Nuclear data for application

Today, nuclear production for electricity uses mainly the neutron induced fission of the 235 isotope of uranium (Z=92). This method of production has disadvantages: it requires isotopic enrichment in ²³⁵U and generates radioactive waste (fission fragments and actinides) for which no definitive solution yet exists. In order to imagine a sustainable and clean electronuclear cycle, new generation reactors are being studied [1]. These reactors will have to be adapted to meet economic constraints (reactor construction costs, reprocessing of used fuel), safety (accident prevention, proliferation) and sustainability (resources, waste storage). These new reactor concepts and new fuel cycles will produce fewer actinides, use other fissile nuclei (such as the isotopes ²³³U or ²³⁹Pu), or allow transmutation of waste.

The design of these systems requires precise numerical simulations in order to integrate all the mechanical, thermal and nuclear physics constraints and to ensure the safety conditions in their operation. These simulations use evaluated databases [2]^, [3]^, [4] which contain the physical quantities describing the various processes considered. They gather the cross sections, the angular distributions, the spectra of emitted particles… for the nuclear reactions induced by neutron or charged particles on the elements of the fuel or of the structure. These evaluations are the result of both theoretical and experimental work, and represent the best estimate of the value of these physical quantities. Sensitivity studies [5] show that the current uncertainties in the evaluated databases prevent reaching the expected accuracy objectives on the simulation of core parameters.

These uncertainties are explained by a lack of experimental data and by a need for theoretical developments for a better description of the reaction mechanisms. In order to consider industrial applications, the current uncertainties must be significantly reduced. This will necessarily require new measurement campaigns for the reactions of interest. The nuclear physics experiments will provide new constraints for the models and will allow improvements of the evaluations and the theoretical description of the processes of the nucleon-nucleus interaction.

Inelastic scattering

Among the reactions that take place in the reactor, the inelastic neutron scatterings \((\text{n},~x\text{n})\) are important. Indeed, they modify the energy distribution and the number of neutrons, and, for \(x > 1\), create new isotopes in the medium. They therefore have a significant impact on the behavior of the reactor. However, the effective cross sections of reactions \((\text{n},~x\text{n})\) on uranium isotopes are only known with accuracies of \(20~\%\) in certain energy domains. This leads to significant uncertainties about the power, reactivity, or criticality of next-generation reactors. For example, sensitivity studies [5] have determined that the uncertainty in the neutron multiplication factor k_eff in new lead-cooled fast reactor designs is \(1.4~\%\) in total, of which \(0.7 \%\) is due to the inelastic scattering cross section on the ²³⁸U core (see reference [5] and Figure 1).

../_images/sg26uncertainty.png — Figure 1 Break down of uncertainty contributions (in %) associated with the total combined uncertainty on the k_eff of a Gas Fast Reactor (GFR) by isotope and reaction channel. (From reference [5].)

These uncertainties come, for one part, from a lack of experimental data (see Figure 2) to constrain the evaluation, and, on the other hand, from deficiencies in models. To improve the reaction models and their ingredients (level density, transition strength functions, …) theoretical work is needed, but this work requires new, more microscopic data to guide and/or test the new reaction description.

../_images/X4sPlotZvd2.png — Figure 2 Cross section of inelastic neutron scattering off Uranium 238 according to four principal evaluations (JEFF-3.3 [3] and TENDL-2021 [7] are the same), compared with the experimental data (data collected from Exfor and ENDF).

Following sensitivity analysis works [5], one can establish a list of required improvement, with target uncertainty in the final evaluation. The NEA Nuclear Data High Priority Request List [6] is such a list, compiling the nuclei and reactions of interest to be improved, including quantity (cross-section, yield, angular distribution…), energy range and motivation. For example, request number 18H lists the inelastic neutron scattering off ²³⁸U cross-section as a quantity of interest.

Recently, the importance of quality nuclear structure information for reliable nuclear data as emerged. Indeed, in experiments, or in the evaluation process, the level scheme of the nucleus is often used as input to interpret or process the measured data. Unfortunately, just as the reaction databases may present defaults, nuclear structure databases [8]^, [9] also present uncertainties and holes in the level schemes of nuclei of interest [10]. It’s typical to observe transitions with large uncertainties on intensities, or just a limit on the intensity given, as well as noting a significantly low number of states listed in certain spin/parity/excitation energy regions [11]. This will have an impact on the accuracy of the derived nuclear data, even if the underlying experimental data has a very good precision [10].

Nuclear Data study program at IPHC

The Nuclear Data for Reactors group (DNR, formerly “Grace”) at the IPHC [12] has started since 2000 a program of measurements and studies of \((\text{n},~x\text{n}~\gamma)\) reactions. The experiments are carried out at the Gelina neutron beam at the JRC-Geel (Belgium) [13]^, [14]^, [15] with the GeRmanium array for Actinides PrEcise MEasurements (Grapheme), seen in Figure 3 and, later, Figure 12. The latter consists (today) of 6 planar germanium detectors - one of which is segmented into 36 pixels, connected to digital electronics [16].

../_images/100_0094.jpg — Figure 3 Photography of Grapheme in 2010, at the time when the data analyzed later in this manuscript was recorded. The liquid nitrogen dewars of the HPGe detectors can be seen sticking out of a lead and copper castle shield, with the active Ge crystal being inside, surrounding the target. The neutron beam comes, in the air, from the right and pass through a gap in the shielding (not distinguishable on the picture).

The experimental method combines prompt \(\gamma\)-ray spectroscopy with time-of-flight neutron energy measurement [17]^, [18]. The accuracy on the measured \((\text{n},~\text{n}'~\gamma)\) cross sections is \(3 \text{-} 15~\%\) depending on the considered \(\gamma\) ray, the neutron energy , …

The \((\text{n},~\text{n}')\) and \((\text{n},~2\text{n})\) reactions were studied on the isotopes of ^natZr, ^{nat,182,183,184,186}W [19], ^233,235,238U [20]^, [21], and ²³²Th [22].

The experimental \((\text{n},~x\text{n}~\gamma)\) cross sections are compared to model predictions and used to improve reaction codes such as Talys [23]^, [24], Empire [25], or CoH3 [26]. The interpretation of differences between measures and calculations is a way to reveal the points needing refinement in the codes. In particular, we showed, first in ²³⁸U [20], then in even-even tungsten isotopes [27], the importance of the spin distribution in the pre-equilibrium steps of the reaction modeling [28].

Important

One of the key issues in producing experimental values is to publish them with their uncertainties (and covariances) so that they can be fully exploited during evaluation. And beyond just giving the uncertainties and covariances, the method for obtaining them needs to be clearly explained, so that evaluators can take them properly into account in their work. (See later, The important thing about uncertainties)

The work presented in this manuscript offers one way to produce such experimental results, along with methods and tools to make the process accessible to be studied.

Perspective for the DNR group

In the near future, the DNR team will follow several research paths.

First, at Gelina, data as been recorded for ²³³U and results will be published soon [29]. Data taking for the experimental study of \((\text{n},~x\text{n}~\gamma)\) reactions on a ²³⁹Pu target is in progress (since mid-2023, including lengthy technical beam shutdown periods).

Additionally, to study the highly converted transitions in the actinides, not available experimentally in \((\text{n},~x\text{n}~\gamma)\) study, we are developing, in collaboration with Ifin-HH and JRC-Geel, the Delco setup (Detecteur d’ELectrons de COnversion) [30].

Finally, the new neutron beam facility NFS at Ganil recently started operations. The neutron beam there has an average energy higher than the one at Gelina and this will allow us to study \((\text{n},~2\text{n})\) and \((\text{n},~3\text{n})\) reactions [31]^, [32].

Important

For these future works, the availability of the full Monte Carlo analysis code described in this manuscript will be an asset. First, because it is designed to be flexible and accommodate more detector inputs, or in different file format. Then, because it will be completely open, with a detailed documentation, it will meet the criteria for accurate and meaningful evaluation of experimental values.

Footnotes