Polarization transfer measurements for the ${}^{13}\mathrm{C}(\overrightarrow{p},\overrightarrow{n}{)}^{13}\mathrm{N}$ reaction at 197 MeV and empirical isovector spin-longitudinal response for the ${\mathrm{}(1/2)\mathrm{}}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{-}\to {\mathrm{}(1/2)\mathrm{}}_1^{+}$ transition

We present differential cross sections and complete sets of polarization-transfer coefficients, $D_{\mathrm{ij}},$ obtained in the ${}^{13}\mathrm{C}(\overrightarrow{p},\overrightarrow{n}{)}^{13}\mathrm{N}$ reaction studied at 197 MeV incident proton energy and laboratory angles between $0°$ and $33°.$ These complete sets of polarization observables are used to obtain spin-longitudinal and spin-transverse components for transitions to the ground state, to the first, and to the unresolved second and third excited states in ${}^{13}\mathrm{N}$ at 2.36 MeV and $\mathrm{}(3.50+3.55)\mathrm{}\hspace{0.5em}\mathrm{MeV},$ respectively. The results are used to obtain the two $\Delta J^{\pi }$ contributions for the ground and first excited state transitions and are compared with corresponding distorted-wave impulse approximation (DWIA) calculations. In particular, empirical angular distribution values for the unique spin-longitudinal $\Delta {J=0\mathrm{}}^{-}$ transition to the first excited state in ${}^{13}\mathrm{N}$ are obtained and compared with DWIA calculations.