${}^{12}\mathrm{C}(n, 2n){}^{11}\mathrm{C}$ cross section from threshold to 26.5 MeV

The ${}^{12}\mathrm{C}(n,2n){}^{11}\mathrm{C}$ cross section was measured from just below threshold to 26.5 MeV using the Pelletron accelerator at Ohio University. Monoenergetic neutrons, produced via the ${}^3\mathrm{H}\left(d,n\right){}^4\mathrm{He}$ reaction, were allowed to strike targets of polyethylene and graphite. Activation of both targets was measured by counting positron annihilations resulting from the ${\beta }^{+}$ decay of ${}^{11}\mathrm{C}$. Annihilation gamma rays were detected, both in coincidence and singly, using back-to-back NaI detectors. The incident neutron flux was determined indirectly via ${}^1\mathrm{H}\left(n,p\right)$ protons elastically scattered from the polyethylene target. Previous measurements fall into upper and lower bands; the results of the present measurement are consistent with the upper band.

Figure 1

Cross sections for the ${}^{12}\mathrm{C}$($n, 2n){}^{11}\mathrm{C}$ reaction near threshold. The empty symbols are previously published data: Brolley et al. (blue circles) [8], Brill et al. (pink circles) [9], Anders et al. (green circles) [6], Welch et al. (blue triangles) [7], Soewarsono et al. (pink triangles) [10], Uno et al. (green triangles) [11], and optical model calcualtions of Dimbylow (blue diamonds) [5]. The solid red symbols are from this experiment using the polyethylene target and both NaI detectors in coincidence; the larger of the associated error bars indicates the increase in overall uncertainty when the uncertainty in incident neutron energy is included.

Figure 2

The experimental setup for activating targets. Deuterons traveling down the beam pipe were collimated, then struck the tritium target to produce neutrons. These neutrons activated the graphite and polyethylene targets via the ${}^{12}\mathrm{C}$($n,2n$) reaction. The polyethylene target also acted as the converter for the recoil proton telescope. The recoiling protons were identified and counted using a dE-E telescope.

Figure 3

(b) Histogram of dE versus E for 23.7-MeV neutrons striking the polyethylene target. The proton island is clearly visible. The marked region of interest (black) indicates the elastically scattered protons. (a) Same, but with the polyethylene target removed.

Figure 4

A 2D histogram showing the pulse height in each NaI detector for coincidence events. The events in the large coincidence peak were counted for 50-s intervals to produce the ${}^{11}\mathrm{B}$ growth curve.

Figure 5

(a) Fit of Eq. (1) to the coincidence growth curve and (b) residuals for the graphite target activated by 26.3-MeV neutrons. The uncertainties shown were calculated using the integrated number of counts (a) and the incremental number for each time bin $\sqrt{N_i-N_{i-1}}$ (b).

Figure 6

Schematic diagram showing quantities used to calculate the $\left(N_p/N_n\right)$ proton to neutron ratio for extended targets. A neutron can travel from an infinitesimal area element at polar coordinates $(r_t,{\theta }_t)$ on the tritium target to an area element at polar coordinates $(r,\theta )$ on the polyethylene target along vector ${\mathbf{R}}_{\mathbf{n}}$. A proton can then travel from there to the area element at polar coordinates $(r_{\det },{\theta }_{\det })$ on the detector along vector ${\mathbf{R}}_{\mathbf{p}}$. The total number of neutrons or protons were determined by integrating over the surfaces of the involved targets or detector. The $z$ coordinate axis is along the center of the beamline.

Figure 7

The ratio of $\left(N_p/N_n\right)$ determined by integration using Eqs. (10) and (9) to the value determined using the simple approximate approach of Eqs. (7) and (8) for the graphite (red squares) and the polyethylene targets (blue diamonds).

Figure 8

Comparison of the cross sections measured in this experiment using the graphite (circles) and polyethylene (diamonds) targets for (b) both NaI detectors in coincidence (red), and (c) NaI detector 1 (blue) and (d) NaI detector 2 (green) in singles mode. (a) Shows cross sections determined using both coincidence and singles information for both targets on the same plot. For each cross section, the larger of the associated error bars indicates the increase in overall uncertainty when the uncertainty in incident neutron energy is included.