# Development of a new LS counter using 6 channel photomultipliers and a CdTe detector

Philippe Cassette

► To cite this version:

Philippe Cassette. Development of a new LS counter using 6 channel photomultipliers and a CdTe detector. LSC 2008 - Advances on Liquid Scintillation Spectrometry, May 2008, Davos, Switzerland. cea-05457816

HAL Id: cea-05457816

https://cea.hal.science/cea-05457816v1

Submitted on 5 Feb 2026

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# Development of a TDCR LS counter using 6 channel photomultiplier tubes and a CdTe detector

**Philippe Cassette**

*Laboratoire National Henri Becquerel, CEA-LNE, CE-Saclay, 91191 Gif sur Yvette Cedex, France*
# Goal

* Design a portable LS counter for primary standardization

* Including an external gamma source

* Including a gamma detector (CdTe)

* Using minimum data acquisition hardware (FPGA module)

## Applications:

* Primary standardization using 3 different methods on the same instrument (CNET method, Compton tracer method, TDCR)

* Instrument for international comparisons

* In situ standardization of short half-life radionuclides (e.g. $^{11}$C, $^{18}$F)
Free parameter model

μ: mean number of photons emitted per unit of energy absorbed in the scintillator

p: probability that a photon created in the scintillator is detected by 1 detector

If - the statistics of the number of photoelectrons is a Poisson law

- the detection probability of 1 photoelectron is not zero

Then : detection efficiency = 1- non-detection efficiency = $1-e^{-p\mu E}$

Detection efficiency for 2 identical photodetectors in coincidence :

$$ (1 - e^{-p\mu E})^2 $$

Detection efficiency for 3 identical photodetectors in coincidence :

$$ (1 - e^{-p\mu E})^3 $$
# Detection efficiency

For a radionuclide transferring an energy spectrum S(E) in the scintillator

$$ \epsilon_D = \int_{\text{spectrum}} S(E)(1-e^{-p\mu EQ(E)})^2 dE \quad \text{with} $$

$$ E \cdot Q(E) = \int_{0}^{E} \frac{dE}{1+kB \frac{dE}{dx}} $$

If you know (pμ) you can calculate detection efficiency...

2 main methods to find (pμ):

1. Efficiency tracing (including CIEMAT/NIST method)

2. Triple to Double Coincidence Ratio Method (TDCR)

<figure><img src="image_2.png" /></figure>
# LSC radionuclide standardization methods

<figure><img src="image_3.png" /></figure>
Drawbacks of these methods

Efficiency tracing

* Requires a standard (generally ³H)

* Requires a perfect match between standard source and radionuclide to measure source

* Needs accurate Birks function for low-energy e.c. radionuclides (kB, $dE/dx$)

* Needs accurate spectrum (especially for low-energy emitters)

TDCR

* Requires a specific counter

* Needs accurate Birks function for low-energy beta radionuclides (kB, $dE/dx$)

* Needs accurate spectrum (especially for low-energy emitters)
But you can still have your cake and eat it!

Using both methods is a useful way to control all the
parameters of the model, e.g. $kB$, $dE/dx$, spectra...

If the model is OK, the 2 method should give the same result...
Or, you can optimize the model parameters to get the same
results from both models

Useful applications: measurement of low-energy radionuclides
with more or less known spectrum ($^{99}$Tc, $^{241}$Pu, $^{93}$Zr, $^{36}$Cl...)

But, of course, this need a lot of efforts, except...if you can use
tracer method without a tracer!
## Idea: create a well defined tracer source inside the source-to-measure

<figure><img src="image_4.png" /></figure>

How: produce a temporary electron source inside a LS vial using the Compton interaction and select the energy of this source using a gamma-ray detector

*This source can be monoenergetic or polyenergetic with a measurable spectrum*
Principle of this tracer method

* External 59.5 keV $\gamma$ source ($^{241}$Am)

* $\gamma$-ray detector with calibrated spectrum

* Coincident measurement (rejection of other electron source)

* Energy of electron source controlled by energy selection of the diffused Compton photon spectrum

<figure><img src="image_5.png" /></figure>
# Electron energy spectrum

<figure><img src="image_6.png" /></figure>

$$E_e=h\nu-h\nu'$$

Scattering angle 90°: 6.2 keV electrons
Scattering angle 180°: 11.3 keV
<figure><img src="image_7.png" /></figure>
Variations on a theme

1. Monoenergetic electrons (selected by SCA): in-situ measurement of the non-linearity of the LS source at low energy

2. Polyenergetic source defined by the collimators and detector geometry: internal low-energy tracer source
# Measurement of the non-linearity of the scintillator

TDCR counter in coincidence with the signal of the gamma detector (giving $E$)

$$ \mathbf{R}_{AB} = (1 - \mathbf{e}^{-\nu_A})(1 - \mathbf{e}^{-\nu_B}) \quad \text{etc. for BC and AC} $$

$$ \mathbf{R}_T = (1 - \mathbf{e}^{-\nu_A})(1 - \mathbf{e}^{-\nu_B})(1 - \mathbf{e}^{-\nu_C}) \qquad \nu_X = \mathbf{p}_X \mu_X \mathbf{E} $$

$$ \leftarrow\right\} \begin{array}{l} \frac{\mathbf{R}_T}{\mathbf{R}_{AB}} = 1 - \mathbf{e}^{-\nu_C} \\ \\ \frac{\mathbf{R}_T}{\mathbf{R}_{BC}} = 1 - \mathbf{e}^{-\nu_A} \\ \\ \frac{\mathbf{R}_T}{\mathbf{R}_{AC}} = 1 - \mathbf{e}^{-\nu_B} \end{array} \leftarrow\right\} \begin{array}{l} \nu_C = -\ln\left(1 - \frac{\mathbf{T}_{\text{experiment al}}}{\mathbf{AB}_{\text{experiment al}}}\right) \\ \\ \nu_A = -\ln\left(1 - \frac{\mathbf{T}_{\text{experiment al}}}{\mathbf{BC}_{\text{experiment al}}}\right) \\ \\ \nu_B = -\ln\left(1 - \frac{\mathbf{T}_{\text{experiment al}}}{\mathbf{AC}_{\text{experiment al}}}\right) \end{array} $$

Free parameter
for each PMT
Example of application (InstaGel)

<figure><img src="image_8.png" /></figure>

Number of
photoelectrons
# Advantages of the method

* Experimental non-linearity: no need of a calculated function using $kB$ and $dE/dx$, a simple polynomial fit is OK

* The measured non-linearity is an intrinsic property of the source to measure. Any radionuclide present in the source is rejected by the coincidence circuit

## Drawbacks of the method

* low efficiency: many events rejected, long counting time

* limited energy range. Higher energy range requires higher excitation energy (e.g. $^{139}$Ce)
Polyenergetic source defined by the collimators and
detector geometry: internal low-energy tracer source

The electron spectrum can be calculated from the measured
Compton photon spectrum (from energy conservation law)

<figure><img src="image_9.png" /><figcaption>Selected spectrum</figcaption></figure>

<figure><img src="image_10.png" /></figure>

The useful portion of this spectrum is selected using a SCA
Method, step 1

LS source with radionuclide X

$^{241}$Am
source

<figure><img src="image_11.png" /></figure>

TDCR counter, coincidence with Compton
photon spectrum

<figure><img src="image_12.png" /></figure>

Experimental TDCR

<figure><img src="image_13.png" /></figure>

TDCR model using experimental
Compton electron spectrum

Free parameter for each PMT
LS source with radionuclide X

<figure><img src="image_14.png" /></figure>

Experimental TDCR

<figure><img src="image_15.png" /></figure>

Free parameter
for each PMT
from step 1

TDCR model using calculated
spectrum of radionuclide X

Detection efficiency of radionuclide X
# Summary

Tracer method, similar in principle to the CIEMAT/NIST method but:

* Free parameter deduced from the source to measure (no quenching parameter to consider)

* Tracer from internal source created by Compton effect

* The counting rate of the Compton source does not matter

* The spectrum of the tracer source is only defined by the geometry of the detector and can be measured

* The detection efficiency can also be calculated using the traditional TDCR model with the same data set
Suitable LS counter

By principle, each photodetector must give a logical information:
Generate a pulse if 1 or more photoelectron is detected

<figure><img src="image_16.png" /></figure>

The photodetector must have a non-ambiguous
response to one (SER) or more photoelectron in
order to correctly adjust the detection threshold

<figure><img src="image_17.png" /></figure>
# Photodetectors

Photomultiplier tubes are generally used

* **Advantages:**

* Well known technology

* High gain

* Various available geometries

* Moderate price

* **Drawbacks:**

* Quantum efficiency < 30 %

* Modest resolution of the Single Electron Response peak

* Dark noise

* After pulses

* Gain stability

<figure><img src="image_18.png" /></figure>
# Alternative photodetectors
with photocathodes:

• Microchannel plates PMT

• Hybrid photomultipliers (PIN diode or APD)

• Channeltron photomultipliers

• Gaseous detectors (TMAE, etc.)

## without photocathodes:

• PIN photodiodes

• Avalanche photodiodes (APD)

• Silicon photomultipliers (multipixel Geiger mode APDs)

<figure><img src="image_19.png" /></figure>
Single Electron Responses (SER)

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>
# Channel photomultipliers (Perkin Elmer®)

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>
# LS counter prototype

<figure><img src="image_26.png" /></figure>
Optical chamber

<figure><img src="image_27.png" /><figcaption>CdTe detector</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>TiO$_2$ paint</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>Upper chamber</figcaption></figure>
Optical chamber

<figure><img src="image_30.png" /></figure>

vial
# Data acquisition

CdTe controller

<figure><img src="image_31.png" /></figure>

MCA

PXI controller

FPGA module
# Experimental results with a ³H source

## Comparison Compton/TDCR

<table><thead><tr><th rowspan="2">kB</th><th colspan="4">Compton source method</th><th colspan="3">Difference %</th></tr><tr><th>vA</th><th>TDCR</th><th>Eff. Double</th><th>Eff. Triple</th><th>TDCR</th><th>Eff. Double</th><th>Eff. Triple</th></tr></thead><tbody><tr><td>0,007</td><td>0,7515</td><td>0,4849</td><td>0,5475</td><td>0,2655</td><td>1,543%</td><td>1,369%</td><td>2,890%</td></tr><tr><td>0,008</td><td>0,7801</td><td>0,4867</td><td>0,545</td><td>0,2652</td><td>1,198%</td><td>1,089%</td><td>2,284%</td></tr><tr><td>0,009</td><td>0,8083</td><td>0,4883</td><td>0,5428</td><td>0,265</td><td>0,873%</td><td>0,786%</td><td>1,670%</td></tr><tr><td>0,01</td><td>0,8362</td><td>0,4897</td><td>0,5407</td><td>0,2648</td><td>0,569%</td><td>0,497%</td><td>1,046%</td></tr><tr><td>0,011</td><td>0,864</td><td>0,4912</td><td>0,5389</td><td>0,2647</td><td>0,264%</td><td>0,222%</td><td>0,489%</td></tr><tr><td>0,012</td><td>0,8913</td><td>0,4924</td><td>0,5371</td><td>0,2644</td><td>0,020%</td><td>-0,019%</td><td>0,038%</td></tr><tr><td>0,013</td><td>0,9187</td><td>0,4936</td><td>0,5355</td><td>0,2643</td><td>-0,223%</td><td>-0,225%</td><td>-0,456%</td></tr><tr><td>0,014</td><td>0,9456</td><td>0,4947</td><td>0,5339</td><td>0,2641</td><td>-0,426%</td><td>-0,414%</td><td>-0,840%</td></tr><tr><td>0,015</td><td>0,9728</td><td>0,4959</td><td>0,5326</td><td>0,2641</td><td>-0,670%</td><td>-0,642%</td><td>-1,304%</td></tr></tbody></table>

In a defined *kB* value range, there is a good agreement between the 2 methods... And this range is not too exotic!
# Conclusion and perspectives

A simple Compton spectrometer can be added to a TDCR
counter using a gamma-ray spectrometer, a SCA and a
coincidence unit

This allows:

* the measurement of the scintillator non-linearity which can be included in the TDCR model

* the possibility to use the Compton electrons as an efficiency tracing source

* preliminary tests using ³H source

Developments: integrate all the data acquisition in the FPGA module
Test with various radionuclides, scintillators, etc.