Runs 4111(D2O)/4112(H2O)

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

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 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 (14.8 cm) [math]U(l_n) = 14.8cm/2 \cdot cos(\theta)[/math] and uncertainty in zero time definition in neutron TOF spectrum [math]U(t_n)=10 ns[/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 the flight pass length uncertainty [math]U(l_n)[/math] for Det M(1,2):

Cylindrical target with dimensions of real target was used. It was filled with liquid D2. 1 MeV neutrons were generated inside the target unoformly 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).

The correlation of neutron energy [math]E_N = m_nc^2/2 \cdot 1/c^2 \cdot (l_n/t_n)^2[/math] and uncertainty [math]U(E_n)= 2 \sqrt{U^2(l_n)/l^2_n + U^2(t_n)/t^2_n} \cdot 100\%[/math]