D2O bank

Relative photon flux

Relative photon flux obtained during the experiment using D2O target.

Normalization?

Flux fluctuation over the runs:

run # equivalent 1 corresponds to run 4187, 2 - 4186, 3 - 4185, 4 - 4164, 5 - 4162, 6 - 4161, 7 - 4148, 8 - 4138, 9 - 4126, 10 - 4111.

The thing is that the pair spectrometer is sensitive to the low energy background which may be present in the beam (e- beam finite size and, hence, scraping) so the value of the flux may be affected by low energy component. This thing may not be reflected in the number of neutrons detected by the neutron detectors. So, it is arguable that the pair spectrometer can be used for the flux normalization procedure. One has to investigate the energy spectra of the positrons detected.

Neutron energy spectra

Neutron energy spectra restored from all the runs with D2O target are plotted below. Statistical error bars only presented. All the histograms have same number of channels.

Neutron number vs neutron detector central angle is plotted below:

Detector efficiency

The main experimental setup used to determine the neutron detection efficiencies is shown below:

The relative neutron yield obtained by weighting the D2 photodisintegration cross section by bremsstahlung photon flux and solid angle of each of the detector is plotted below as a function of the neutron kinetic energy recalculated from the photon energy using simple kinematics:

As an example of the efficiency calculation let's find the efficiency of Det M in terms of the known absolute efficiency of Det E (14%):

For the efficiency calculation see slide 15 of [1]

[math]\displaystyle{ \frac{\epsilon_E}{\epsilon_M} = \frac{N_n^E \cdot Area_M}{N_n^M \cdot Area_E} }[/math], [math]\displaystyle{ \epsilon_M = \epsilon_E \cdot \frac{N_n^M \cdot Area_E}{N_n^E \cdot Area_M} }[/math]

Without regards to the neutron energy range one gets the following:

[math]\displaystyle{ \frac{0.14}{\epsilon_M} =\frac{5932 \cdot 7.92E-5}{2982 \cdot 5.83E-5} }[/math] and, hence, [math]\displaystyle{ \epsilon_M = 5.1 % }[/math]

[math]\displaystyle{ \epsilon_F = 14.8 % }[/math]

However, doing the same calculation fro the rest of the detectors one will get

[math]\displaystyle{ \epsilon_G = 33.3 % }[/math]

[math]\displaystyle{ \epsilon_H = 113.9 % }[/math]

[math]\displaystyle{ \epsilon_K = 126.6 % }[/math]

[math]\displaystyle{ \epsilon_I = 117.05 % }[/math]

In order to get the correct values of the neutron detection efficiency for the detectors I, K and H we did another calibration run where the D2O target was moved towards the neutron detectors as shown below:

The solid angles changed and were obtained from the simulation:

[math]\displaystyle{ \delta \Omega_G = 0.0037 sr }[/math]

[math]\displaystyle{ \delta \Omega_H = 0.0067 sr }[/math]

[math]\displaystyle{ \delta \Omega_K = 0.1 sr }[/math]

[math]\displaystyle{ \delta \Omega_I = 0.099 sr }[/math]

The relative neutron yield obtained by weighting the D2 photodisintegration cross section by bremsstahlung photon flux and solid angle of each of the detector is plotted below as a function of the neutron kinetic energy recalculated from the photon energy using simple kinematics:

From the experimental data it was defined the total number of neutrons detected by the neutron detectors I, K and H during the calibration run:

Nn(I) = 512

Nn(K) = 4175

Nn(H) = 4202

Now we can calculate the efficiency of the detectors I, K and H in terms of the efficiency of detector E obtained during the regular calibration run:

[math]\displaystyle{ \epsilon_I = \epsilon_E \cdot \frac{N_n^I \cdot Area_E}{N_n^E \cdot Area_I} }[/math]

Hence, [math]\displaystyle{ \epsilon_I = 2.5% }[/math].

Doing the same calculation for the other detectors it was obtained:

[math]\displaystyle{ \epsilon_K = 8.26% }[/math]

[math]\displaystyle{ \epsilon_H = 20.8% }[/math]

The neutron detector G was closer to the D2O target during the regular calibration run and its efficiency is more accurate as in the alternative efficiency measurement run.

Conclusions on the efficiency

The values of the neutron detector efficiencies obtained over all photo disintegration neutron energy spectrum summarized:

[math]\displaystyle{ \epsilon_E = 14.0 % }[/math]

[math]\displaystyle{ \epsilon_M = 5.1 % }[/math]

[math]\displaystyle{ \epsilon_F = 14.8 % }[/math]

[math]\displaystyle{ \epsilon_G = 33.3 % }[/math]

[math]\displaystyle{ \epsilon_H = 20.8% }[/math]

[math]\displaystyle{ \epsilon_K = 8.26% }[/math]

[math]\displaystyle{ \epsilon_I = 2.5% }[/math]

Energy uncertainty issue

Statistical errors on the number of neutrons per energy bin are not bad, however, big uncertainties in energy come due to the wide width of the photon peak: