Runs 4111(D2O)/4112(H2O)

Subtraction of stops for D2O

Subtraction of the stops for each detector in the case of D2O target. The length of the active area (scintillator) of the detector is 75.3 cm.

Subtraction of stops for H2O

Subtraction of the stops for each detector in the case of H2O target:

Subtraction of D2O and H2O ToF

Normalized superimposed timing spectra from D2O(black line)/H2O(red line) targets and bin-by-bin subtraction (green line) of D2O-H2O data:

Neutron energy analysis

Neutron energy distribution data analysis for run 4111:

File:D2O neutron spectra.pdf

Errors on the neutron energy for the case of Det M:

[math]E_n \pm U(E_n)=m_nc^2/2 \cdot 1/c^2 \cdot (l_n/t_n)^2 \cdot [1 \pm 2 \sqrt{U^2(l_n)/l^2_n + U^2(t_n)/t^2_n}][/math]

Where uncertainty in the neutron flight pass due to the finite width of the detector [math]U(l_n)[/math] was simulated using GEANT4 and uncertainty in zero time definition in neutron TOF spectrum [math]U(t_n)[/math] was defined from the experimental data as sigma of the zero time photon peak.

The neutron flight path length was calculated using the following expression: [math]l_n = \sqrt{l_c^2 + (X_c-X_i)^2}[/math], where [math]X_c=75/2=37.5cm[/math] is the coordinate of the middle of the neutron detector active area and [math]X_i[/math] is the current x-coordinate extracted from time difference spectrum. [math]l_c[/math] is the distance from the middle of the target to the middle of the neutron detector surface. The current coordinate can be defined as [math]X_i = (((TDC_{left}-TDC_{right}) \cdot 0.223 ns/ch) \pm S) \cdot R[/math], where [math]S[/math] is a shift factor due to the difference in delays for the two channels and should be taken to be the lowest value in [math](TDC_{left}-TDC_{right}) \cdot 0.223[/math] spectrum. The coefficient [math]R[/math] is equal to active area dimension divided by the total width of [math](TDC_{left}-TDC_{right}) \cdot 0.223[/math] spectrum measured at base.

Neutron ToF to the surface of the detector can be calculated as [math]t_n = 0.5 \cdot ((TDC_{left}+TDC_{right})-ToF_{sint+lg})[/math], where [math]ToF_{sint+lg}[/math] is the total light ToF inside the detector and it was taken to be a const [math]ToF_{sint+lg} = 100cm \cdot \frac{1}{2.5 cm/ns} \simeq 40 ns[/math]. So, the neutron ToF can be calculated as [math]t_n = 0.5 \cdot ((TDC_{left}+TDC_{right})-40)[/math]

Correlation between the neutron energy and neutron energy uncertainty is plotted below:

The above plot may look better if you plot [math]Energy[/math] -vs- ([math]Energy \pm Energy[/math]) 
As the energy increased the uncertainty increases to the point the the error bar is as big as the magnitude of the energy.

Simulation of n-flight path. DetM.

Simulation of the flight path length uncertainty [math]U(l_n)[/math] for Det M(1,2) placed right below the target:

Cylindrical target with dimensions of real target was used. It was filled with liquid D2. 1 MeV neutrons were generated inside the target uniformly and isotropically. The shortest distance from the target to the detector surface was 97.4 cm (corresponds to zero in the plot of the Delta_L)

The whole range fit:

Central region fit:

As can be seen we have [math]U(l_n)[/math] of ~ 3.3 cm for the whole detector (no binning).

If we apply the binning (total # of events sampled [math]4 \cdot 10^5[/math]):

Region 4	Region 3	Region 2	Region 1
x <= -18.97 cm	0 >= x >= -18.97 cm	0 <= x <= 18.97 cm	x >= 18.97 cm

Experimental data Det M

The correlation of neutron energy [math]E_n = m_nc^2/2 \cdot 1/c^2 \cdot (l_n/t_n)^2[/math] and its uncertainty [math]U(E_n)= 2 \sqrt{(3cm)^2/l^2_n + (8.8ns)^2/t^2_n} \cdot 100\%[/math] for the case neutron ToF cut [25,65] ns:

If we consider the neutron time of flight uncertainty [math]U(t_n) = 7 ns[/math] and [math]U(l_n) = 3.3 cm[/math] then the correlation plot changes to

If we consider the neutron time of flight uncertainty [math]U(t_n) = 1 ns[/math] and [math]U(l_n) = 3.3 cm[/math] then the correlation plot changes to

It can be concluded that the neutron energy uncertainty is really sensitive to the neutron ToF uncertainty. In our case we had a long tail in photon peak which could possibly distort the zero time definition and the precision of neutron energy calculation.

Data analysis for DetH

Simulation of n-flight path. DetH.

Simulated neutron flight pass lenrgth distribution is presented below:

The width of the distribution is about 10 cm wide.

The active area of the detector is ~ 75 cm. If we bin the detector in four, we will get for [math]4 \cdot 10^5[/math] generated events

Region 4	Region 3	Region 2	Region 1
x <= -18.97 cm	0 >= x >= -18.97 cm	0 <= x <= 18.97 cm	x >= 18.97 cm

So it can be seen that the neutron flight path uncertainty, if taken to be the RMS in a flight path spectrum, is [math]U(l_n) \simeq 3.5 cm[/math].

Experimental data

Data with no binning:

After binning the detector and taking for the neutron flight path uncertainty [math]U(l_n) = 3.5 cm[/math] we got:

Region 4	Region 3	Region 2	Region 1
x <= -18.97 cm	0 >= x >= -18.97 cm	0 <= x <= 18.97 cm	x >= 18.97 cm

According to my observation the uncertainty in the neutron flight path does not influence the uncertainty in neutron energy too much. Main contribution is from the zero-time definition in ToF spectrum.

Data analysis for Det_E

Simulated neutron flight path for detector F w/o binning and [math]2 \cdot 10^5[/math] events simulated:

The uncertainty in neutron flight path is RMS = 2.36 cm.

Angular distribution of neutrons (experimental data):

If we apply the binning:

Region 4	Region 3	Region 2	Region 1
x <= -18.97 cm	0 >= x >= -18.97 cm	0 <= x <= 18.97 cm	x >= 18.97 cm

Data analysis for Det_F

Simulated neutron flight path for detector F w/o binning and [math]2 \cdot 10^5[/math] events simulated:

The uncertainty in neutron flight path is RMS = 2.5 cm.

If we apply the binning:

Region 4	Region 3	Region 2	Region 1
x <= -18.97 cm	0 >= x >= -18.97 cm	0 <= x <= 18.97 cm	x >= 18.97 cm

Experimental data

Data analysis for Det_G

Simulated neutron flight path for detector F w/o binning and [math]2 \cdot 10^5[/math] events simulated:

The uncertainty in neutron flight path is RMS = 3.24 cm.

If we apply the binning:

Region 4	Region 3	Region 2	Region 1
x <= -18.97 cm	0 >= x >= -18.97 cm	0 <= x <= 18.97 cm	x >= 18.97 cm

Data analysis for Det_K

Data analysis for Det_I

Simulated neutron flight path for detector F w/o binning and [math]4 \cdot 10^5[/math] events simulated:

The uncertainty in neutron flight path is RMS = 4.27 cm.

If we apply the binning:

Region 4	Region 3	Region 2	Region 1
x <= -18.97 cm	0 >= x >= -18.97 cm	0 <= x <= 18.97 cm	x >= 18.97 cm

The uncertainty on the zero time is [math]U(t_n) \simeq 24 ns[/math]. Squared value [math]U(t_n)^2 = 576 ns[/math] which is comparable to [math]t_n^2[/math] and the uncertainty is big while the neutron flight path uncertainty for the whole detector is ~ 3 cm and its squared value is much less than the squared value of the distance traveled by neutrons, e.g. [math]3^2/253^2 = 9/64009 \simeq 1.4 \cdot 10^{-4}[/math]