C13(p, p)C13: Experiment and Analysis

The differential cross sections for the ${\mathrm{C}}^{13}(p, p){\mathrm{C}}^{13}$ elastic scattering interactions were measured over an energy range from 1.5 to 3.4 Mev (incident proton energy) at scattering angles of 45.0°, 54.4°, 74.1°, 90.0°, 106.4°, 127.8°, 148.9° in the center-of-mass system. Methane gas, enriched to 72.5% in ${\mathrm{C}}^{13}$, was used as a target material. The absolute differential cross sections computed through this experiment were accurate to about 6% in the nonresonant energy regions. The measured nonresonant cross sections at about 2 Mev were essentially equal to those for Coulomb scattering at $\theta =45\mathrm{}°$ and increased to about seven times Coulomb cross section at $\theta =148.9\mathrm{}°$. There was also an increase in measured cross section relative to the Rutherford cross section at all scattering angles as the proton energy was increased. Maxima in the cross sections were observed at incident proton energies of 2.00, 2.12, 2.33, 2.90, and 3.12 Mev. A phase-shift analysis of the resonances at 2.00, 2.12, and 2.33 Mev yielded assignments for $J$ and $\pi$ of $1^{-}$, $3^{-}$, and $1^{+}$, respectively, and reduced widths relative to single-particle reduced widths of 0.10, 0.11, and 0.005, respectively.