From an analysis of the effective potentials and the surface region behavior of quantum mechanical radial wave functions, we find that the most interesting physical phenomena taking place in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ scattering at $E_{\mathrm{lab}}=55\mathrm{}$ MeV is the orbiting mechanism for $l=24, 25, 26$. We find that the orbital amplitude $A_0\left(\theta \right)$ generated by these partial waves acts coherently at large angles with the background amplitude $A_b\left(\theta \right)$ describing the remainder of the full amplitude. The enhanced large angle oscillations are caused by the almost, but not complete, destructive interference between $A_0\left(\theta \right)$ and $A_b\left(\theta \right)$. Using appropriate mathematical techniques, we show that at large angles $\theta \lesssim 180°$, both $A_0\left(\theta \right)$ and $A_b\left(\theta \right)$ are dominated essentially by the same Legendre polynomial. This explains the observation of Takemasa and Tamura that the cross sections generated by exact Regge pole terms behave quite similarly to that generated by the corresponding Regge background terms. Furthermore, our analysis clarifies the underlying reason for the success of the purely parametric Regge pole model at large angles. We also compare the infinite sequence of Regge poles generated by the barrier term in the Wentzel-Kramers-Brillouin formula for the "nuclear" $S$ matrix and the exact quantum mechanical orbiting Regge pole. The oscillatory behavior of the reflection function ${\eta }_l$ of the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ system at $E_{\mathrm{lab}}=55\mathrm{}$ MeV as a function of $l$ for $l$ below the orbiting region is also explained.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$-${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ scattering at $E_{\mathrm{lab}}=55\mathrm{}$ MeV. Analysis of orbiting phenomena. Regge poles related to orbiting.

• Received 1 October 1982

DOI:https://doi.org/10.1103/PhysRevC.27.2042