Results for the Cross Section of the Reaction $^{12}$C(n,n'$\gamma$)$^{12}$C* (4.44 MeV) at E$_n$ = 6.20 and 6.34 MeV using Gamma Ray Detection*

The $\bar{\nu}$ energy spectrum measured by KamLAND is contaminated with background events which are a result of the neutrons from the $^{13}$C($\alpha$,n)$^{16}$O reaction. Because the energy range of these neutrons reaches E$_n$ = 7.3 MeV, the inelastic scattering off $^{12}$C to the 2$^+$ first excited state at 4.44 MeV can occur in the liquid scintillator for E$_n$ exceeding 4.85 MeV. The neutron from the inelastic scattering is indistinguishable from the neutron of interest in the anti-neutrino detection process $\bar{\nu}$ + p $\rightarrow$ e$^+$ + n, and the subsequent $\gamma$ from the deexcitation mimics the positron. Using the Shielded Neutron Source at TUNL with a gamma ray detection setup, we have measured the differential gamma-ray production cross section for this reaction. Clover detectors were placed 62$^{\circ}$, 90$^{\circ}$, and 135$^{\circ}$ from the incident pulsed neutron beam direction at distances of 9.75 cm, 5.7 cm, and 9.2 cm respectively from a 0.75" diameter by 1.0" high graphite cylinder. The differential cross section was measured at neutron energies of 6.20 and 6.34 MeV with an energy spread of 0.14 MeV.