Structure of 14C via elastic and inelastic neutron scattering from 13C: Measurement and R-matrix analysis.

Abstract

Differential cross sections for neutrons elastically scattered from $^{13}\mathrm{C}$ and inelastically scattered to the first three excited states $^{13}$${\mathrm{C}}^{\mathrm{*}}$(3.09, 3.68, and 3.85 MeV) were measured at 69 incident energies for 4.5\ensuremath{\le}${E}_{n}$\ensuremath{\le}11 MeV. A multiple scattering code provided a simulation of the experimental scattering process allowing accurate corrections to the small measured inelastic cross sections. The integrated $^{13}$C(n,\ensuremath{\alpha}${)}^{10}$Be cross section was determined by subtracting the sum of the measured integrated cross sections from the total. Shell-model calculations were used to generate the R-matrix parameters for the elastic and first three inelastic channels of $^{13}$C+n, and, after some minor adjustments, the predicted structure generally agreed with experiment for ${E}_{n}$4 MeV. Previous elastic $^{13}$C+n data were refitted to replace constant ${R}_{0}$ R-matrix background terms by more realistic broad states and to achieve better agreement with model calculations and the data. R-matrix fitting of the full data set produced new $^{14}\mathrm{C}$ level information. For ${E}_{n}$g4 MeV (${E}_{x}$g12 MeV), five states were given definite ${J}^{\ensuremath{\pi}}$ assignments and three states tentative assignments.