Alpha-Particle Scattering fromSi28at 21 to 28 MeV

60-point angular distributions for the scattering of $\alpha$ particles to the first four states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ ($0^{+}$, $2^{+}$, $4^{+}$, $0^{+}$) were measured from 21 to 28 MeV in 125-keV steps. Fluctuations with full width at half maximum of less than 300 keV were observed in all four channels. Compound-nuclear contributions to energy-averaged data have been estimated (20% to the $2^{+}$ state, 30% to the $4^{+}$ and $0_{4.97}^{+}$ states) at 25.2, 26.2, and 27.2 MeV. Optical-model fits to the elastic scattering and coupled-channel fits to the $0^{+}$, $2^{+}$, $4^{+}$ states give slightly better agreement with an angular-momentum-dependent absorption. The coupled-channel calculations give an over-all poor reproduction of the and it is not possible to extract a hexadecapole deformation for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The extracted value of the quadrupole deformation parameter is ${\beta }_2=-0.26\mathrm{}\pm 0.08$ while an upper limit can be placed on the hexadecapole deformation parameter $\left|{\beta }_4\right|\le 0.1$.