Nuclear Recoil and Simple Nuclear Reactions

The nuclear-recoil properties of simple nuclear reactions are studied in the distorted-wave impulse approximation. Calculations of the differential recoil cross section $\frac{d^2\sigma }{d{\Omega }_{K}d{T}_K}$, and the recoil angular distribution $\frac{d\sigma }{d{\Omega }_K}$, for the ${\mathrm{C}}^{12}(p, pn){\mathrm{C}}^{11}$ and ${\mathrm{Ni}}^{58}(p, pn){\mathrm{Ni}}^{57}$ reactions at 450 MeV are presented and discussed. Relativistic kinematics are used and the calculations are not limited to coplanar events: they are valid for any type of kinematically allowed event. Harmonic-oscillator and exponential radial wave functions are used along with a complex, energy-dependent, Woods-Saxon optical potential. The calculations show appreciable differences between the exponential and harmonic-oscillator forms and also between distorted- and plane-wave calculations. In general, curves of $\frac{d^2\sigma }{d{\Omega }_{K}d{T}_K}$ plotted as a function of $T_K$ for fixed ${\theta }_K$, show steeper narrower peaks and larger flatter tails at ${\theta }_K=90\mathrm{}°$ than at ${\theta }_K=0\mathrm{}° or 180°$. Comparison of the recoil angular distribution for outlying target neutron shells ($1p$ in ${\mathrm{C}}^{12}$ and $2p$ in ${\mathrm{Ni}}^{58}$) and interior shells ($1s$ in ${\mathrm{C}}^{12}$ and $1f$ in ${\mathrm{Ni}}^{58}$) shows a definite sideways peaking for the outlying shells which is lacking for the interior shells. This effect is explained as being a result of the equatorial localization of reaction sites which is greater for outer shells than for inner shells. Comparison with the small number of experimental data available indicates satisfactory agreement, except possibly for sideways recoil angles where, according to Remsberg, another reaction mechanism may be contributing.