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 d²σ/dΩ_KdT_K, and the recoil angular distribution dσ/dΩ_K, for the C¹²(p, pn)C¹¹ and Ni⁵⁸(p, pn)Ni⁵⁷ 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 d²σ/dΩ_KdT_K plotted as a function of T_K for fixed θ_K, show steeper narrower peaks and larger flatter tails at θ_K=90° than at θ_K=0° or 180°. Comparison of the recoil angular distribution for outlying target neutron shells (1p in C¹² and 2p in Ni⁵⁸) and interior shells (1s in C¹² and 1f in Ni⁵⁸) 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.