Alpha-Particle Scattering byP31at 18.2 MeV

The differential cross sections for the inelastic (1.265- and 2.232-MeV states) and elastic scattering of 18.2-MeV alpha particles from vacuum-evaporated phosphorous targets have been measured using silicon surface-barrier detectors. The measurements were made at 2.5° intervals in the nominal angular range from 10 to 173°. All the angular distributions exhibit an oscillatory diffraction-like structure with rather uniformly spaced maxima for angles less than about 90°. In each angular distribution the oscillatory behavior persists to backward angles but becomes less distinct and regular. The elastic cross section increases rapidly at extreme backward angles, a behavior exhibited to a lesser degree by the inelastic cross sections. Analyses of the ground-state angular distribution were made in terms of the simple diffraction model yielding $R=6.28\mathrm{}$ F and the sharp-cutoff Akhieser-Pomeranchuk-Blair (APB) model yielding $l_0=9\mathrm{}$. A graphical compilation of experimental elastic alpha-particle angular distributions for a series of light nuclei corresponding to incident alpha-particle energies in the range from 18.0 to 22.5 MeV is presented, and the possible existence of a systematic difference in the backward-angle behavior of the cross sections for certain even-even and odd-$A$ nuclei is discussed. A Blair diffraction-model analysis of the inelastic angular distribution associated with the 2.232-MeV state resulted in the following values for the collective-model parameters: $\frac{C_2}{{\left(C_2\right)}_{\mathrm{irrot}}}=7.9\mathrm{}$ and $\frac{B_2}{{\left(B_2\right)}_{\mathrm{irrot}}}=50\mathrm{}$ assuming a pure vibrational transition; and $\left|{\beta }_2\right|=0.13\mathrm{}$ assuming a pure intra-band rotational transition with $K=\frac{1}{2}$. The inelastic angular distributions associated with the 1.265- and 2.232-MeV states were analyzed using the direct-interaction theories of Austern, Butler, and McManus; and McCarthy and Pursey. Satisfactory fits were obtained at forward angles for both angular distributions with ${j_2}^2\mathrm{}\left(\mathrm{QR}\right)\mathrm{}$ using $R=6.52\mathrm{}$ F, and with the expressions of McCarthy and Pursey using $R=6.62\mathrm{}$ F, $\lambda =1.0\mathrm{}$ F, and $\gamma =0.8\mathrm{}$.