Inelastic Scattering by Deformed Nuclei

The techniques of the sharp and rounded cutoff models for elastic scattering have been extended to the calculation of nuclear monopole and quadrupole excitation in the adiabatic approximation. In the case of scattering from nuclei with quadrupole deformations, a spheroidal coordinate system is introduced where one of the coordinate ellipsoids coincides with the nuclear surface; the wave equation separates outside the range of the nuclear potential. Formal expressions and results of numerical calculations for the cross sections are presented for a case where simple assumptions are made about the functional form of the partial wave amplitudes and where only terms linear in nuclear deformation are retained. One limit of the form for the spherical partial wave amplitudes leads to a sharp-cutoff model which goes over into the Fraunhofer results for moderate and large values of the critical angular momentum. It is found that graphs of the excitation cross section (and to a lesser extent the elastic scattering cross section) fall into a single-parameter family of "universal curves" when plotted against (scattering angles) × (critical angular momentum+½). The single parameter is (thickness of transition region in $l$ space) ÷ (critical angular momentum). No detailed comparisons with experiment are made, but the model is capable of reproducing the qualitative results of alpha-particle scattering at energies well above the Coulomb barrier.