Nucleus Recoil-Energy in Neutron Capture Reactions

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A nucleus which captures a thermal neutron must, since the momentum is conserved, receive a recoil energy. Immediately after capturing a neutron, the nucleus will emit γ quantas to get rid of the excess energy liberated when the neutron is bound to the nucleus. This also result in a certain amount of recoil energy on the nucleus. 

Recoil energy from n-capture

The conservation of momentum demands that

[math]\overrightarrow{P}_n + \overrightarrow{P}_T = \overrightarrow{P}_{T+n} = \overrightarrow{P}_R[/math]

where P denotes the momentum, index n denots the neutron, index T the target nucleus, and index R the recoil. 

The kinetic energy, EK, is given by:

[math]E_K = \frac{\overleftarrow{p}^2}{2m}[/math]

Recoil energy from γ emission