\text{n}'~\gamma)\) data
Exfor lists one data set related to \((\text{n},~\text{n}'~\gamma)\) cross section. The 1996 data [10] is presented as the cross section of \(210 \pm 30~\text{keV}\) \(\gamma\) rays (detected with NaI scintillator) at \(E_\text{n} = 3~\text{MeV}\). The \(210 \pm 30~\text{keV}\) energy can be matched to 8 \(\gamma\) rays in the output of Talys calculations [11] for \((\text{n},~\text{n}')\) reaction on 183W (a few more transitions with energy within the 30 keV range around 210 keV can be found, from high excitation energy states or stopped by long live isomers):
decay from the 208.8 keV \(\tfrac{3}{2}^{-}\) state to the ground state (\(E_\gamma =\) 208.8 keV),
from the 291.7 keV \(\tfrac{5}{2}^{-}\) state to the 99 keV \(\tfrac{5}{2}^{-}\) one (\(E_\gamma =\) 192.6 keV),
from the 308.9 keV \(\tfrac{9}{2}^{-}\) state to the 291.7 keV \(\tfrac{5}{2}^{-}\) one (\(E_\gamma =\) 209.9 keV),
from the 412.1 keV \(\tfrac{7}{2}^{-}\) state to the 208.8 keV \(\tfrac{3}{2}^{-}\) one (\(E_\gamma =\) 203.3 keV),
from the same \(\tfrac{7}{2}^{-}\) state to the 207.0 keV \(\tfrac{7}{2}^{-}\) one (\(E_\gamma =\) 205.1 keV),
from the 739.95 keV \(\tfrac{11}{2}^{-}\) state to the 551.2 keV \(\tfrac{9}{2}^{-}\) one (\(E_\gamma =\) 188.8 keV),
from the 849.9 keV \(\tfrac{15}{2}^{-}\) state to the 631.1 keV \(\tfrac{13}{2}^{-}\) one (\(E_\gamma =\) 219.4 keV),
and from the 965.13 keV \(\tfrac{15}{2}^{-}\) state (at 973.9 keV according to the Talys structure file) to the 766.3 keV \(\tfrac{11}{2}^{-}\) one (772 keV in Talys) (\(E_\gamma =\) 198.6 keV (201.9 keV in Talys)).
The quoted cross section in the Exfor entry is \(2523 \pm 730~\text{mbarns}\) [10]. This value is of the order of the total \((\text{n},~\text{n}')\) cross section (as shown in Figure 6), but is much lower than the sum of all possible \(210 \pm 30~\text{keV}\) \(\gamma\) contributions. Different Talys calculations lead to the same results, so the discrepancy does not come from specific parameters in the computation.
Figure 6 Experimental data from the I. Lashuk, 1996’s data [10], as seen in Exfor. The data point is compared to Talys calculations by P. Romain [11]. The transitions matching the \(210 \pm 30~\text{keV}\) criteria are plotted in full color line. The sum of these \((\text{n},~\text{n}'~\gamma)\) cross sections is in full black line. The sum of transitions cross sections (corrected for electronic conversion) is in full gray line. The total \((\text{n},~\text{n}')\) cross section is in dashed blue line.
Unfortunately, when compared to \(\gamma\) ray cross section (predicted by Talys), there’s no obvious match (Figure 6). As the original paper cited as source in Exfor is not available [12], it’s difficult to conclude about this, but we can guess there’s an error somewhere, whether in the numerical value, in the actual quantity reported, …
Note
This case is actually an example why the integration of data in the Exfor database is not enough to ensure that the data can be understood later. The Exfor format may not contain all the information needed to interpret the value. Or the referenced articles might not be available anymore (or be very hard to find).
Population of an isomer in \((\text{n},~\text{n}')\) reactions
The final data set of interest available in Exfor is an isomer decay cross-section at 14.6 MeV. The \(\tfrac{11}{2}^{+}\) state at 309.5 keV has a 5.30 seconds lifetime and the production has been measured by B. Anders, et al. [13], [14]. The reference states a \(127 \pm 14\) mbarns for the 108 keV \(\gamma\) ray (which decays from the \(\tfrac{7}{2}^{-}\) state at 207 keV, which is fed by the only transition decaying from the \(\tfrac{11}{2}^{+}\) isomer state). In Figure 7, we compare the data point to Talys predictions for the direct excitation of the \(\tfrac{11}{2}^{+}\) state, the total cross section of populating the \(\tfrac{11}{2}^{+}\) (either directly or from feeding by states above), and the 108 keV \(\gamma\) ray, with a very different value predicted by the code. However, the fact that this is an isomer may confuse the code and the outputted cross section might not be the same quantity as has been measured. We note that the value by [14] is on the same order of magnitude than the plateau cross section at lower incident neutron energy, so, some interpretation of the effective energy of the interaction might be playing an effect here.
Figure 7 Current experimental data point [13] and [14] for \((\text{n},~\text{n}')\) reaction on the \(\tfrac{11}{2}^{+}\) isomeric level, compared with Talys calculations [11].
\((\text{n},~\text{n}'~\gamma)\) cross sections measurements for 183W
Using Grapheme, the neutron inelastic scattering off 183W was investigated by measuring \((\text{n},~\text{n}'~\gamma)\) cross sections.
The data presented later, will fill a gap in the (as we saw) sparse data on \((\text{n},~\text{n}')\) reaction. Furthermore, in conjunction with \((\text{n},~\text{n}'~\gamma)\) and \((\text{n},~2\text{n}~\gamma)\) on even-even isotopes [5] (in particular 182W and 184W) will allow a chaining of experimental results along the isotopic chain, thanks to overlapping \((\text{n},~\text{n}'~\gamma)\) and \((\text{n},~2\text{n}~\gamma)\) measurements.
This will provide a valuable data set to constrain the models and parameters for the reactions code.
Footnotes