Proton Angular Distributions for ($\alpha , p$) Reactions on ${\mathrm{C}}^{12}$, ${\mathrm{Al}}^{27}$, and ${\mathrm{P}}^{31}$

Angular distributions of protons corresponding to single and multiple levels of excitation have been measured for the reactions ${\mathrm{C}}^{12}(\alpha , p){\mathrm{N}}^{15}$, ${\mathrm{Al}}^{27}(\alpha , p){\mathrm{Si}}^{30}$, and ${\mathrm{P}}^{31}(\alpha , p){\mathrm{S}}^{34}$ using 42-Mev alpha particles. Distributions corresponding to the ground state and third-excited state of ${\mathrm{N}}^{15}$ and to the ground state and first-excited state of ${\mathrm{S}}^{34}$ show pronounced diffraction-like structure. Distributions from ${\mathrm{Si}}^{30}$ show a marked lack of structure. The data indicate that simple phasing relationships between distributions from levels of even and odd parity, predicted by models based on the plane-wave Born approximation, do not agree with experiment. The ground-state distribution from ${\mathrm{N}}^{15}$ is in agreement with the theories of Butler and Bhatia. However, the observed distribution from the third-excited state of ${\mathrm{N}}^{15}$ does not agree with the predictions of these theories. Total cross sections obtained for the ground state and third-excited state of ${\mathrm{N}}^{15}$ were large compared with those for low-level transitions in the reactions on phosphorus and aluminum. These in turn have much larger cross sections than those for ${\mathrm{Na}}^{23}(\alpha , p){\mathrm{Mg}}^{26}$, ${\mathrm{F}}^{19}(\alpha , p){\mathrm{Ne}}^{22}$, and ${\mathrm{Cl}}^{35}(\alpha , p){\mathrm{Ar}}^{38}$, which were too small to be investigated with our apparatus. There is some indication from this investigation that those distributions which show pronounced angular structure have cross sections that are more highly dependent on bombarding energy than those that lack structure.