CH HPGe Efficiency

Efficiency Measurements Summer 2022

Electronics Chain

Click here to view the electronics chain used for these efficiency measurements.

Measurements

Energy Calibration

A linear regression was performed on the (ADC Channel Number, Peak Energy) data set. The data set is included in the table below.

Index	ADC Channel Number	Eu152 Peak Energy (KeV)
1	689	244.70
2	937	344.28
3	1105	411.12
4	1187	443.96
5	2025	778.90
6	2247	867.37
7	2490	964.08
8	2796	1085.9
9	2862	1112.1
10	3607	1408.0

The conversion from ADC Channel to KeV is as follows:

[math] \text{Photon Energy (KeV)}=0.398344*(\text{Channel Number})-28.5131 [/math]

The KeV per bin can be found by taking the derivative of the energy conversion, leading to a constant 0.398 KeV per bin.

On Axis

• 

  Figure 3: Eu152 Emission spectrum captured using HPGe detector and ADC in clean room on 7/26/22. Eu152 source placed 45cm from end cap of detector directly on central axis. The red arrows indicate peaks used in regression for energy calibration.

• 

  Figure 4: Energy calibrated and time normalized spectrum from Figure 4.

Run Parameters

Date Performed	7/26/22
File Name	r7222.root
Run Time	726 Seconds
Count Rate	2442.06 Hz

90 Degrees Off Axis

• 

  Figure 5: Eu152 Emission spectrum captured using HPGe detector and ADC in clean room on 7/26/22. Eu152 source placed 45cm from the side of the cap of detector, 90 degrees from central axis of detector crystal.

• 

  Figure 6: Energy calibrated and time normalized spectrum from Figure 6.

Run Parameters

Date Performed	7/26/22
File Name	r7223.root
Run Time	542 Seconds
Count Rate	2634.47 Hz

Past Work

Most likely incorrect

Eu152 Calibration

• HPGe calibrated using Eu152 source

As of 9/28/21

The calibration used to map from ADC channel number to KeV is:

[math]Photon\ Energy\ =\ -36.2928\ +\ 0.449519\ x\ -\ 0.000000861277\ x^2[/math]

Where x = channel 9 of the ADC and is input as PADC.PADC785N[9].

Total Efficiency

This is total efficiency using the Gadolinium foil as the source.

[math] (line\ intensity)\ (incident\ thermal\ neutrons\ per\ second)\ (\sigma_{total})\ (MCNP\ fudge\ factor\ from\ Paul\ approx\ 4)\ =\ Theoretical\ Rate [/math]

For the ease of calculation, I will use the outgoing photon rate from the Gd foil as tabulated by MCNP, thanks to Paul Stonaha. The number given was into 2pi, towards the HPGe detector, multiplying by 2 should give the rate into 4pi.

The 897 KeV peak found in the Gd in/out measurements can be attributed to two different lines created by neutron capture on Gd157. The high purity germanium detector used in this experiment would not be able to resolve the two distinct lines as the resolution is not fine enough. However, adding the intensities together should yield the theoretical rate for the peak measured at that energy.

The first peak is 897.506 KeV with a relative intensity of 17.846%, according the capgam nndc data repository.

The second peak is 897.62 KeV with a relative intensity of 16%, according the capgam nndc data repository.

(0.17846 + 0.16) (2*1374Hz) (234000) = Rate

234000 is the total thermal neutron capture cross section for ¹⁵⁷Gd

Note: the fudge factor comes from the nucleus being excited and then de-exciting from the neutron absorption and emits on average, 4 photons per neutron capture

Then find detected rate using HPGe

Divide (detected rate) by (theoretical rate) for total detector efficiency

An easier way to calculate the detector efficiency is

[math]Det.\ Eff.\ =\ \frac{Detected\ Rate}{(Normalized\ Line\ Intensity)(Theoretical\ Total\ Rate)}[/math]

Theoretical total rate = 2748 Hz from simulations

Line Energy	Line Weighting	Detected Rate	Detector Efficiency
897 KeV (2 lines)	0.03967382135	0.357 Hz	0.33% [math]\pm[/math] 0.03
1107 KeV	0.02885336857	0.264 Hz	0.33% [math]\pm[/math] 0.03
~1186 KeV (2 lines)	0.05145546699	0.511 Hz	0.36% [math]\pm[/math] 0.03

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