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

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=\frac{E_{K,n}}{A+1}</math> | =\frac{E_{K,n}}{A+1}</math> | ||

− | (remember that the momemtun of the target nucleus initially is 0.) | + | (remember that the momemtun of the target nucleus initially is 0.) |

==== Recoil energy from γ emission<br> ==== | ==== Recoil energy from γ emission<br> ==== | ||

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<math>E_{K,R}=\frac{\overrightarrow{P}^2_R}{2(A+1)} | <math>E_{K,R}=\frac{\overrightarrow{P}^2_R}{2(A+1)} | ||

= \frac{\overrightarrow{P}^2_\gamma c^2}{2(A+1) c^2} | = \frac{\overrightarrow{P}^2_\gamma c^2}{2(A+1) c^2} | ||

− | = \frac{E^2_\gamma (MeV)}{2(A+1) 931.5 MeV}</math> | + | = \frac{E^2_\gamma (MeV)}{2(A+1) 931.5 MeV}</math> |

+ | |||

+ | ==== The iodine case<br> ==== | ||

+ | |||

+ | For iodine, A = 127. Thermal neutrons have E<sub>K,n</sub> = 0.025 eV. E<sub>γ</sub><sub></sub> will be around 3 MeV. We then get that <br> | ||

+ | |||

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

## Revision as of 14:39, 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. 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