Difference between revisions of "CH HPGe Efficiency"

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='''Efficiency Measurements Summer 2022'''=
 
='''Efficiency Measurements Summer 2022'''=
 +
 +
<big>This page is ''mostly'' correct, but will need to be updated to reflect the final methodologies. </big>
  
 
=='''Electronics Chain'''==
 
=='''Electronics Chain'''==
Line 6: Line 8:
  
 
=='''Experimental Setup'''==
 
=='''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•10<sup>6</sup> Bq).
  
 
=='''Measurements'''==
 
=='''Measurements'''==
Line 11: Line 15:
 
==='''Energy Calibration'''===
 
==='''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.  
+
A linear regression was performed on the (ADC Channel Number, Peak Energy) data set. The data set is included in the table below.  
−
 
+
<center>
−
{| class="wikitable"
+
{| class="wikitable mw-collapsible mw-collapsed" border="2" style="text-align:center;" |cellpadding="20" cellspacing="1
−
|+ Caption text
 
 
|-
 
|-
−
! Header text !! Header text !! Header text
+
! Index !! ADC Channel Number !! Eu152 Peak Energy (KeV)
 
|-
 
|-
−
| Example || Example || Example
+
| 1 || 689 || 244.70
 
|-
 
|-
−
| Example || Example || Example
+
| 2 || 937 || 344.28
 
|-
 
|-
−
| Example || Example || Example
+
| 3 || 1105 || 411.12
 
|-
 
|-
−
| Example || Example || Example
+
| 4 || 1187 || 443.96
 
|-
 
|-
−
| Example || Example || Example
+
| 5 || 2025 || 778.90
 
|-
 
|-
−
| Example || Example || Example
+
| 6 || 2247 || 867.37
 
|-
 
|-
−
| Example || Example || Example
+
| 7 || 2490 || 964.08
 
|-
 
|-
−
| Example || Example || Example
+
| 8 || 2796 || 1085.9
 
|-
 
|-
−
| Example || Example || Example
+
| 9 || 2862 || 1112.1
 
|-
 
|-
−
| Example || Example || Example
+
| 10 || 3607 || 1408.0
 
|}
 
|}
 +
</center>
 +
 +
The conversion from ADC Channel to KeV is as follows:
 +
 +
<center><small><math> \text{Photon Energy (KeV)}=0.398344*(\text{Channel Number})-28.5131 </math></small></center>
 +
 +
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'''===
 
==='''Background Spectrum'''===
  
 
<gallery heights="300" widths="550" class="center">
 
<gallery heights="300" widths="550" class="center">
−
|'''Figure 1:''' ADC readout of background spectrum.  
+
CH_Background_ADC_7-27-22.png|'''Figure 1:''' ADC readout of background spectrum.  
−
|'''Figure 2:''' Energy calibrated and time normalized spectrum from Figure 1.
+
CH_Background_Energy_Spectrum_7-27-22.png|'''Figure 2:''' Energy calibrated and time normalized spectrum from Figure 1.
 +
CH_150_230KeV_Background_7-27-22.png|'''Figure 3:''' Background spectrum ranging from ~150KeV to ~230KeV to show low energy cut off caused by discriminator threshold.
 
</gallery>
 
</gallery>
 +
 +
===='''Run Parameters'''====
 +
 +
{| class="wikitable sortable mw-collapsible mw-collapsed" border="2" style="text-align:center;" |cellpadding="20" cellspacing="1
 +
|-
 +
|
 +
|-
 +
| Date Performed || 7/27/22 - 7/28/22
 +
|-
 +
| File Name || r7224.root
 +
|-
 +
| Run Time || 82129 Seconds
 +
|-
 +
| Count Rate || 24.97 Hz
 +
|}
  
 
==='''On Axis'''===
 
==='''On Axis'''===
  
 
<gallery heights="300" widths="550" class="center">
 
<gallery heights="300" widths="550" class="center">
−
CH_ADC_Eu152_OnAxis_7-26-22.png|'''Figure 1:''' 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.
+
CH_ADC_Eu152_OnAxis_10-18-22.png|'''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.
−
CH_Eu152_OnAxis_Log_7-26-22.png|'''Figure 2:''' Energy calibrated and time normalized spectrum from Figure 1.
+
CH_Eu152_OnAxis_Log_10-18-22.png|'''Figure 5:''' Energy calibrated and time normalized spectrum from Figure 4.
 +
CH_Eu152_OnAxis_Background_Subtacted_7-26-22.png|'''Figure 6:''' Background subtracted and energy calibrated on axis spectrum from Eu152.
 
</gallery>
 
</gallery>
 +
 +
===='''Run Parameters'''====
 +
 +
{| class="wikitable sortable mw-collapsible mw-collapsed" border="2" style="text-align:center;" |cellpadding="20" cellspacing="1
 +
|-
 +
|
 +
|-
 +
| Date Performed || 7/26/22
 +
|-
 +
| File Name || r7222.root
 +
|-
 +
| Run Time || 726 Seconds
 +
|-
 +
| Count Rate || 2442.06 Hz
 +
|}
  
 
==='''90 Degrees Off Axis'''===
 
==='''90 Degrees Off Axis'''===
  
 
<gallery heights="300" widths="550" class="center">
 
<gallery heights="300" widths="550" class="center">
−
CH_ADC_Eu152_OffAxis_7-26-22.png|'''Figure 1:''' 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.  
+
CH_ADC_Eu152_OffAxis_10-18-22.png|'''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.  
−
CH_Eu152_OffAxis_Log_7-26-22.png|'''Figure 2:''' Energy calibrated and time normalized spectrum from Figure 1.
+
CH_Eu152_OffAxis_Log_10-18-22.png|'''Figure 8:''' Energy calibrated and time normalized spectrum from Figure 6.
 +
CH_Eu152_OffAxis_Background_Subtacted_7-26-22.png|'''Figure 9:''' Background subtracted energy spectrum from 90 degree off axis measurements.
 +
</gallery>
 +
 
 +
===='''Run Parameters'''====
 +
 
 +
{| class="wikitable sortable mw-collapsible mw-collapsed" border="2" style="text-align:center;" |cellpadding="20" cellspacing="1
 +
|-
 +
|
 +
|-
 +
| Date Performed || 7/26/22
 +
|-
 +
| File Name || r7223.root
 +
|-
 +
| Run Time || 542 Seconds
 +
|-
 +
| Count Rate || 2634.47 Hz
 +
|}
 +
 
 +
==='''Overlays'''===
 +
 
 +
<gallery heights="300" widths="550" class="center">
 +
CH_On-Off_Axis_Overlay_Eu152_7-26-22.png|'''Figure 10:''' Overlay of the on-axis and 90 degree off axis Eu152 calibration measurements.
 +
CH_200-600KeV_On-Off_Axis_Overlay_Eu152_7-26-22.png|'''Figure 11:''' Overlay of the on-axis and 90 degree off axis Eu152 calibration measurements from ~200KeV to ~600KeV.
 +
CH_600-1000KeV_On-Off_Axis_Overlay_Eu152_7-26-22.png|'''Figure 12:''' Overlay of the on-axis and 90 degree off axis Eu152 calibration measurements from ~600KeV to ~1000KeV.
 +
CH_1000-1500KeV_On-Off_Axis_Overlay_Eu152_7-26-22.png|'''Figure 13:''' Overlay of the on-axis and 90 degree off axis Eu152 calibration measurements from ~1000KeV to ~1500KeV.
 +
</gallery>
 +
 
 +
==='''Dead Time Analysis'''===
 +
 
 +
<gallery heights="300" widths="550" class="center">
 +
CH_Dead_Time_Missed_ROC_Trigger.png|Caption1
 +
CH_Dead_Time_Wiggle.png|Caption2
 +
CH_Dead_Time_Wiggle_ENHANCED.png|Caption2
 +
</gallery>
 +
 
 +
=='''Efficiency Calculations'''==
 +
 
 +
==='''Photon Emission Rate and Flux'''===
 +
 
 +
The radioactive source used in the efficiency experiments (on and off axis as defined above) was <sup>152</sup>Eu 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<small><math>\frac{\text{Bq}}{\text{μCi}}</math></small>, yielding a decay rate for the <sup>152</sup>Eu source of ~1.3949•10<sup>6</sup> <small><math>\frac{\text{decays}}{\text{sec}}</math></small>.
 +
 
 +
The γ emission rate into 4π was found by totaling the intensities of photon lines produced via the EC and β- decay channels of <sup>152</sup>Eu, for a result of 159.69%. ''Data sourced from IAEA Nuclear Data Section, decay radiation subsection for <sup>152</sup>Eu.''
 +
 
 +
<center> ''γ-rate'' = 1.3949×10<sup>6</sup> <small><math>\frac{decays}{sec}</math></small> × 1.5969 <small><math>\frac{photons}{decay}</math></small> = 2.22752×10<sup>6</sup> <small><math>\frac{{photons}}{{sec}}</math></small> into 4π. </center>
 +
 
 +
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.
 +
 
 +
<center>''flux (Φ)'' = <small><math>\frac{γ-rate}{4π(45^2)}</math></small> = <small><math>\frac{2.22752 {×10^6}} {25446.9} \frac{photons}{sec\ cm^2}</math></small> = 87.5358 <small><math>\frac{photons}{sec\ cm^2}</math></small> </center>
 +
 
 +
==='''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
 +
 
 +
<center>''γ-rate into detector<sub><small><small>On Axis</small></small></sub>'' = ''flux (Φ)'' × ''X-area'' = 87.5358 <small><math>\frac{photons}{sec\ cm^2}</math></small> × π (4.9)<sup>2''</sup>cm<sup>2</sup>'' = 6602.8 <small><math>\frac{photons}{sec}</math></small>
 +
 
 +
''γ-rate into detector<sub><small><small>Off Axis</small></small></sub>'' = ''flux (Φ)'' × ''X-area'' = 87.5358 <small><math>\frac{photons}{sec\ cm^2}</math></small> × (9.8)<sup>2''</sup>cm<sup>2</sup>'' = 8406.94 <small><math>\frac{photons}{sec}</math></small>
 +
 
 +
{| class="wikitable mw-collapsible mw-collapsed" border="2" style="text-align:center;" |cellpadding="20" cellspacing="1
 +
|-
 +
! Peak Energy (KeV) !! Line Intensity (%) !! <small><math>\frac{Photons}{sec}</math></small> 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
 +
|}
 +
 
 +
</center>
 +
 
 +
==='''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.
 +
 
 +
<center> ''γ-rate<sub><small><small>E<sub>i</sub></small></small></sub>'' = 2.22752×10<sup>6</sup> <small><math>\frac{{photons}}{{sec}}</math></small> × ''Prob<sub><small><small>E<sub>i</sub></small></small></sub>''
 +
 
 +
 
 +
{| class="wikitable mw-collapsible mw-collapsed" border="2" style="text-align:center;" |cellpadding="20" cellspacing="1
 +
|-
 +
! Peak Energy (KeV) !! Line Intensity (%) !! <small><math>\frac{Photons}{sec}</math></small> 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
 +
|}
 +
<gallery heights="400" widths="600" class="center">
 +
CH_Int_Efficiencies_Oct22.png|''On and Off axis intrinsic efficiency of the HPGe detector as a function of energy using a <sup>152</sup>Eu 45cm away from the detector casing.''
 +
CH_Abs_Efficiencies_Oct22.png|''On and Off axis absolute efficiency of the HPGe detector as a function of energy using a <sup>152</sup>Eu 45cm away from the detector casing.''
 
</gallery>
 
</gallery>
 +
 +
</center>
  
 
='''Past Work'''=
 
='''Past Work'''=

Latest revision as of 14:24, 31 October 2022

Efficiency Measurements Summer 2022

This page is mostly correct, but will need to be updated to reflect the final methodologies.

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

  • Figure 1: ADC readout of background spectrum.

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

  • 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

  • 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.

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

  • 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

  • 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.

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

  • 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

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

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

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

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

Dead Time Analysis

  • Caption1

  • Caption2

  • Caption2

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 detectorOn 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 detectorOff 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-rateEi = 2.22752×106 [math]\frac{{photons}}{{sec}}[/math] × ProbEi


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

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

  • 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
CH Eu152 Calibration Spectrum.png

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

Previous Page

CaGaS Phase II

PAS_Experiment

PAS HPGe Detector

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