Inelastic scattering of 65 MeV protons from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$

Measurements of angular distributions of the cross sections and analyzing powers for the elastic and inelastic scatterings of 65 MeV polarized protons from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ are reported. Coupled channels analyses of the scattering data are presented assuming the $0_1^{+}$, $2_1^{+}$, and $4_1^{+}$ states to be members of the ground band, the $0_2^{+}$ state to begin the

β band, and the $3_1^{\mathrm{-}}$ state to begin the $K^{\pi }$${=3\mathrm{}}^{\mathrm{-}}$ band in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$; the $0_1^{+}$, $2_1^{+}$, and $4_1^{+}$ states to comprise the ground band, the $2_2^{+}$, $3_1^{+}$, and $4_2^{+}$ states to comprise the γ band, the $3_1^{\mathrm{-}}$ state to begin the $K^{\pi }$${=3\mathrm{}}^{\mathrm{-}}$ band, and the $1_1^{\mathrm{-}}$ and $3_2^{\mathrm{-}}$

states to comprise the $k^{\pi }$${=0\mathrm{}}^{\mathrm{-}}$ band in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$; and the $0_1^{+}$, $2_1^{+}$, and $4_1^{+}$ states to comprise the ground band, the $0_2^{+}$ state to begin the β band, the $3_1^{\mathrm{-}}$, $4_1^{\mathrm{-}}$, $5_1^{\mathrm{-}}$, and $6_1^{\mathrm{-}}$ states to comprise the $k^{\pi }$${=3\mathrm{}}^{\mathrm{-}}$ band, and the $1_1^{\mathrm{-}}$

and $3_1^{\mathrm{-}}$ states to comprise the $K^{\pi }$${=0\mathrm{}}^{\mathrm{-}}$ band in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The fit of the analyzing power of the β band $0_2^{+}$ level is improved by mixing the breathing mode of oscillation into the β vibration. Coupled channels analyses of the experimental angular distributions are presented for the levels in ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ in which the $0_1^{+}$, $2_1^{+}$, and $4_1^{+}$ states were assumed to belong to the ground band, the $0_2^{+}$ and $2_3^{+}$ states to the β band, the $2_2^{+}$, $3_1^{+}$,

and $4_2^{+}$ states to the γ band, the $3^{\mathrm{-}}$ state to the $3^{\mathrm{-}}$ band, and the $1^{\mathrm{-}}$ state to the $0^{\mathrm{-}}$ band. These states were treated assuming a symmetric rotator model. The coupled channels calculations in terms of a vibrational model were also performed for ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$. Multipole moments obtained from present data are compared to the moments deduced from hadron scattering and electromagnetic measurements. Transition strengths deduced from the (p,p’) scattering are compared with gamma-ray decay widths for $2^{+}$ states in the ground bands.