Scattering of 18.4-MeV Alpha Particles by Beryllium

The differential cross sections for inelastic (1.75-, 2.43-, and 3.04-MeV states) and elastic scattering of 18.4-MeV alpha particles from a self-supporting 176-μg/${\mathrm{cm}}^2$ beryllium foil have been measured using silicon surface-barrier detectors. The elastic and inelastic (1.75- and 2.43-MeV states) angular distributions exhibit marked diffraction patterns with regularly spaced maxima which systematically diminish in amplitude with increasing scattering angle. However, the elastic cross section, after reaching a minimum at about 90°, shows a definite tendency to increase again at back angles reaching 63 mb/sr at 174.4°. In the case of the inelastic scattering to the 2.43-MeV state, this tendency is suggested but not clearly indicated by the present results. The angular distributions associated with scattering to the 1.75- and 3.04-MeV states only extend to about 90°, which precluded any generalization concerning large-angle scattering. An analysis of the angular distributions associated with the ground state and the 2.43-MeV state was made in terms of the Blair diffraction model, assuming that these states are members of the $K=\frac{3}{2}$ rotational band and that the spin of the 2.43-MeV state is $\frac{5}{2}$. This analysis yielded an interaction radius of 5.7 F and 0.44 for the magnitude of the collective rotational deformation parameter. The angular distributions associated with the 1.8-MeV anomaly and 2.43-MeV state were also analyzed in terms of the direct-interaction theory of Austern, Butler, and McManus. Satisfactory fits were obtained for the 1.8-MeV anomaly with ${j_1}^2\mathrm{}\left(x\right)\mathrm{}$ and for the 2.43-MeV state with ${j_2}^2\mathrm{}\left(x\right)\mathrm{}$ using an interaction radius of 5.93 F. Under the assumptions of the applicability of the direct-interaction model and the constancy of the interaction radius, the assignment for the state associated with 1.8-MeV anomaly is argued to be ${\mathrm{½}}^{+}$. Its anomalous shape was fit, assuming a three-particle decay mode ${\mathrm{Be}}^8+n+{\alpha }^{\prime }$, with an $S$-wave potential-scattering final-state interaction between the neutron and the ${\mathrm{Be}}^8$ characterized by a scattering length of 30 F. The width of the 3.04-MeV state was measured by fitting various calculated line shapes to the experimental spectrum and was found to be 300±50 keV.