# Neutron inelastic scattering

Maëlle Kerveno

► To cite this version:

Maëlle Kerveno. Neutron inelastic scattering. 7th International Workshop on Compound-Nuclear Reactions and Related Topics (CNR*24), AIEA, Jul 2024, Vienna, Austria. pp.08001, 10.1051/epj-conf/202532208001. hal-04996936

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# Neutron inelastic scattering

Maëlle Kerveno¹, *

¹Université de Strasbourg, CNRS, IPHC/DRS UMR 7178, 23 rue du Loess 67037 Strasbourg, France

**Abstract.** Neutron inelastic scattering is a process involved in many applications as nuclear energy or security and safeguard but also for background studies supporting more fundamental research area. In the fast energy range, it is one of the major nucleon-nucleus interactions and its cross section constantly increases above the threshold energy of the first excited state up to a few MeV. During these last decades, despite significant advances in modeling and experimental efforts, cross section calculations still pose a major challenge to nuclear theory and evaluated inelastic cross section are still not at the level of the required accuracy by applications. This contribution is an occasion to present the status of the current knowledge of the neutron inelastic scattering process and to mention how it impacts the field of nuclear energy applications. A description of the different experimental techniques is presented, highlighting some recent advances. Finally, challenges that still need to be met in order to provide accurate neutron inelastic cross sections, as well as current research tracks, will be discussed.

## 1 Introduction

Compared to neutron elastic scattering, neutron inelastic scattering, written (n, n') or (n, inl), is a threshold reaction that occurs in the neutron energy range from a few dozen of keV to 20 MeV. It involves one neutron in the entrance channel and one neutron in the exit channel, but it lets the residual nucleus be in an excited state. Above a few MeV, when $S_n$ is reached and beyond, more neutrons can be emitted, and these reactions are called (n, xn) reactions, x being the number of emitted neutrons. The first experimental evidence [1] and references therein, of the neutron emission in neutron-induced reaction was made in 1936, four years after the discovery of the neutron, in the case of (n, 2n) reaction on $^{63}$Cu and $^{65}$Zn using activation method and radio-chemistry. The inelastic process was experimentally established a year later (1937) by studying the interaction of neutrons (Ra-Be source) with different configurations involving a Lead-Block. It was demonstrated that the neutrons are not significantly captured, and they lose their excitation ability when they lose energy, an effect historically called the "fast neutron effect". Only 15 years later, the first measurement (with photographic emulsion) of discrete energies of the emitted neutron after collision with $^{56}$Fe was done. Then, during the fifties, using quasi monoenergetic pulsed neutron sources, two experimental methods were developed to detect either the emitted $\gamma$ or neutrons with NaI scintillator counters and fast hydrogenous scintillator detectors (using the time of flight method), respectively. In the seventies, new developments were engaged with germanium detectors types near neutron time of flight facilities which deliver white neutron beam spectrum. At present, experimental studies of neutron inelastic

scattering are still on going with rather the same detection techniques but profiting of new generation of detectors and the advent of new neutron beam facilities. In the next section 2, one describes the level of knowledge that has been achieved after 70 years of researches and how this knowledge impacts the applications of nuclear energy, for example, in the development of new nuclear systems. Section 3 presents how to improve our experimental knowledge of neutron inelastic scattering. A focus is made, in section 4, on the prompt $\gamma$-ray spectroscopy method and the last achievements obtained both from measurements and modeling. Finally, conclusions with perspectives are given in the last section 5.

## 2 Current knowledge of neutron inelastic scattering and its impact on nuclear energy application

In a nuclear reactor core, neutron inelastic scattering and (n, xn) reactions partially drive the neutron population evolution (number and energy distribution) and can also produce radioactive elements that can cause radioprotection issues. Neutron inelastic cross section can reach a few barn at maximum and can compete with capture at low neutron energy, elastic scattering but also, with fission in case of some actinides. Practically, this process has an impact on core parameters like the $k_{eff}$, the leakage rates or the power distribution. In the nineties, a first study conducted in the frame of NEA's WPEC-4 (Working Party on International Nuclear Data Evaluation Co-operation) [2], has shown the importance of improving the knowledge of neutron inelastic scattering off $^{238}$U. In the report, the authors mention the difficulties they encountered in resolving the differences between the databases using the exper-

<footnote>*e-mail: maelle.kerveno@iphc.cnrs.fr</footnote>
imental data and theoretical calculations available at the time. They also highlighted the scarcity of experimental data and the need to know precisely not only the total inelastic cross-section but also the energy distribution of the emitted neutrons. Later, the sensitivity work performed in the frame of WPEC-26 [3] has demonstrated the impact on core parameters of the lack of knowledge of the neutron inelastic scattering process in the case of advanced reactor concepts. It has resulted in new entries in the NEA High Priority Request List (HPRL) [4] related to $^{238}$U, $^{56}$Fe and $^{206,207}$Pb nuclei. More recently, in the case of $^{238}$U, some studies have shown that, despite a real experimental effort performed in the latest years, the level of uncertainties associated to the evaluated inelastic scattering cross section leads to nonlinear and skewed distributions for safety-related core parameters in Gen-III reactors [5], to large contributions to $k_{eff}$ uncertainty in the MYRRHA reactor [6]. And finally, it has been demonstrated that, the cross section is overestimated by about 10% in JEFF-3.1.1 in the 2-5 MeV energy region [7]. Another significant but surprising example concerns $^{56}$Fe, the most common element of structural material in reactors for which elastic and inelastic reactions play a significant role in shielding, reflection and leakage. As shown in Figure 1, the cross section presents a resonating shape up to a relatively high energy in the MeVs which complicates its theoretical modeling. Despite non-negligible amount of experimental data, still discrepancies among various libraries exist and an underestimation (up to 50%) of the neutron leakage spectra is observed in shielding benchmark testing with IPPE iron sphere [8]. Regarding the (n, xn), for x>1, process, its im-

<figure><img src="image_2.png" /><figcaption>**Figure 1.** (color online) $^{56}$Fe(n, inl) cross section from evaluated database compared to measured data available in the EXFOR data base [10].</figcaption></figure>

pact concerns more specifically the production of specific radionuclides. A significant example is the production of $^{232}$U which produces, at the end of its decay chain, $^{208}$Pb associated with the emission of an energetic $\gamma$ (2.6 MeV). This emission must be estimated to well define the shielding but also the handling procedure for spent fuel. In the current power reactors, it has been shown that this production was underestimated in old, matured un-irradiated and irradiated fuel [9], because the cross sections of the (n, xn) processes involved in the creation of $^{232}$U via $^{238}$U-$^{237}$Np-$^{232}$Th-$^{233}$U(n, 2n) and $^{234}$U-$^{238}$Pu(n, 3n) reactions, are very

poorly known. In future breeding fuels based on $^{232}$Th as fertile and $^{233}$U as fissile nucleus, the $^{233}$U(n, 2n) process will play an important role. However, as shown in Figure 2, evaluated cross sections present large discrepancies, and no experimental data are available.

<figure><img src="image_3.png" /><figcaption>**Figure 2.** (color online) $^{233}$U(n, 2n) cross section from evaluated database (no experimental data are compiled in the EXFOR data base [10].).</figcaption></figure>

With only these few examples, it is clear that, despite 70 years of experimental studies and constant theoretical development, our knowledge of the neutron inelastic scattering process requires to be still improved to reach the accuracy level demanding by the applications.

## 3 How to measure and how to model?

The (n, n') and (n, xn) processes can be measured mainly by three experimental methods. Since neutrons and $\gamma$'s are emitted, one can either detect the neutrons or detect the $\gamma$'s.

The latter technique is called the prompt $\gamma$-ray spectroscopy method (PGRS). In the case of (n, xn) reaction, if the residual nucleus is unstable and presents a suitable half-life, one can also use the activation technique, that means irradiate the sample and then count the decay (mainly $\alpha$ or $\gamma$) of the nuclei. Each method presents strengths and weaknesses, however all have to deal with the ability of neutrons to scatter not only on the sample of interest, but also on the experimental environment, producing a high neutron background. It is thus of importance to perform measurements in as low as possible neutron background environment.

The activation technique gives access to the total (n, xn) cross section, but is only doable for radioactive products presenting adequate lifetimes for decay measurements. Mono-energetic neutron beams are also required to determine the excitation function, otherwise integrated cross section is obtained and, if it is possible, an unfolding procedure has to be applied.

The neutron detection is directly linked to the inelastic scattering process, it allows the measurement of the angular distribution, which gives insights on reaction mechanism. The method can be used at both mono-energetic and white neutron beams. It requires using the time of
flight technique and also a good neutron energy resolution to separate neutrons that are elastically and inelastically scattered. If a fissionable nucleus is under study, neutrons from fission and those that are inelastically scattered should be distinguished.

In the case of the prompt γ-ray spectroscopy method, the reaction channel can be well identified due to the high detector energy resolution (HPGe detector) contrary to the case of the neutron detection method. Time-of-flight measurements are also possible with PGRS method, which makes it a powerful technique for neutron time-of-flight facilities. The PGRS method gives access to the exclusive (n, xγ) cross sections that can be used in combination with nuclear structure information to infer the level production and (n, xn) total cross section.

Above all these detection techniques, a neutron beam must be available to perform the experiment. This kind of beam is less common than charged particle or ion beams, but nevertheless, the different facilities present a variety useful to implement the various experimental techniques mentioned earlier. Neutron beams can be categorized into two main families. The mono- or quasi monoenergetic neutron beams, which use two body reactions near Van de Graaff type accelerators. There, neutrons are created at all angles, and present a divergent fluence with the highest flux in the forward direction. Another types of facilities are the time-of-flight facilities which produce white neutron beams. The neutrons are generated by spallation like at WNR-LANSCE (LANL, US) or at n-TOF (CERN, Switzerland), or by photo-production like at GELINA (EC-JRC-Geel, Belgium), The Gaerttner Linear Accelerator (RPI, USA), ORELA (ORNL, USA) or n-ELBE (HZDR, Germany) or by deuteron break up like at the new facility SPIRAL2/NFS (GANIL, France). These facilities produce a well collimated neutron fluence with a rather flat profile. Depending on the available flight paths, high neutron energy resolution measurements can be achieved.

In the case of the PGRS experimental method, when the residual nucleus presents a dense nuclear structure (levels with close energies) or prominent transitions with energy below 150 keV that favors the deexcitation via conversion electron, the collected experimental information can be too fragmented or inaccurate to infer directly the total cross section from (n, xγ) ones. This situation often occurs when studying actinides. In those cases, to infer the total inelastic scattering process from this partial experimental information, complementary theoretical modeling is required [11]. This modeling involves different nuclear reaction mechanisms as the compound, pre-equilibrium, and direct reactions as schematically presented in Figure 3. Even if this contribution is focused on the experimental point of view, one can, nevertheless, mentioned some of the ongoing efforts to improve the modeling of the neutron inelastic scattering and the understanding of the whole process. Main theoretical developments include the coupled-channels and DWBA methods for the direct reaction, the quantum-mechanical pre-equilibrium theories and the statistical Hauser-Feshbach decay for deformed targets.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** (color online) Schematic view of the reaction mechanisms involved in the modeling of neutron inelastic scattering.</figcaption></figure>

**3.1 Some examples of major experiments for the last 50 years**

Major experiments of neutron inelastic scattering were done in the eighties by G. Haouat and coworkers [12] and references therein. They have used the neutron time-of-flight (TOF) facility of the CEA DAM Ile de-France tandem accelerator laboratory. A multidetector spectrometer was installed in a largesize “neutron hall” especially designed to perform fast-neutron scattering measurements with a high energy resolution in a low background environment. Many isotopes have been studied like Pb and Bi, but one can highlight the first attempt to resolve experimentally the elastic and inelastic scattering groups for different actinides [13] : $^{232}$Th, $^{233}$U, $^{235}$U, $^{238}$U, $^{239}$Pu, and $^{242}$Pu at incident neutron energies where the deformation effects play a dominant role (above 1.5 MeV). Figure

<figure><img src="image_5.png" /><figcaption>Fig. 2. The experimental arrangement.</figcaption></figure>

<caption>**Figure 4.** Experimental arrangement used by G.Haouat *et al*. for high resolution measurement at CEA DAM. From [13].</caption>

4 shows the experimental arrangement done to clean as much as possible the experimental area and minimize the neutron background surrounding the detectors. Huge detector shielding (1600 kg) and 1-m-long shadow bars were used to protect the NE2013 liquid scintillators placed at flight paths ranging from 6 to 10 m. In this work, the
unprecedented good energy resolution allowed the separation of the TOF peaks corresponding to elastic and inelastic scattering to the first collective excited states of the even nuclei $^{232}$Th, $^{238}$U, and $^{242}$Pu and of the odd nucleus $^{233}$U. The cross sections for $^{235}$U and $^{239}$Pu were extracted only for groups of states due to their close level spacing. From the TOF data, angular differential cross section has been obtained as well as, scattered (elastic and inelastic) cross section as function of incident neutron energy for the first excited states. These data have been used to deduce accurate values of the optical potential parameters and of the nuclear quadrupole and hexadecapole deformations. It has been also demonstrated that the neutron-nucleus optical potential is nearly the same for these actinides and only the nuclear deformations vary from nucleus to nucleus and account for differences in neutron scattering.

From the side of the prompt γ-ray spectroscopy method, first experiments were done in the seventies for (n, xn) reaction studies at the Karlsruhe cyclotron and at the Oak Ridge electron linear accelerator ORELA with Ge(Li) and NaI detectors, respectively. Twenty years later, a step has been taken with the advent of the GEANIE (germanium array for neutron-induced excitations) high-purity Germanium array at the WNR spallation time-of-flight facility of Los Alamos. Twenty-six HPGe detectors (planar and coaxial) coupled to BGO detectors were assembled to cover the reaction space (Figure 5) and placed at 20 m from the spallation source. In the middle of the nineties,

<figure><img src="image_6.png" /><figcaption>The GEANIE Array</figcaption></figure>

<caption>**Figure 5.** (color online) Photo of the GEANIE apparatus. https://lansce.lanl.gov/facilities/wnr/flight-paths/geanie/about.php.</caption>

several experiments have been performed at WNR on a large variety of isotopes (Pb, Al, Pt, Mo, Ti, Sm, but also U and Pu, etc.) and for the neutron energy range from a few MeV up to 400 MeV (see [14] and references therein). All these data were intensively used to constrain the GNASH code as shown in Figure 6 in the case of the $^{239}$Pu(n, 2n)$^{238}$Pu reaction which is especially important for applications [15].

In a more recent period, following notably the work done in the CIELO project [16] for iron isotopes evaluation, new measurements with the neutron detection techniques have been launched in the USA and in Europe. One can mention the work done at the University of Kentucky Accelerator Laboratory [17], where C$_{6}$D$_{6}$ liquid scintillation detectors using pulse-shape discrimination and time-

<figure><img src="image_7.png" /><figcaption>**Figure 6.** (color online) $^{239}$Pu(n, 2n)$^{238}$Pu cross section measured with the GEANIE apparatus compared to previous experimental data and evaluations [15], https://lansce.lanl.gov/facilities/wnr/flight-paths/geanie/about.php.</figcaption></figure>

of-flight techniques have been used to measure the neutron $^{56}$Fe elastic and inelastic differential cross section for $^{56}$Fe. The integrated cross sections have also been deduced for neutron elastic and inelastic scattering for the two excited levels at 847 keV and 2085 keV. These data gave new insights on evaluated data considerations and have been used to test the predictions given by the TALYS nuclear reaction code [18] with default parameters and coupled-channel calculations based on the vibrational model. The EMPIRE nuclear reaction code [19] based on the soft-rotor model has also been tested. Figure 7 shows one example of results achieved in this experiment for elastic and inelastic cross sections.

The second new measurement has been very recently performed at the GELINA facility (EC-JRC-Geel) with the ELISA setup with which $^{54,56}$Fe have been studied. ELISA is composed of 32 liquid organic scintillators placed at 27 m from the neutron source. The neutron and photon-induced events separation is done via pulse-shape analysis, and the discrimination between elastic and inelastic channels is done using light output distribution analysis and kinematic calculations. For $^{54}$Fe [20], this was the first experimental measurement providing high-resolution data for elastic scattering. The angular distributions and integral cross sections have been measured from $E_n = 1$ to 8 MeV. For the inelastic channel, partial differential and angle-integrated cross sections were estimated from the first excited state of $^{54}$Fe ($E_x$ = 1.408 MeV) from $E_n$ = 2.5 to 5.5 MeV as shown in Figure 8.

The most modern and significant works using the prompt γ-ray spectroscopy method are performed by the two HPGe arrays installed at the GELINA (EC-JRC-Geel) facility: GAINS (Gamma Array for Inelastic Neutron Scattering) [21] (Figure 9) and GRAPhEME (GeRmanium array for Actinides PrEcise MEasurements) [22] (Figure 10). They were developed in the early 2000s, for light and intermediate mass, and actinides, respectively. With GAINS, from 2007, 21 nuclei ($^{52}$Cr, $^{209}$Bi, $^{208,206}$Pb, $^{23}$Na, $^{28}$Si, $^{76}$Ge, $^{54,56,57}$Fe, $^{24}$Mg, $^{206}$Pb, $^{7}$Li, $^{46,50}$Ti, $^{16}$O and $^{58,60,61,62,64}$Ni) have been measured and many (n, xny) cross sections have been produced and used in the eval-
<figure><img src="image_8.png" /><figcaption>**Figure 7.** (color online) Angle-integrated elastic (a) and inelastic scattering cross sections for excitation of the 847-keV (b) and 2085-keV (c) levels. From [17].</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 8.** (color online) Angle-integrated cross section of neutron inelastic scattering from the first excited state of <sup>54</sup>Fe as a function of the neutron incident energy compared with data available in the EXFOR library and evaluations. From [20].</figcaption></figure>

uation process and/or to test the TALYS nuclear reaction code. With GRAPhEME, four actinides have been measured <sup>233,235,238</sup>U, <sup>232</sup>Th, but also stable isotopes of tungsten (<sup>nat</sup>182,183,184,186W), <sup>nat</sup>Zr and <sup>57</sup>Fe. A measurement with a <sup>239</sup>Pu sample is in progress. It has to be noticed that, due the complexity of the γ spectra in the case of actinides samples, very good statistics are mandatory, therefore measurements last several months and, can even run over 2 or 3 years. In the section 4.2, some details about the GRAPhEME setup are presented as well as the last achievements obtained for the modeling of the (n, n'γ) cross sections produced with GRAPhEME.

To end this section about the main works performed on neutron inelastic scattering these last decades, it is also

<figure><img src="image_10.png" /><figcaption>**Figure 9.** (color online) The GAINS setup as it is nowadays. From A. Olacel *et al.*, WINS 2023, https://indico.cern.ch/event/1201892/contributions/5529654/.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 10.** (color online) The GRAPhEME setup installed at 30 m from the GELINA neutron source.</figcaption></figure>

interesting to mention that other kind of experiments are relevant to improve our knowledge of neutron scattering, even if they don't provide cross sections. A good example is the ones done at the Rensselaer Polytechnic Institute (RPI) in Troy, USA. A neutron time of flight setup is installed at a pulsed white neutron beam. Multiple neutron detectors are positioned at different angles around the sample to measure the neutrons emitted by the sample. Using time sensitive simulations, the measurements are compared to detailed simulations of the setup. This type of experiments is sensitive to the scattering (or fission) cross sections and angular distributions. Experiments were performed for Be, Mo, Fe, Pb, Cu, Zr, <sup>238</sup>U, <sup>235</sup>U, <sup>239</sup>Pu. The <sup>238</sup>U data [23] was used, for example, to improve <sup>238</sup>U angular distributions and cross section in the ENDF/B-8.0 library [24].

# 4 Prompt γ-ray spectroscopy, last achievements obtained with GRAPhEME@GELINA facility

## 4.1 The prompt γ-ray spectroscopy method

It is certainly useful to recall here the main principles of the prompt γ-ray method. Using high energy resolution detector as HPGe, one can detect the γs coming from the de-excitation of the nucleus formed in the (n, inl) or (n, xn)
reaction. The energy resolution of this kind of detector is mandatory to identify with no ambiguity the reaction channel. It is especially important when nucleus presenting closed level scheme, like actinides, or in the case where the fission channel is also opened in the energy range of (n, n') and (n, xn) reactions. Coupled to time-of-flight measurements with appropriate flight path, despite the poorly time resolution of HPGe detector compared to scintillator, rather accurate description of the excitation curve can be achieved with this technique. From the counts obtained in the γ peaks of interest, one can deduce the (n, xny), x ≥ 1, cross section from the angular differential cross sections measured at specific angles. Once these cross sections for

<figure><img src="image_12.png" /><figcaption>**Figure 11.** (color online) How to infer inelastic scattering or (n, xn) cross section from the measured (n, xny) ones.</figcaption></figure>

specific γ transitions are determined, they can be used in combination with nuclear structure information to infer the level production and (n, xn) total cross section as illustrated in Figure 11. Level production cross sections are obtained by doing a balance of incoming and outgoing γ transitions. If some transitions are not measured, information can be deduced from other measured ones, knowing the branching ratios. The total cross section is calculated by summing all the (n, xny) cross sections for γ transitions that go directly to the ground state. Nucleus structure information is thus a key ingredient for this method. An important remark is that, with this method, the inferred level production or total cross sections are exact only up to an neutron incident energy limit corresponding to the highest excited level from which the experiment has been able to see a γ. Above this limit, the inferred cross sections are a high limit or a low limit, respectively. This is relatively penalizing in the case of nuclei where the level densities increased rapidly as a function of the excitation energy, like in the actinides for which this limit can be around 1.5 MeV. Another way to infer the total cross section, from the partial measured ones, is to put into play the nuclear reaction codes, which are then constrained by the measured (n, xny) cross sections. Indeed, these exclusive cross sections are severe constraints for modeling. This was thoroughly used for the data obtained at Los Alamos with the GEANIE detector and the GNASH code. This is also a path we are following with the GRAPhEME data

in the frame of a close collaboration between theoreticians from CEA/DAM, LANL and IAEA [25].

## 4.2 GRAPhEME: main achievements

As a quick reminder, GRAPhEME, installed at 30 m from the GELINA neutron source, is currently composed of one fission chamber and 6 HPGe detectors coupled to the FASTER digital acquisition system. The $^{235}$U ionization chamber, used for neutron flux determination, is positioned ≈1 meter upstream the sample. The six Germanium detectors are planar types. They are placed around the sample at 110° and 150° with regards to the neutron beam to allow the precise angular integration of the γ-ray production cross sections. One HPGe detector is segmented in 36 pixels. It allows to manage high counting rates without too high dead time and its very good energy resolution gives a precise γ-peak identification. These are real assets when performing measurement with highly active and fissile actinide samples. At a flight path of 30 m and with the time resolution of the Germanium detectors, the typical neutron energy resolution achieved is 10 keV at $E_n$ = 1 MeV.

In [22], a detailed recap of the main results obtained with GRAPhEME for these last 20 years can be found. Experimentally, one can highlight the determination of the $2^+$ to $0^+$ γ-transition cross section in $^{238}$U and $^{232}$Th ever measured. The high internal conversion coefficient (ICC = 610 and 332, respectively) of these two low γ-energy transition explained the difficulty to obtain precise measurement, but this information is however important taking into account the fact that, in even-even actinides, this transition, from the first excited level, carries the most part of the total γ cascade (typically ~90% or more) as shown in Figure 12, which describes, in the $^{238}$U case, the contribution of different γ transition to the total neutron inelastic cross section. It is clear that the de-excitation of the first level (in red) is the main transition and the γ part of this transition is very low (red dashed line in the insert). The second experimental highlight is the measurement performed on $^{233}$U. This nucleus poses the challenge of highly active target combined to high fission to inelastic ratio of measured actinides. The counting rate coming from the radioactivity of this kind of sample will induced a huge γ background in the spectra, but, even more penalizing for accurate measurements, a huge dead time will be generated and a loss of γ-energy resolution could be also observed. Moreover the deexcitation of the fission products generates additional γ peaks in the spectra, which contaminates the peaks of interest. The proposed solution was then to use a segmented germanium detector to reduce the counting rate on each active parts of the detector and thus an acceptable dead time while maintaining an excellent energy resolution. A new HPGe detector segmented in 36 pixels has therefore been installed at GRAPhEME in 2016 for the measurement on $^{233}$U. With a 8.3 g of metallic $^{233}$U sample (thickness of 0.64 mm for an activity of 3 GBq), the measurement lasted 4500 hours of beam time. After a difficult but meticulous data analysis, (n, n'γ) cross sections have been
<figure><img src="image_13.png" /><figcaption>**Figure 12.** (color online) Neutron inelastic scattering off $^{238}$U (black) calculated by TALYS and the different contributions of the main $\gamma$ transitions. The full colored lines correspond to the total de-excitation (conversion electrons and $\gamma$s) and the dashed line is the $\gamma$ de-excitation only. The insert is the same figure in the logarithm scale to show the very low proportion of emitted $\gamma$s in the case of the $2^+$ to $0^+$ $\gamma$ transition.</figcaption></figure>

obtained for 12 $\gamma$ transitions in $^{233}$U never measured before [26].

Beyond the experimental work done with GRAPhEME itself, an important contribution is the use of the measured cross section for the improvement of the modeling (see [25] for more details). In the frame of a close collaboration with theoreticians, we test modeling aspects especially relative to the description of compound nucleus and pre-equilibrium mechanisms, but also the influence of the structure knowledge via the test of different branching ratio prescriptions, $\gamma$-strength functions and level densities models. One important result of this work obtained with the $^{238}$U data, is the validation of quantum mechanical microscopic approaches for the modeling of the pre-equilibrium process. Indeed, it has been demonstrated that these approaches (DWBA/lp-1h1 [27] and QRPA2 [28]), which explicitly calculate the spin-parity distribution, give more realistic distributions than the exciton model. These lead to a better calculation of (n, n' $\gamma$) cross sections for $\gamma$ transitions at high spin in the ground state band. Additionally to these results, it has been then possible to find new values of the spin cutoff parameter used in the prescription of Gruppelaar [29] which is included in the TALYS nuclear reaction code to determine the spin-parity distribution in the frame of the exciton model.

The measurement done on the three even tungsten isotopes, which will be published soon [30], was the occasion to pursue deeply this theoretical work and test in detail other models' ingredients like embedded level in continuum, different $\gamma$-strength functions and models of level densities. Another significant step on the path to reliable calculations has also been achieved. Indeed, calculations with TALYS using all possible combinations of models, included parameters and prescriptions, have been performed. For $^{182,184,186}$W isotopes (simultaneously), the best choice of parameters has been selected using the

smallest $\chi^2$ value that gives a reasonable description of most $\gamma$ transitions. With this method, theoretical predictions come with uncertainties, which helps for comparisons with experimental data.

## 5 Perspectives and conclusions

As seen previously, the neutron inelastic scattering process is an important reaction in applications, but its knowledge, despite seventy years of studies, is not yet precise enough, and both experimental studies and modeling still require improvements. To improve the quality of experimental data, it is important to continue to take advantage of the variety of methods that bring complementary information, and also to use various neutron beam facilities, continuing then the experimental effort, especially for nuclei that are relevant for applications ($^{238}$U, $^{239}$Pu, $^{233}$U, $^{235}$U, Fe, Zr, Pb, etc.). From the detection side, one could mention, for example, new initiatives (at CERN/n_TOF or JRC-Geel/GELINA) to use LaBr3 detectors for $\gamma$ detection taken advantage of their high efficiency and fast timing response compared to HPGe detector. Regarding facilities, the operation of the new SPIRAL2/NFS neutron beam offers new opportunities to study (n, 2-3n) reactions that will lead to better experimental constrain for the pre-equilibrium process.

Another experimental initiative that could be mentioned, is being conducted by IFIN-HH with the measurement of proton-induced inelastic cross sections coupled with theoretical calculations to infer neutron inelastic cross sections [31].

Concerning the prompt $\gamma$-ray spectroscopy method, several ways of improvement are being studied to better infer the total inelastic cross section from the (n, xny) ones. The first one concerns the measurement of the de-excitation of the low-lying levels, especially the first level in actinides, which are highly converted. As we have seen for $^{238}$U in section 4.2, this level represents the major part of the cross section. Measuring the $\gamma$ deexcitation of this level brings thus major uncertainties when inferring the total inelastic cross section as it can be seen in Figure 13 in the case of $^{232}$Th [32]. A challenging measurement will be to measure conversion electrons, as the major part of the deexcitation goes via these particles. The collaboration (CNRS/IPHC, IFINI-HH and EC-GRC-Geel) is thus working on a new instrument, named DELCO (Detection of ELectrons from COnversion), which measures electrons. The first test case will concern $^{238}$U.

A second area for improvement is related to nuclear structure, which is an important ingredient of the experimental methodology. This is not only the case for inelastic scattering, but also for many other experimental topics like measurements of fission yields or $\beta$-decay. So based on this, the French NACRE collaboration has published a paper [33] that highlights special needs in new nuclear structure information for nuclear energy applications. The aim is to inform and raise awareness to our colleagues from the nuclear structure community to these needs. A first consequence of that initiative was the work done in the $\nu$-ball
<figure><img src="image_14.png" /><figcaption>**Figure 13.** (color online) Total neutron inelastic scattering off $^{232}$Th (blue dots) inferred from prompt γ-ray spectroscopy measurements. From [32]</figcaption></figure>

experimental campaign performed at the ALTO facility to
produce an improved level scheme of $^{238}$U [34].

The last relevant items for the improvement of the
prompt γ-ray spectroscopy, is the importance of close col-
laboration between experimentalists and theoreticians, as
shown in section 4.2. This boosts improvements in mod-
eling and finally, achieve the initial goal to coupled mea-
sured (n, n'γ) cross sections with optimized nuclear reac-
tion codes to produce as accurate as possible total inelastic
scattering cross section.

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