Scattering of 18.4-MeV Alpha Particles by Beryllium

Abstract

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-\ensuremath{\mu}g/${\mathrm{cm}}^{2}$ 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\ifmmode^\circ\else\textdegree\fi{}, shows a definite tendency to increase again at back angles reaching 63 mb/sr at 174.4\ifmmode^\circ\else\textdegree\fi{}. 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\ifmmode^\circ\else\textdegree\fi{}, 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 ${{j}_{1}}^{2}(x)$ and for the 2.43-MeV state with ${{j}_{2}}^{2}(x)$ 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 ${\mathrm{\textonehalf{}}}^{+}$. Its anomalous shape was fit, assuming a three-particle decay mode ${\mathrm{Be}}^{8}+n+{\ensuremath{\alpha}}^{\ensuremath{'}}$, 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\ifmmode\pm\else\textpm\fi{}50 keV.