= Neutron detection by proton recoil
In <neutron detection by proton recoil>, a neutron strikes a <hydrogen> <atomic nucleus>, namely a <proton>, and the moving <proton> produces detectable <ionization>. <Paraffin wax> provides many <hydrogen> targets. There are two distinct questions: how much <kinetic energy> can a collision transfer, and how often does it occur? <Elastic collision> kinematics answers the first. It does not determine a <collision cross-section> or a detector's efficiency.
For the following derivations the target is initially at rest in the laboratory but is free to recoil. Its <mass> is finite. In particular a <proton> must not be treated as an immovable target. All massive particles are <nonrelativistic particles>, their translational <kinetic energies> are $mv^2/2$, and the collision changes no internal state. Target binding and thermal motion are neglected relative to the incident <kinetic energy>. These assumptions suit an introductory description of fast-neutron <elastic collisions>; they do not cover every <neutron capture> or other <nuclear reaction>.
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