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

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The conservation of momentum demands that<br>  
 
The conservation of momentum demands that<br>  
  
<math>\overrightarrow{P}_n + \overrightarrow{P}_T = \overrightarrow{P}_{T+n} = \overrightarrow{P}_R</math>  
+
&nbsp;&nbsp;&nbsp;&nbsp; <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.&nbsp;  
+
where P denotes the momentum, index ''n'' denots the neutron, index ''T'' the target nucleus, and index ''R'' the recoil.&nbsp;  
  
The kinetic energy, E<sub>K</sub>, is given by:  
+
The general relationship between kinetic energy, ''E<sub>K</sub>'', and momentum ''p'' is given by:  
  
<math>E_K = \frac{\overleftarrow{p}^2}{2m}</math>
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&nbsp;&nbsp;&nbsp; <math>E_K = \frac{\overrightarrow{p}^2}{2m}</math>  
 +
 
 +
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
 +
 
 +
&nbsp;&nbsp;&nbsp;
  
 
==== Recoil energy from γ emission<br> ====
 
==== Recoil energy from γ emission<br> ====
  
 
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Revision as of 13:16, 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

     [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 general relationship between kinetic energy, EK, and momentum p is given by:

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

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

   

Recoil energy from γ emission

d