Elastic and Inelastic Scattering of 18.4-MeV Alpha Particles fromNa23

Abstract

Absolute differential cross sections for the elastic and inelastic (0.439-MeV and 2.080-MeV states) scattering of 18.4-MeV alpha particles from 100-\ensuremath{\mu}g/${\mathrm{cm}}^{2}$ sodium targets have been measured using silicon surface-barrier detectors. The targets were prepared by the vacuum evaporation of sodium metal onto Formvar backings. The elastic and inelastic (2.080-MeV state) cross sections were measured at 2.5\ifmmode^\circ\else\textdegree\fi{} intervals in the laboratory angular range from 10\ifmmode^\circ\else\textdegree\fi{} to 172.5\ifmmode^\circ\else\textdegree\fi{}. The 0.439-MeV state angular distribution was measured from 30\ifmmode^\circ\else\textdegree\fi{} to 172.5\ifmmode^\circ\else\textdegree\fi{}. The elastic cross section exhibits four evenly spaced diffraction maxima between 10\ifmmode^\circ\else\textdegree\fi{} and 110\ifmmode^\circ\else\textdegree\fi{}. At larger angles the pattern becomes irregular, and starts to rise rapidly at about 145\ifmmode^\circ\else\textdegree\fi{}. Both inelastic cross sections exhibit pronounced forward-angle oscillatory structure and backward-angle peaking. The elastic scattering cross section was analyzed using both the simple diffraction model which yielded a "best" interaction radius of 6.14 F, and the five-parameter, smooth-cutoff model of McIntyre, Wang, and Becker. The inelastic cross sections were analyzed using a plane-wave Born-approximation procedure and the direct-interaction theory of McCarthy and Pursey taking $l=2, 4$ and an interaction radius of 6.3 F in each case. A Blair analysis of the inelastic cross sections yielded an average value of 0.17 for the magnitude of the quadrupole deformation parameter. An alpha-particle group corresponding to inelastic scattering from the 2.39-MeV state of ${\mathrm{Na}}^{23}$ was observed, and the cross section was estimated to be nominally 0.1 of the ($\ensuremath{\alpha}, {\ensuremath{\alpha}}_{2}$) scattering cross section.