Reaction Kinematics for NRA

If the total energy Et = Ei + Q = Es + E4, it is simple to establish the following relations applying the laws of conservation of energy and momentum and using the reaction kinematics on the reactants and products (as shown in Fig. 7.1). 

Ratio of the energy of light product w.r.t total kinetic energy 

It is to note that A + B + C + D= 1 and AC = BD. Most nuclear reactions, called resonant nuclear reactions, have sharp resonance in the cross-section at certain energies. The resonant cross-section width is of the order of several keV. This fact is used to obtain a depth scale for the measured impurity concentration and the technique is called Resonant NRA. Reactions with suitable cross-sections exist for many elements. The N( H, ay) C nuclear reaction is widely used as a well established tool to measure hydrogen in all kinds of solids. On the other hand, in those cases where the nuclear reaction cross-sections vary slowly with energy, the technique employed is called Non-Resonant NRA. In such cases, taking NRA kinematics into account, the technique is identical to RBS. 

For the nuclear reaction to take place, the kinetic energy Ei of the charged particle must be sufficient to overcome the nuclear force, called the Coulomb barrier (Sc), given by 

---