Difference between revisions of "Nucleus Recoil-Energy in Neutron Capture Reactions"
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− | 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. <br> | + | 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. <br> |
==== Recoil energy from n-capture<br> ==== | ==== Recoil energy from n-capture<br> ==== | ||
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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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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} | ||
+ | = \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> 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> | ||
+ | |||
+ | 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> | ||
+ | |||
+ | 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 14:53, 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, EK, 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 EK,n = 0.025 eV. Eγ 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.