Levels of ${\mathrm{P}}^{29}$ from ${\mathrm{Si}}^{28}(p, p){\mathrm{Si}}^{28}$ and ${\mathrm{Si}}^{28}(p, p^{\prime }){\mathrm{Si}}^{28*}$

Differential cross sections for the elastic and inelastic scattering of protons from ${\mathrm{Si}}^{28}$ have been measured at center-of-mass scattering angles of 167.7°, 141.3°, 90.0°, and 54.7° for proton energies between 1.4 and 3.8 Mev. Resonances were observed at proton energies of 1.66, 2.09, and 2.88 Mev, in addition to the resonances at 3.10, 3.34, 3.58, and 3.71 Mev which correspond to levels in ${\mathrm{P}}^{29}$ reported previously by other investigators from studies of the $\gamma$ rays from ${\mathrm{Si}}^{28}(p, p^{\prime }\gamma ){\mathrm{Si}}^{28}$. Differential cross sections and angular distributions for inelastic scattering to the 1.78-Mev first excited state of ${\mathrm{Si}}^{28}$ were also measured for proton energies above 3 Mev. Measurements were made with a gas scattering chamber containing silane (Si${\mathrm{H}}_4$) as the target gas. The elastic scattering data were analyzed in terms of the single-level approximation of the dispersion theory to determine the resonance parameters. This analysis, together with the analysis of the inelastic scattering cross sections and angular distributions, has resulted in the following assignments of resonance energies (Mev) and spins and parities for the resonance levels of ${\mathrm{P}}^{29}$: 1.660 ($\frac{3}{2^{-}}$); 2.090 ($\frac{1}{2^{+}}$); 2.88 ($\frac{1}{2^{-}})$; 3.100 ($\frac{5}{2^{-}}$); 3.337 ($\frac{3}{2^{+}}$); 3.575 ($\frac{3}{2^{-}}$); and 3.711 ($\frac{3}{2^{+}}$). The large reduced elastic scattering widths of the $p$-wave resonances at 1.660 and 2.88 Mev suggest that these levels correspond to single-particle excitations of ${\mathrm{P}}^{29}$.