Inelastic Scattering in the $2s-1d$ Shell. II. Odd-$A$ Nuclei

The inelastic scattering of 17.5-MeV protons from ${\mathrm{F}}^{19}$, ${\mathrm{Na}}^{23}$, ${\mathrm{Mg}}^{25}$, ${\mathrm{Al}}^{27}$, and ${\mathrm{P}}^{31}$ has been studied with lithium-drifted silicon detectors with an over-all energy resolution of order 50 keV. Differential cross sections are presented for most of the low-lying levels. Using previously obtained data for the adjacent even-even nuclei, the results are compared with the predictions of strong- and weak-coupling models. The results are most consistent with strong coupling for ${\mathrm{F}}^{19}$, ${\mathrm{Na}}^{23}$ and ${\mathrm{Mg}}^{25}$, while ${\mathrm{Al}}^{27}$ and ${\mathrm{P}}^{31}$ seem to be more consistent with weak coupling, although extensive mixing is required in ${\mathrm{Al}}^{27}$. The differential cross section for the most strongly excited levels are compared with a distorted-wave Born-approximation calculation using collective form factors. Reasonable fits for $l=2\mathrm{}$ excitations in ${\mathrm{F}}^{11}$, ${\mathrm{Al}}^{27}$, and ${\mathrm{P}}^{31}$ and $l=3\mathrm{}$ transitions in ${\mathrm{P}}^{31}$ are obtained, and the appropriate reduced transition strengths are extracted. Previously unreported levels are observed in ${\mathrm{Na}}^{23}$ (5.38, 5.76, and 5.94 MeV), ${\mathrm{Al}}^{27}$ (7.66, 7.79, and 7.99 MeV), and ${\mathrm{P}}^{31}$ (5.34 MeV).