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dRic2
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Hi, I'm reading Lamarsh's book "Introduction to nuclear reactor theory" and in chapter two there is a brief description of neutron scattering theory. I have a few questions about it.
1) In the book the author says that it is easier to analyze the interaction process in the center of mass frame, but then there is the problem to "convert" the differential cross section found in the center of mass frame to the laboratory system. In order to do so he says:
And he later continues:
This is all crystal-clear, but then he says:
Which I do not understand. (I read Section 2-8 but I didn't find anything useful...) I'd appreciate any help on this.
2) In the next part of the chapter he says that ##H^1## elastic scattering is always isotropic in the center of mass frame for all the energies of interest in reactor theory. If you adopt spherical coordinates and you call ##\theta## the scattering angle in the laboratory frame, he shows that you can find the following relation for the differential cross section:
$$\sigma( \theta) = \frac k {\pi} cos( \theta)$$
where ##0 < \theta < \frac {\pi} 2## and ##k## is a constant. He then concludes that in this situation you can't have backward scattering. I also noticed that the highest values of the cross section (in the laboratory frame) happens when ##\theta = 0##... What does it mean? That the neutron is more likely to pass "through" the hydrogen ? Is this still called scattering ?
3) The author also says that all inelastic processes require the formation of a compound nucleus. I think this is true only when we are dealing with a single "isolated" nucleus, am I right? Otherwise if I'm dealing with molecules or solids I can easily think of inelastic interaction without the formation of a compound nucleus, right ? (for example: ionization of a molecule or exiting the lattice of a cristalline structured solid)
Thanks in advance
Ric
1) In the book the author says that it is easier to analyze the interaction process in the center of mass frame, but then there is the problem to "convert" the differential cross section found in the center of mass frame to the laboratory system. In order to do so he says:
And he later continues:
This is all crystal-clear, but then he says:
Which I do not understand. (I read Section 2-8 but I didn't find anything useful...) I'd appreciate any help on this.
2) In the next part of the chapter he says that ##H^1## elastic scattering is always isotropic in the center of mass frame for all the energies of interest in reactor theory. If you adopt spherical coordinates and you call ##\theta## the scattering angle in the laboratory frame, he shows that you can find the following relation for the differential cross section:
$$\sigma( \theta) = \frac k {\pi} cos( \theta)$$
where ##0 < \theta < \frac {\pi} 2## and ##k## is a constant. He then concludes that in this situation you can't have backward scattering. I also noticed that the highest values of the cross section (in the laboratory frame) happens when ##\theta = 0##... What does it mean? That the neutron is more likely to pass "through" the hydrogen ? Is this still called scattering ?
3) The author also says that all inelastic processes require the formation of a compound nucleus. I think this is true only when we are dealing with a single "isolated" nucleus, am I right? Otherwise if I'm dealing with molecules or solids I can easily think of inelastic interaction without the formation of a compound nucleus, right ? (for example: ionization of a molecule or exiting the lattice of a cristalline structured solid)
Thanks in advance
Ric
