Correlated $n\text{−}\gamma$ angular distributions from the $Q=4.4398 \mathrm{MeV}$ ${}^{12}\mathrm{C}(n,n^{\prime }\gamma )$ reaction for incident neutron energies from 6.5 MeV to 16.5 MeV

Neutron scattering cross sections and angular distributions represent one of the most glaring sources of uncertainty in calculations of nuclear systems. Even simple nuclei like ${}^{12}\mathrm{C}$ show indications of errors in nuclear databases for scattering reactions. Measurements of inelastic neutron scattering have historically measured either the scattered neutrons or the nuclear deexcitation $\gamma$ emission. Only a very small number of experiments attempted correlated measurements of both the neutron and $\gamma$ data simultaneously, even though these $n\text{−}\gamma$ correlations could be essential for understanding particle transport in nuclear systems. In this work we describe a measurement of the $n, \gamma$, and correlated $n\text{−}\gamma$ angular distributions from the $Q=4.4398 \mathrm{MeV}$ ${}^{12}\mathrm{C}(n,n^{\prime }\gamma )$ reaction in a single experiment using an EJ-309 liquid scintillator detector array with wide angular coverage, and with a continuous incident neutron energy range from 6.5 to 16.5 MeV. We also provide a thorough covariance description of these results, including normalization of the probability distribution. While the measured $n$ distributions agree well with the relatively large number of available literature measurements, there are comparatively very few measurements of the $\gamma$ distributions from this reaction. However, our data support the presence of a nonzero $a_4$ Legendre polynomial component of the $\gamma$ angular distribution suggested in past measurements, which is currently not incorporated in the ENDF/B-VIII.0 library despite the use of these same literature data for evaluation of the ${}^{12}\mathrm{C}(n,n^{\prime }\gamma )$ cross section. The correlated $n\text{−}\gamma$ distribution measurements are limited to three measurements at incident neutron energies near 14 MeV. Our results do not generally agree with any of these literature measurements. We observe clear indications of significant changes in the $n$ distribution for specific $\gamma$-detection angles and vice versa especially near thresholds for other reaction channels, which shows the potential for significant bias in experiments that, for example, tag on inelastic scattering using a single or small number of $\gamma$-detection angles and could impact particle transport calculations.

Figure 1

A level diagram of ${}^{12}\mathrm{C}$. Level energies, $\gamma$ intensities, and $3\alpha$ breakup branching ratios are from Ref. [12]. Note that the $\gamma$ intensities are relative within any given $\gamma$ decay, and do not describe the relative split between $\gamma$ and other decay modes. The percentage near the $3\alpha$ branches are branching ratios relative to $\gamma$ decay. While all of the levels shown here are potentially populated within the incident energy range employed here, only excitations of the 4.4398 MeV state are reported in this work, isolated utilizing neutron kinematics. See the text for more details.

Figure 2

The measured PSD spectrum. The $n$ and $\gamma$ counts are labeled with their corresponding gates shown in red and black, respectively.

Figure 3

The kinematic spectrum from the ${}^{12}\mathrm{C}(n,n^{\prime }\gamma$) measurement with the kinematic gate required to select the desired neutrons shown in black with the approximate trend of the peak of the signal integral versus measured neutron time of flight as the red dashed line.

Figure 4

(a) The measured data in the form of a two-dimensional $E_n^{\mathrm{out}}$ vs $E_n^{\mathrm{inc}}$ spectrum for carbon neutron scattering with an intermediate $\gamma$ tag integrated over all angles, (b) the background-subtracted data spectrum integrated over all angles, (c) the measured background for a neutron-detection angle of ${30}^{\text{o}}$, and (d) a calculation of the expected background from the ${}^{12}\mathrm{C}(n,n$) elastic scattering reaction for a neutron-detection angle of ${30}^{\text{o}}$ assuming a random $\gamma$ ray uniformly distributed in time and no neutron scattering effects. See the text for a discussion.

Figure 5

A missing mass representation of the observed counts. The vertical line of counts at an excitation energy of 4.44 MeV is clearly seen.

Figure 6

The angle-integrated neutron detection efficiency curve shape. Uncertainties shown are statistical only.

Figure 7

An example normalized correlation matrix for the measured $n$ distribution corresponding to $E_{\alpha }=13.80–14.13\mathrm{MeV}$.

Figure 8

An example normalized correlation matrix for the measured $\gamma$ distribution corresponding to $E_{\alpha }=13.80–14.13\mathrm{MeV}$.

Figure 9

An example normalized correlation matrix for the measured correlated $n\text{−}\gamma$ distribution corresponding to $E_{\alpha }=13.80–14.13\mathrm{MeV}$. Each ${\theta }_n$ bin on each axis contains each of the nine possible ${\theta }_{\gamma }$ angles. These ${\theta }_{\gamma }$ axis labels are not shown as they would be too small to display.

Figure 10

Results for normalized $n$ distributions for (a) $E_{\alpha }=6.61–6.76\mathrm{MeV}$, (b) $E_{\alpha }=7.59–7.76\mathrm{MeV}$, (c) $E_{\alpha }=8.91–9.12\mathrm{MeV}$, (d) $E_{\alpha }=10.47–10.72\mathrm{MeV}$, (e) $E_{\alpha }=13.80–14.13\mathrm{MeV}$, and (f) $E_{\alpha }=15.49–15.85\mathrm{MeV}$. All $E_{\alpha }$ values are in MeV. The present results are scaled to ENDF/B-VIII.0 evaluation as described in the text. Literature data $E_{\alpha }$ values in (e) are all near 14 MeV.

Figure 11

Results for normalized $\gamma$ distributions for (a) $E_{\alpha }=6.46–6.61\mathrm{MeV}$, (b) $E_{\alpha }=7.41–7.59\mathrm{MeV}$, (c) $E_{\alpha }=9.55–9.77\mathrm{MeV}$, (d) $E_{\alpha }=11.48–11.75\mathrm{MeV}$, (e) $E_{\alpha }=13.80–14.13\mathrm{MeV}$, and (f) $E_{\alpha }=15.14–15.49\mathrm{MeV}$. All $E_{\alpha }$ values are in MeV. The present results are scaled to ENDF/B-VIII.0 evaluation as described in the text.

Figure 12

The results for the normalized correlated $n\text{−}\gamma$ distribution data at $E_{\alpha }\approx 14$ MeV as $\gamma$ distributions compared to the available literature data for (a) ${\theta }_n={30}^{\circ }$, (b) ${\theta }_n={45}^{\circ }$, (c) ${\theta }_n={60}^{\circ }$, (d) ${\theta }_n={75}^{\circ }$, (e) ${\theta }_n={90}^{\circ }$, and (f) ${\theta }_n={105}^{\circ }$. The literature data on these plots are scaled to the present results.

Figure 13

A three-dimensional representation of a correlated $n\text{−}\gamma$ distribution corresponding to $E_{\alpha }=9.77–10.00\mathrm{MeV}$.

Figure 14

Two-dimensional representations of the measured normalized correlated $n\text{−}\gamma$ distributions with separate $n$ distributions for each ${\theta }_{\gamma }$. Laboratory angles are shown along the $x$ axis for consistency between the plots of $n$ and $\gamma$ distributions. Note that uncertainties are not shown on the data in these figures.

Figure 15

Two-dimensional representations of the measured normalized correlated $n\text{−}\gamma$ distributions with separate $\gamma$ distributions for each ${\theta }_n$. Laboratory angles are shown along the $x$ axis for consistency between the plots of $n$ and $\gamma$ distributions. Note that uncertainties are not shown on the data in these figures.