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Added discussion about transforming COM to LAB system in documentation.

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Paul Romano 2012-07-25 20:13:42 -04:00
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docs/source/methods/physics.rst
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@ -617,8 +617,30 @@ Transforming a Particle's Coordinates
Once the cosine of the scattering angle :math:`\mu` has been sampled either from
a angle distribution or a correlated angle-energy distribution, we are still
left with the task of transforming the particle's coordinates. The scattering
cosine that we sampled only tells us the cosine of the angle between the
left with the task of transforming the particle's coordinates. If the outgoing
energy and scattering cosine were given in the center-of-mass system, then we
first need to transform these into the laboratory system. The relationship
between the outgoing energy in center-of-mass and laboratory is
.. math::
:label: energy-com-to-lab
E' = E'_{cm} + \frac{E + 2\mu_{cm} (A + 1) \sqrt{EE'_{cm}}}{(A+1)^2}.
where :math:`E'_{cm}` is the outgoing energy in the center-of-mass system,
:math:`\mu_{cm}` is the scattering cosine in the center-of-mass system,
:math:`E'` is the outgoing energy in the laboratory system, and :math:`E` is the
incident neutron energy. The relationship between the scattering cosine in
center-of-mass and laboratory is
.. math::
:label: angle-com-to-lab
\mu = \mu_{cm} \sqrt{\frac{E'_{cm}}{E'}} + \frac{1}{A + 1}
\sqrt{\frac{E}{E'}}.
where :math:`\mu` is the scattering cosine in the laboratory system. The
scattering cosine still only tells us the cosine of the angle between the
original direction of the particle and the new direction of the particle. If we
express the pre-collision direction of the particle as :math:`\mathbf{\Omega} =
(u,v,w)` and the post-collision direction of the particle as