Cos(Theta) between two correlated neutrons. Unpolarized case.

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Revision as of 17:24, 10 June 2011 by Shaproma (talk | contribs)
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Below is the energy spectrum of two correlated neutrons in LAB frame. 10 million events. Sampled up to 10 MeV.

Sum 2n energy correlated.png


Below is [math]cos(\Theta)[/math] between two correlated neutron. No energy cut was made. Integrated over all energy spectrum.

Cos theta 2n correlated.png



And with energy cut.

Cos theta 2n correlated energy cut.png


The calculated asymmetry between correlated neutrons emitted [math]\leftleftarrows[/math] and [math]\leftrightarrows[/math] is:

[math]\mbox{Asymmetry} = \frac{\mbox{counts}\ \leftrightarrows}{\mbox{counts}\ \leftleftarrows} = \frac{209,578}{3,219} = 65.11[/math]

here:

  • [math]\mbox{counts}\ \leftrightarrows[/math] are all events with angle between two neutrons is [math]\Theta \approx (180\pm25)^o[/math]
  • [math]\mbox{counts}\ \leftleftarrows[/math] are all events with angle between two neutrons is [math]\Theta \approx (0\pm25)^o[/math]


[math]\mbox{Energy}\ \mbox{Cut}\ \mbox{Yield} = \frac{\mbox{counts}\ \mbox{with}\ \mbox{cut}}{\mbox{total}\ \mbox{counts}} = \frac{1,227,505}{10,000,000} = 0.12277[/math]
[math]\mbox{Asymmetry}\ \mbox{Yield} = \frac{(\mbox{counts}\ \leftrightarrows) + (\mbox{counts}\ \leftleftarrows)}{\mbox{total}\ \mbox{counts}} = \frac{209,578 + 3,219}{10,000,000} = 0.02128[/math]


Looks good, but we need big statistics!