Difference between revisions of "Observables"

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(New page: A couple of words about A<sub>xx</sub> and how to measure it:<br> 180px with an absolute systematic uncertainty estimated from, 180px [[Image:3.png|18...)
 
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[[Image:1.png|180px]]
 
[[Image:1.png|180px]]
  
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with an absolute systematic uncertainty estimated from,
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A<sub>xx</sub> is an asymmetry so take advantage of numerator denominator  systematics cancellation:
 +
1.) Measure N<sub>p</sub> and N<sub>u</sub> with same cup same exact material <br>
 +
2.) Use same B-field <br>
 +
3.) Use NMR on both to measure polarization and un-polarization <br>
 +
4.) Let beam heating an off larmor microwave control un-polarization <br>
 +
5.) Keep both cold (~1K) <br>
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6.) Switch from pol to unpol frequently <br>
  
 +
For unpolarized electron beam:
 
[[Image:2.png|180px]]
 
[[Image:2.png|180px]]
  
 +
[[Image:3.png|150px]]
  
 +
Which means there is a direct relationship to first component analyzing power
  
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[[Image:3.png|180px]]
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[[Image:4.png|230px]]
  
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which is very much accessible with e+D->e+N+X <br>
  
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[[Image:4.png|180px]]
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In addition we have a direct relationship to b1 for low x but be weary uncertainties
  
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To obtain tensor polarization by optimizing vector polarization we expect a tensor polarization of
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[[Image:5.png|200px]]
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P<sub>zz</sub>=2-(4-3P<sup>2</sup>)<sup>1/2</sup> assuming a Boltzman distribution at thermal equilibrium. <br>
 
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[[Image:5.png|180px]]
 
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But not at thermal equilibrium under experiment (trying not to under estimate error)<br>
 
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Analytic relation not applicable for tensor Optimization (hole burning)<br>
 
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General limitations for all tensor polarized experiments to keep in mind: <br>
 
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1.) Ideal P<sub>zz</sub> =2.5%-5% <br>
 
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2.) Vector Optimized P<sub>zz</sub> =6.5%-12% <br>
 
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3.) Tensor Optimized P<sub>zz</sub> =15%-25% <br>
 
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4.) Negative tensor polarization not yet achieved without hole burning (very unstable) <br>
 

Revision as of 10:50, 25 April 2013

A couple of words about Axx and how to measure it:

1.png

Axx is an asymmetry so take advantage of numerator denominator systematics cancellation: 1.) Measure Np and Nu with same cup same exact material
2.) Use same B-field
3.) Use NMR on both to measure polarization and un-polarization
4.) Let beam heating an off larmor microwave control un-polarization
5.) Keep both cold (~1K)
6.) Switch from pol to unpol frequently

For unpolarized electron beam: 2.png

3.png

Which means there is a direct relationship to first component analyzing power

4.png

which is very much accessible with e+D->e+N+X

In addition we have a direct relationship to b1 for low x but be weary uncertainties

5.png

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