# 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:

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

### Background Spectrum

#### 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

#### Run Parameters

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

### 90 Degrees Off Axis

#### Run Parameters

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

## Efficiency Calculations

### Photon Emission Rate and Flux

The radioactive source used in the irradiation 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, yielding a decay rate for the 152Eu source of ~1.3949•106 .

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 × 1.5969 = 2.22752×106 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) = = = 87.5358

### 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 × π (4.9)2cm2 = 6602.8

γ-rate into detectorOff Axis = flux (Φ) × X-area = 87.5358 × (9.8)2cm2 = 8406.94

Peak Energy (KeV) Line Intensity (%) 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 × ProbEi

Peak Energy (KeV) Line Intensity (%) 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

# 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:

## Total Efficiency

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

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

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% 0.03
1107 KeV 0.02885336857 0.264 Hz 0.33% 0.03
~1186 KeV (2 lines) 0.05145546699 0.511 Hz 0.36% 0.03