Measurement of ${}^{238}\mathrm{U}(n,n^{\prime }\gamma$) cross section data and their impact on reaction models

A better knowledge of $(n,xn)$ reaction cross sections is important for both reaction modeling and energy applications. This article focuses on inelastic scattering of neutrons off ${}^{238}\mathrm{U}$ for which improvements are needed to better constrain evaluations and solve inconsistencies in nuclear power reactor calculations. A new precise measurement of $(n,xn\gamma )$ reaction cross sections on ${}^{238}\mathrm{U}$ has been performed at the GELINA (Geel Electron LINear Accelerator) neutron facility operated by EC-JRC-Geel (Belgium) with the GRAPhEME (GeRmanium array for Actinides PrEcise MEasurements) setup. The prompt $\gamma$-ray spectroscopy method coupled to time-of-flight measurements is used to extract $(n,xn\gamma )$ cross section values which can be further combined to infer the total neutron inelastic scattering cross section. Cross section data for 18 $\gamma$ transitions (five never measured before) are presented and compared to the data in the literature. Emphasis is especially given to the uncertainty determination to produce partial cross section data as accurate as possible. Due to intrinsic limitations of the experimental method, the use of additional nuclear structure information coupled with theoretical modeling is required to determine the total $(n,n^{\prime })$ cross section over the whole neutron energy range. We have investigated modeling aspects of the ${}^{238}\mathrm{U}(n,n^{\prime }\gamma )$ cross sections related to the description of compound nucleus and preequilibirum mechanisms as well as the discrete part of nuclear structure. Through comparison between experimental and calculated $(n,n^{\prime }\gamma )$ cross sections, we pinpoint inaccuracies in the description of specific reaction mechanisms and challenge recently implemented models. This helps improving the whole modeling of the $(n,n^{\prime })$ reaction.

Figure 1

Evaluated [21, 22, 23, 24, 25, 26] and experimental ${}^{238}\mathrm{U}$ inelastic scattering cross section data [7, 8, 10, 11, 12, 13, 14, 15, 16]. The experimental data marked with * have been corrected using model calculations.

Figure 2

Two-dimensional plot for $\gamma$-ray energy (keV) as a function of the time of flight (channels) where one sees the $\gamma$ rays from different sources [$\gamma$ flash, ${}^{238}\mathrm{U}$ radioactivity, $(n,xn)$ reactions, etc.].

Figure 3

Portion of $\gamma$-ray energy distributions for one detector from 20 to 950 keV. The red spectra were obtained by applying a time window corresponding to the inelastic scattering incident energies range. The blue spectra correspond to the radioactive decay selected for the same time window width as the red spectra and before the arrival of the neutrons. The ${}^{238}\mathrm{U}\gamma$ transitions for which the cross section data are presented in this article are labeled; the others (measured but not shown in this article) are marked with a star.

Figure 4

(a) Differential cross section data at ${110}^{\circ }$ and ${150}^{\circ }$ for each detector (G110, G150, B110, and R150). (b) Differential cross section data at ${110}^{\circ }$ (TOT 110) after adding the statistics for two detectors; (c) the same for ${150}^{\circ }$. (d) Angle-integrated $(n,n^{\prime }\gamma )$ cross section data obtained for all the possible combinations of two detectors, “TOT” is the combination of the four detectors.

Figure 5

Zoomed-in look of the time-amplitude matrix corresponding to the low-energy $\gamma$ lines with unamplified (a) and amplified (b) signals. The so-called “walk” effect is clearly visible in panel (a).

Figure 6

(a) Time distributions for the detector G110 and for $\gamma$ energy at 103.5 keV. The black distribution is not affected by CFD shift while the red one is. These two distributions are used to define the time correction to apply to the data for each impacted $\gamma$ transition. (b) Cross section data for the 103.5-keV $\gamma$ transition before the CFD shift correction (in red) and after (in black).

Figure 7

Experimental ${}^{238}\mathrm{U}(n,n^{\prime }\gamma )$ cross sections (symbols) for $E2$ transitions in the GS band [panels (a)–(e)] or from the levels of the first $K^{\mathrm{\Pi }}=0^{-}$ octupole-vibration band to the GS band [panels (f)–(k)], compared to calculations (curves; see details in Sec. 4). The Olsen datum at 680.2 keV corresponds to the sum of the 680.2-keV ($1_1^{-}\to 0_1^{+}$) and 678.3-keV ($5_1^{-}\to 4_1^{+}$) transitions.

Figure 8

Same as Fig. 7 for transitions from levels in the $K^{\mathrm{\Pi }}=1^{-}, \alpha =0$ band [46] [panels (p)–(r)] and in the $K^{\mathrm{\Pi }}=1^{-}, \alpha =1$ band [46] [panels (l)–(o)] bands.

Figure 9

Calculated $(n,n^{\prime }\gamma )$ cross sections with (full black curves) and without (dashed red curves) the EWT (see details in Sec. 4c). The contribution from the compound inelastic scattering, that is ${\sigma }_i^{\mathrm{CN}}\frac{b(i\to j)}{1+\alpha }$, to the $\gamma$-ray production $\sigma \left({\gamma }_{i\to j}\right)$ [see Eq. (4)] is also displayed as dotted blue curves for calculations with the EWT and dotted-dashed green curves for calculations without. Symbols represent experimental data as defined in Figs. 7 and 8.

Figure 10

(a) Spin distribution for the incident energy 10 MeV and an excitation energy of 5 MeV. Average spin as a function of the excitation energy for the two incident energies 10 MeV (b) and 20 MeV (c). On these plots, results from the exciton model are compared to those of the two microscopic preequilibrium models (see Secs. 4d and 4d2).

Figure 11

Data for ${}^{238}\mathrm{U}(n,n^{\prime }\gamma )$ cross sections for transitions within the ground state rotational band. Spin and parity of the initial and final states, energy of the $\gamma$ ray, experimental data (symbols) and calculations (curves) are defined in the plots. Calculations based on four different preequilibrium models are compared: excitons with $s=0.24$ or $s=0.04$, JLM/QRPA (talys code) and DWBA (CoH code).

Figure 12

Ratio of $\gamma$ intensity obtained for the levels at 680.11 keV (a) and 997.58 keV (b), compared to values from ENSDF and from reference Govor et al. [67].

Figure 13

Sensitivity matrix for calculated $\gamma$-production cross sections for 1.2 MeV incident neutron energy to BRs in ${}^{238}\mathrm{U}$. $L_i$ is the number of the level in talys (figure from Ref. [20]).

Figure 14

Experimental ${}^{238}\mathrm{U}(n,n^{\prime }\gamma )$ cross sections (symbols) compared to the nuclear reaction code calculations with various BR determination methods (see Sec. 5c).

Figure 15

$(n,n^{\prime }\gamma )$ cross sections calculated with (full black curves) and without (dashed red curves) discrete states embedded in the continuum (see Sec. 5d). Symbols represent experimental data as defined in Figs. 7 and 8.