Difference between revisions of "Neutron Polarimeter"
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|<math>l</math> | |<math>l</math> | ||
|<math>T_n</math> | |<math>T_n</math> | ||
− | |<math> | + | |<math>\delta t_n</math> |
|<math>\beta_n</math> | |<math>\beta_n</math> | ||
|<math>\delta T_n</math> | |<math>\delta T_n</math> |
Revision as of 04:53, 17 June 2010
Analysis of energy dependence
four-vectors algebra
writing four-vectors:
Doing four-vector algebra:
Detector is located at
, so
and visa versa
how it looks
low energy approximation
As we can see from Fig.2 for low energy neutrons (0-21 MeV)
energy dependence of incident photons is linear
Find that dependence. We have:
So, the equation of the line is:
Finally for low energy neutrons (0-21 MeV):
example of error calculation
example 1
Say, we have, 10 MeV neutron with uncertainty 1 MeV, the corresponding uncertainly for photons energy is:
example 2
Say, we have, neutron with time of flight uncertainly is 1 ns
The neutron's kinetic energy as function of the neutron's time of flight is:
It follows, the neutron's kinetic energy error as function of the neutron's time of flight error is:
Also we need the neutron time of flight as function of neutron kinetic energy:
Say, we have 10 MeV neutron, 1 m away detector, and neutron time of flight error is 1 ns
Using formulas above:
neutron time of flight
absolute neutron kinetic energy error
relative neutron kinetic energy error
absolute photon energy error
relative photon energy error
Some other calculations for different detector distance and neutron kinetic energy are:
1 m | 20 MeV | 1 ns | 4.79 cm | 75 cm | 7.49 cm |