Nucleus Recoil-Energy in Neutron Capture Reactions
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 (usually refered to as "promt γ to distinguis it from the "normal" γs which is emitted after the nucleus has disintegrated). This also result in a certain amount of recoil energy on the nucleus.
Recoil energy from n-capture
The conservation of momentum demands that
where P denotes the momentum, index n denots the neutron, index T the target nucleus, and index R the recoil.
The general relationship between kinetic energy, EK, and momentum p is given by:
The mass of the neutron is 1 (atomic mass unit). the mass of the target nucleus is A. The new nucleus will therefore have mass A+1. Then
(remember that the momemtun of the target nucleus initially is 0.)
Recoil energy from γ emission
For emission of the mass-less quantas we have the following relationship:
In this case the nucleus has mass A+1, then
The iodine case
For iodine, A = 127. Thermal neutrons have EK,n = 0.025 eV. Eγ will be around 3 MeV. We then get that for neutron capture the recoil energy is
and for the prompt γ-emission it is