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

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For emission of the mass-less quantas we have the following relationship: | For emission of the mass-less quantas we have the following relationship: | ||

− | <math>\overrightarrow{P}_R = \overrightarrow{P}_\gamma</math> | + | <math>\overrightarrow{P}_R = \overrightarrow{P}_\gamma</math> |

− | and | + | and |

− | <math>P_\gamma = \frac{E_\gamma}{c}</math> | + | <math>P_\gamma = \frac{E_\gamma}{c}</math> |

+ | |||

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

+ | |||

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

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

## Revision as of 14:33, 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