Two-Body Reactions

Two-body reactions, such as elastic scattering, neutron inelastic scattering to a level, or (p,n) to a discrete level, obey simple kinematical formulas that couple the outgoing energy E' , the incident energy E, and the scattering cosine μ. The parameters for two-body collisions are shown below in both center-of-mass and laboratory reference frames:

kinematic diagrams

The non-relativistic kinematical formulas can now be written as follows:

kinematics formulas

kinematics formulas

kinematics formulas

If the incident and scattered particles are the same, A'=1, and these formulas reduce to the more familiar set often given for neutron scattering. The elastic reaction corresponds to A'=1 and Q=0.

Note that the energy-angle distribution of the emitted particle and the full energy-angle distribution of the recoil nucleus are completely determined by A, A', Q, and the angular distribution f(E,μ).


15 December 2012 T-2 Nuclear Information Service