Measurement of the cross section of the $Q=4.4398$ MeV ${}^{12}\mathrm{C}(n,n\text{'}\gamma )$ reaction from threshold to 16.5 MeV using $\gamma$ and correlated $n\text{−}\gamma$ detection

The $Q=4.4398$ MeV ${}^{12}\mathrm{C}(n,n\text{'}\gamma )$ cross section was measured using a white incident neutron source through the detection of $\gamma$ rays only and $n\text{−}\gamma$ coincidences using a segmented liquid scintillator detector array. While the $n\text{−}\gamma$ technique utilized here is more generally applicable to a wide variety of neutron scattering measurements, the $\gamma$-only technique was successfully applied to this reaction to exploit the precise time resolution and high efficiency of this detection system to yield results with unprecedented statistical precision and total uncertainties $<2\%$ from reaction threshold up to 16 MeV incident neutron energy, clearly resolving many features in this reaction that were previously not well known. The $\gamma$-only and $n\text{−}\gamma$ results are consistent with each other for the majority of the incident energy range covered in this paper, thereby lending validation to the $n\text{−}\gamma$ technique for future measurements, though significant disagreements are observed between both results and with the ENDF/B-VIII.0 nuclear data evaluation. These differences are particularly noticeable in the recently evaluated energy range below 6.5 MeV, and also near 14 MeV where a “sawtooth”-like feature is observed similar to that in other ${}^{12}\mathrm{C}+n$ reaction channels. Both $\gamma$-only and $n\text{−}\gamma$ results are presented here with thorough covariance derivations.

Figure 1

The level scheme of ${}^{12}\mathrm{C}$ based on Ref. [1], with percent branches to $3\alpha$ emission shown on the left-hand side. Only the 4.4398 and 15.110 MeV levels have a significant non-$3\alpha$ branch. Thus, $\gamma$-only measurements are not contaminated from other inelastic excitations.

Figure 2

A rendering of the array of liquid scintillator detectors used for the results shown in this paper. Incident neutrons enter from the lower-left side of the array, and the target was placed in the center of this array. This figure is a reproduction of Fig. 3 of Ref. [16].

Figure 3

The liquid scintillator signal integral vs the $t_{\gamma }-t_0$ time difference spectrum for the $\gamma$-only analysis described in this paper relative to the $\gamma$ transit time. Time bins are each 0.293 ns wide.

Figure 4

The correlation matrix for the $\gamma$-only cross section results is shown in the top panel, with the $1\text{−}\sigma$ uncertainty trend shown in the bottom. The block structures in the covariance are the result of the ${}^{235}\mathrm{U}(n,f)$ cross section. Note that the correlation matrix scale goes from 0 to 1, as opposed to $-1$ to 1. Thus, correlations are relatively high, and therefore the shape of this cross section is well-constrained.

Figure 5

The background-subtracted $n\text{−}\gamma$ data are shown here, summed over all neutron detection angles. The range of outgoing neutron energies observed at each incident neutron energy corresponds to the difference in kinematics for each outgoing neutron detection angle.

Figure 6

A schematic for the unfolding procedure shown in Eq. (7), demonstrated using data for $E_{\alpha }=10.96–11.22$ MeV and ${\vartheta }_n={150}^{\text{o}}$. In panel (a) an initial guess is defined as $m^{\left(0\right)}(E,{\vartheta }_n)$ (blue, dotted line) from Eq. (8), which is used to scale each initial neutron energy (row) of the liquid scintillator neutron environmental response matrix [19, 36, 37] shown in panel (b). This matrix is projected into a measured neutron energy spectrum ($x$ axis) to obtain the summation in the denominator of Eq. (7) (red, dash-dotted line) in panel (c). The ratio of background subtracted counts $[c(E,{\vartheta }_n)$; black, solid line] to this projection is used as a correction to $m^{\left(0\right)}(E,{\vartheta }_n)$ to obtain $m^{\left(1\right)}(E,{\vartheta }_n)$ (green, dashed line) in panel (d). This process can iterate indefinitely, though only a single iteration was required here.

Figure 7

The correlation matrix for the un-normalized $n\text{−}\gamma$ cross section results is shown in the top panel, with the $1\text{−}\sigma$ uncertainty trend shown in the bottom. Again, the block structures in the covariance are the result of the ${}^{235}\mathrm{U}(n,f)$ cross section, and the correlation matrix scale goes from 0 to 1, as opposed to $-1$ to 1.

Figure 8

The present $n\text{−}\gamma$ and $\gamma$-only cross section results are shown as the black and cyan data points, respectively, for the entire measured energy range in panel (a), and from 4.80 to 6.50 MeV in panel (b), 6.5 to 8.25 MeV in panel (c), 8.25 to 12.0 MeV in panel (d), and 12.0 to 16.5 MeV in panel (e). The ENDF/B-VIII.0 evaluation is shown as the black, solid line with the gray shaded region representing the evaluation uncertainties, and literature data are described in the legend, along with the type of measurement (either $\gamma$ or $n$ for literature data). The preliminary data from Negret et al. [3, 44] are shown here as the open, brown triangles in Fig. 8.