# Difference between revisions of "Nucleus Recoil-Energy in Neutron Capture Reactions"

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For iodine, A = 127. Thermal neutrons have E<sub>K,n</sub> = 0.025 eV. E<sub>γ</sub> will be around 3 MeV. We then get that for neutron capture the recoil energy is<br> | For iodine, A = 127. Thermal neutrons have E<sub>K,n</sub> = 0.025 eV. E<sub>γ</sub> will be around 3 MeV. We then get that for neutron capture the recoil energy is<br> | ||

− | <math>E_{K,R}= \frac{0.025 eV}{128} = 0.2 meV</math> | + | <math>E_{K,R}= \frac{0.025 eV}{128} = 0.2 \; meV</math> |

and for the prompt γ-emission it is<br> | and for the prompt γ-emission it is<br> | ||

− | <math>E_{K,R} = \frac{9 \cdot 10^6 eV}{2 \cdot 128 \cdot 931.5 MeV} = 38 eV</math> | + | <math>E_{K,R} = \frac{9 \cdot 10^6 eV}{2 \cdot 128 \cdot 931.5 \; MeV} = 38 \; eV</math> |

+ | |||

+ | Since chemical binding-energies typically are between 0.1 to 1 eV, the recoil from γ emission is large enough to break chemical bounds. However, the recoil from n capture is not. <br> |

## Latest revision as of 13:53, 14 November 2012

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, *E _{K}*, 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:

and

In this case the nucleus has mass *A+1*, then

#### The iodine case

For iodine, A = 127. Thermal neutrons have E_{K,n} = 0.025 eV. E_{γ} will be around 3 MeV. We then get that for neutron capture the recoil energy is

and for the prompt γ-emission it is

Since chemical binding-energies typically are between 0.1 to 1 eV, the recoil from γ emission is large enough to break chemical bounds. However, the recoil from n capture is not.