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.

Why do you want to fit multiple gaussians to the neutron distribution? TF

[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 Ng H2O.jpg

Relation Nn over Ngamma2.jpg

Relation Nn over NgH2O4.jpg

Relation Nn over Ngamma3.jpg

Relation Nn over Ngamma3 H2O3.jpg

Relation Nn over Ngamma5.jpg

Relation Nn over Ngamma55.jpg

Relation Nn over Ngamma7.jpg

Relation Nn over Ngamma77.jpg

Summary tables for [math]\frac{N_n}{N_\gamma}[/math] averaged over runs w/ polarized beam, [math]D_2O[/math] and [math]H_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]H_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]0.15\pm 0.05[/math] [math]0.148\pm 0.042[/math] [math]0.102\pm 0.032[/math] [math]0.11\pm 0.03[/math] [math]0.098\pm 0.025[/math]

[math]\frac{NaI}{N_\gamma (RefDet)}[/math] relation for [math]D_2O[/math] and [math]H_2O[/math] targets

Relation Nn over Ngamma8.jpg

Relation Nn Ng H2O.jpg

Run(21/20), run(25/24) were taken 10/15/2008 and run(38/37), run(34/33) were carried out on 10/16/2008. Some beam conditions might have been changed.

[math]\frac{NaI(peak area)}{N_n (RefDet)}[/math] relation for [math]D_2O[/math] and [math]H_2O[/math] targets

Relation NaI over Nn RefDet2.jpg

Relation NaI over Nn RefDet22.jpg

[math]\frac{NaI(flux)}{N_n (RefDet)}[/math] relation for [math]D_2O[/math] and [math]H_2O[/math] targets

[math]D_2O[/math] target:

Relation NaI flux over Nn RefDet D2O 2.jpg

[math]H_2O[/math] target

Relation NaI flux over Nn RefDet H2O.jpg

Comparison of [math]\frac{N_n}{N_\gamma}[/math] and [math]\frac{NaI}{N_\gamma}[/math] for Ref Det , [math]D_2O[/math] target, polarized beam

Relation NaI over Ngamma.jpg

Where is gamma flash coming from? (H2O target)

[math]\gamma[/math](MT) = [math]\gamma[/math](Plastic shell)+[math]\gamma[/math](room BKG)

[math]\gamma[/math](H2O target) = [math]\gamma[/math](Plastic shell)+[math]\gamma[/math](H2O liquid)+[math]\gamma[/math](room BKG)

[math]\gamma[/math](H2O liquid) = [math]\gamma[/math](H2O target) - [math]\gamma[/math](MT)

[math]\gamma[/math](Plastic shell) = [math]\gamma[/math](MT) - [math]\gamma[/math](room BKG)


[math]\gamma[/math](MT) date 10/17/2008 NaI [math]3.79\cdot 10^9[/math]
run# Duration, sec # of [math]\gamma[/math]'s Rate ([math]\gamma[/math]/sec) Rate ([math]\gamma[/math]/sec[math]\gamma'[/math])

122 (Det A up) 3071.69 27987.5 [math]\pm[/math] 167.3 9.11 [math]\pm[/math]0.054 [math](2.42 \pm 0.014)\cdot 10^{-9}[/math]
123 (Det C side) 3071.69 14227 [math]\pm[/math]119 4.63 [math]\pm[/math]0.038 [math](1.2 \pm 0.01)\cdot 10^{-9}[/math]
124 (Ref Det) 3071.69 24037 [math]\pm[/math]155 7.8 [math]\pm[/math]0.05 [math](2.058 \pm 0.013)\cdot 10^{-9}[/math]

[math]\gamma[/math](room BKG) date 10/17/2008 NaI [math]2.14\cdot 10^9[/math]
run# Duration, sec # of [math]\gamma[/math]'s Rate ([math]\gamma[/math]/sec) Rate ([math]\gamma[/math]/sec[math]\gamma'[/math])

118 (Det A up) 1812.1 15873.5 [math]\pm[/math]125.9 8.76 [math]\pm[/math]0.069 [math](4.09 \pm 0.03)\cdot 10^{-9}[/math]
119 (Det C side) 1812.1 7993 [math]\pm[/math]89 4.41 [math]\pm[/math]0.049 [math](2.06 \pm 0.02)\cdot 10^{-9}[/math]
120 (Ref Det) 1812.1 14128 [math]\pm[/math]119 7.79 [math]\pm[/math]0.065 [math](3.6 \pm 0.03)\cdot 10^{-9}[/math]

[math]\gamma[/math](H2O target(a)) date 10/17/2008 NaI [math]3.085\cdot 10^9[/math]
run# Duration, sec # of [math]\gamma[/math]'s Rate ([math]\gamma[/math]/sec) Rate ([math]\gamma[/math]/sec[math]\gamma'[/math])

110 (Det A up) 1799.57 40725 [math]\pm[/math]202 22.63 [math]\pm[/math]0.11 [math](7.33 \pm 0.036)\cdot 10^{-9}[/math]
111 (Det C side) 1799.57 11511 [math]\pm[/math]107 6.4 [math]\pm[/math]0.06 [math](2.074 \pm 0.019)\cdot 10^{-9}[/math]
112 (Ref Det) 1799.57 18902 [math]\pm[/math]137 10.5 [math]\pm[/math]0.08 [math](3.4 \pm 0.03)\cdot 10^{-9}[/math]

[math]\gamma[/math](H2O target(b)) date 10/17/2008 NaI [math]3.03\cdot 10^9[/math]
run# Duration, sec # of [math]\gamma[/math]'s Rate ([math]\gamma[/math]/sec) Rate ([math]\gamma[/math]/sec[math]\gamma'[/math])

114 (Det A up) 1801.1 41351 [math]\pm[/math]203 22.96 [math]\pm[/math]0.11 [math](7.58 \pm 0.036)\cdot 10^{-9}[/math]
115 (Det C side) 1801.1 11511 [math]\pm[/math]107 6.4 [math]\pm[/math]0.06 [math](2.1 \pm 0.01) \cdot 10^{-9}[/math]
116 (Ref Det) 1801.1 18703 [math]\pm[/math]137 10.38 [math]\pm[/math]0.076 [math](3.42 \pm 0.025)\cdot 10^{-9}[/math]

Separation of [math]\gamma[/math]-sources:

[math]\gamma[/math](room BKG)
run# rate([math]\gamma[/math]/sec) Rate ([math]\gamma[/math]/sec[math]\gamma'[/math])

118 (by Det A up) 8.76 [math]\pm[/math] 0.069 [math](4.09 \pm 0.03)\cdot 10^{-9}[/math]
119 (by Det C side) 4.41 [math]\pm[/math] 0.049 [math](2.06 \pm 0.02)\cdot 10^{-9}[/math]
120 (by Ref Det) 7.79 [math]\pm[/math]0.065 [math](3.6 \pm 0.03)\cdot 10^{-9}[/math]

[math]\gamma[/math](Plastic shell)
[math]\delta[/math]run# [math]\delta[/math]rate([math]\gamma[/math]/sec)

122-118 (by Det A up) 0.35 [math]\pm[/math]0.087
123-119 (by Det C side) 0.22 [math]\pm[/math]0.062
124-120 (by Ref Det) 0.029 [math]\pm[/math]0.082

[math]\gamma[/math](H2O liquid (a))
[math]\delta[/math]run# [math]\delta[/math]rate([math]\gamma[/math]/sec)

110-122 (by Det A up) 13.52 [math]\pm[/math] 0.12
111-123 (by Det C side) 1.77 [math]\pm[/math]0.071
112-124 (by Ref Det) 2.67 [math]\pm[/math]0.094

[math]\gamma[/math](H2O liquid (b))
[math]\delta[/math]run# [math]\delta[/math]rate([math]\gamma[/math]/sec)

114-122 (by Det A up) 13.85 [math]\pm[/math]0.12
115-123 (by Det C side) 1.76 [math]\pm[/math]0.071
116-124 (by Ref Det) 2.56 [math]\pm[/math]0.091

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