A kind of analysis

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[math]\gamma[/math]-peak positions are shifted w.r.t. each other due to the difference in TOF conversion (electronics amplification). If we wanna calculate the asymmetry as a function of TOF for each channel (neutron energy) it is necessary to match the positions of centroids of [math]\gamma[/math]-peaks. However, one needs to take into account the difference between channel-to-TOF calibration coefficients for each detector.

This is what we have if we superimpose TOF-spectra within one plot. It was used used the average channel-to-TOF calibration coefficient (0.179+0.186+0.19)/3 = 0.185 ns/channel (Is it okay to do that?).

Asym 0.jpg


Asym 11.jpg

Channel-to-TOF calibration coefficients used was 0.19 ns/channel. [math]\gamma[/math]-peak positions were matched manually by cutting out the shift in the spectra w.r.t. Ref Det.


The following plot was drawn using upper plot and formula for calculation of asymmetry placed at [[1]]


Asym 2.jpg


Neutron part of spectrum

Separation of TOF.jpg


Separation of TOF2.jpg

We should define how many peaks to use, i.e. we need some physical model for the process we observe.


[math]\frac{N_n}{N_\gamma}[/math] relations

In the calculation of [math]\frac{N_n}{N_\gamma}[/math] it was used just integration of area under the curve instead of fitting neutron spectrum with three peaks (it was observed 0.36% difference between areas calculated in these two ways).


Relation Nn over Ngamma.jpg


Relation Nn over Ngamma2.jpg


Relation Nn over Ngamma3.jpg


Relation Nn over Ngamma5.jpg


Relation Nn over Ngamma7.jpg

Summary table for [math]\frac{N_n}{N_\gamma}[/math] averaged over runs w/ polarized beam and [math]D_2O[/math] target

[math]D_2O[/math] target Det A (side) Det C (side) Det A (up) Det C (up) Ref Det
<[math]\frac{N_n}{N_\gamma}[/math]> [math]4.22\pm 0.15[/math] [math]4.7\pm 0.5[/math] [math]1.011\pm 0.039[/math] [math]1.2\pm 0.09[/math] [math]2.64\pm 0.083[/math]


[math]\frac{NaI}{N_\gamma RefDet}[/math] relation for [math]D_2O[/math] target

Relation Nn over Ngamma8.jpg