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

From mn/safe/nukwik
Jump to: navigation, search
Line 13: Line 13:
 
&nbsp;&nbsp;&nbsp; <math>E_K = \frac{\overrightarrow{p}^2}{2m}</math>  
 
&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
+
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;
+
&nbsp;&nbsp;&nbsp; <math>E_{K,R} = \frac{\overrightarrow{P}^2_R}{2(A+1)}
 +
= \frac{\overrightarrow{P}^2_n m_n}{2 m_n (A+1)}</math>
  
 
==== Recoil energy from γ emission<br> ====
 
==== Recoil energy from γ emission<br> ====
  
 
d
 
d

Revision as of 13:19, 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

    [math]E_{K,R} = \frac{\overrightarrow{P}^2_R}{2(A+1)} = \frac{\overrightarrow{P}^2_n m_n}{2 m_n (A+1)}[/math]

Recoil energy from γ emission

d