Shell Model Assignments for the Energy Levels ofC14andN14

Abstract

Electromagnetic transition widths, reduced widths, and inelastic scattering cross sections are calculated for the following states of ${\mathrm{N}}^{14}$ and ${\mathrm{C}}^{14}$: (1) The levels arising from the ground-state configuration, ${s}^{4}{p}^{10}$, (2) the odd-parity levels arising from excitation of a $1p$ nucleon into the degenerate $2{s}_{\frac{1}{2}}$ and $1{d}_{\frac{5}{2}}$ shells, (3) the even-parity group of levels formed by excitation of two $1p$ nucleons into the $2s$ and $1d$ shells. The calculations for the ${s}^{4}{p}^{10}$ configuration are carried out using the wave functions of Elliott and of Visscher and Ferrell, and in $\mathrm{jj}$ coupling. The calculations for the odd-parity levels are done in the $\mathrm{jj}$-coupling scheme. For the even-parity excited configuration an inert ${\mathrm{C}}^{12}$ core is assumed and $M1$ radiative widths are calculated for states arising from ${s}^{2}+{d}^{2}+sd$. The calculations are compared to the existing data. On the basis of this comparison shell-model assignments are proposed for 19 of the 27 known levels below 11-Mev excitation in ${\mathrm{N}}^{14}$ and for all the known levels in ${\mathrm{C}}^{14}$ below 9-Mev excitation.