CH HPGe Efficiency

Efficiency Measurements Summer 2022

Electronics Chain

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

Experimental Setup

The Eu152 source provided by Roy Dunker was used to determine the efficiency and energy calibration for future experiments. As of 7/26/22, the Eu152 source had decayed to an activity of approximately 37.7μCi (~1.4•10⁶ Bq).

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.

Note that while the ADC is meant to be linear, there may be a nonlinear response as a function of energy, it may be wise to switch to a higher order energy calibration to account for this.

Background Spectrum

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  Figure 1: ADC readout of background spectrum.

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  Figure 2: Energy calibrated and time normalized spectrum from Figure 1.

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  Figure 3: Background spectrum ranging from ~150KeV to ~230KeV to show low energy cut off caused by discriminator threshold.

Run Parameters

Date Performed	7/27/22 - 7/28/22
File Name	r7224.root
Run Time	82129 Seconds
Count Rate	24.97 Hz

On Axis

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  Figure 4: 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.

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  Figure 5: Energy calibrated and time normalized spectrum from Figure 4.

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  Figure 6: Background subtracted and energy calibrated on axis spectrum from Eu152.

Run Parameters

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

90 Degrees Off Axis

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  Figure 7: 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.

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  Figure 8: Energy calibrated and time normalized spectrum from Figure 6.

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  Figure 9: Background subtracted energy spectrum from 90 degree off axis measurements.

Run Parameters

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

Overlays

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  Figure 10: Overlay of the on-axis and 90 degree off axis Eu152 calibration measurements.

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  Figure 11: Overlay of the on-axis and 90 degree off axis Eu152 calibration measurements from ~200KeV to ~600KeV.

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  Figure 12: Overlay of the on-axis and 90 degree off axis Eu152 calibration measurements from ~600KeV to ~1000KeV.

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  Figure 13: Overlay of the on-axis and 90 degree off axis Eu152 calibration measurements from ~1000KeV to ~1500KeV.

Efficiency Calculations

Photon Emission Rate and Flux

The radioactive source used in the efficiency experiments (on and off axis as defined above) was ¹⁵²Eu button source with an activity of ~37.7μCi on the day of irradiation.

The activity of the source was converted from 37.7μCi to Becquerels using the conversion of 37,000[math]\frac{\text{Bq}}{\text{μCi}}[/math], yielding a decay rate for the ¹⁵²Eu source of ~1.3949•10⁶ [math]\frac{\text{decays}}{\text{sec}}[/math].

The γ emission rate into 4π was found by totaling the intensities of photon lines produced via the EC and β- decay channels of ¹⁵²Eu, for a result of 159.69%. Data sourced from IAEA Nuclear Data Section, decay radiation subsection for ¹⁵²Eu.

γ-rate = 1.3949×10⁶ [math]\frac{decays}{sec}[/math] × 1.5969 [math]\frac{photons}{decay}[/math] = 2.22752×10⁶ [math]\frac{{photons}}{{sec}}[/math] into 4π.

The flux of photons 45cm from the source was calculated by using the γ-rate from above and the surface area of a sphere at 45cm.

flux (Φ) = [math]\frac{γ-rate}{4π(45^2)}[/math] = [math]\frac{2.22752 {×10^6}} {25446.9} \frac{photons}{sec\ cm^2}[/math] = 87.5358 [math]\frac{photons}{sec\ cm^2}[/math]

Intrinsic Efficiency

Intrinsic efficiency as a function of energy is calculated by integrating the energy peak of interest and dividing by the number of photons crossing the detector plane at that energy. I used the method outlined below to calculate the intrinsic efficiency as a function of energy for the HPGe detector in the clean room. The number of photons crossing the detector plane was found by multiplying the flux from above by the cross sectional area of the detector crystal in each orientation. The rate of the peak energy photons uses

γ-rate into detector_{On Axis} = flux (Φ) × X-area = 87.5358 [math]\frac{photons}{sec\ cm^2}[/math] × π (4.9)²cm² = 6602.8 [math]\frac{photons}{sec}[/math]

γ-rate into detector_{Off Axis} = flux (Φ) × X-area = 87.5358 [math]\frac{photons}{sec\ cm^2}[/math] × (9.8)²cm² = 8406.94 [math]\frac{photons}{sec}[/math]

Peak Energy (KeV)	Line Intensity (%)	[math]\frac{Photons}{sec}[/math] Across Detector Plane	On Axis Efficiency (%)	Off Axis Efficiency (%)
344.28	26.58	1755.02	11.0864	9.0585
411.12	2.23	147.242	11.1684	9.60532
443.96	3.12	206.007	11.5711	9.45957
778.9	12.96	855.722	8.74022	7.44913
867.37	4.23	279.298	8.26167	7.12743
964.08	14.62	965.329	8.11188	6.78583

Absolute Efficiency

The absolute efficiency as a function of energy is calculated by integrating the energy peak of interest and dividing by photons of that energy emitted into 4π from the source.

γ-rate_Ei = 2.22752×10⁶ [math]\frac{{photons}}{{sec}}[/math] × Prob_Ei

Peak Energy (KeV)	Line Intensity (%)	[math]\frac{Photons}{sec}[/math] Emitted	On Axis Efficiency (%)	Off Axis Efficiency (%)
344.28	26.58	592074	0.0328624	0.034188
411.12	2.23	49673.6	0.0331053	0.0362518
443.96	3.12	69498.5	0.0342989	0.0357017
778.9	12.96	288686	0.0259078	0.028114
867.37	4.23	94223.9	0.0244892	0.0268999
964.08	14.62	325663	0.0240452	0.0256106

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  On and Off axis intrinsic efficiency of the HPGe detector as a function of energy using a ¹⁵²Eu 45cm away from the detector casing.

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  On and Off axis absolute efficiency of the HPGe detector as a function of energy using a ¹⁵²Eu 45cm away from the detector casing.

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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