Developing DRF for 1’’X1’’ LaBr3 Detector

Sangkyu Lee

Detector Response Function • Function: a function is a relation between a set

of inputs and a set of permissible outputs with the property that each input is related to one output.

• DRF (Detector Response Function)

𝑅 = 𝑑𝐸 𝑑𝑉𝑅 (𝑟 , 𝐸)Φ𝑉

∞

0(𝑟 , 𝐸)

𝑅 (𝑟 , 𝐸) is a Detector Response Function.

Simulation Result (MCNP)

Similar Result With Experiment

DRF 𝑅 (𝑟 , 𝐸)

Why do we need DRF?

• Different Result between simulation and experiment • How can I compare between simulation and

experiment?

• Full energy peak is not enough to compare. There are Compton scatter, Compton edge, escape peaks, backscatter, annihilation peak and sum peak other than full energy peak.

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

2000150010005000

- Experiment - Simulation

Components of DRF

• Energy resolution: Gaussian broadening effect

• Detector efficiency (Intrinsic efficiency)

• Background

Gaussian function : 𝑓 𝐸 = 𝐶𝑒−(𝐸−𝐸0

𝐴)2

𝐸 = Broadened energy 𝐸0= Unbroadened energy

𝐴 = Gaussian width = 𝐹𝑊𝐻𝑀

2 𝑙𝑛2

𝐶 = Normalized constant

𝜖𝑖𝑛𝑡 = 𝑑𝑒𝑡𝑒𝑐𝑡𝑜𝑟 𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒

𝑟𝑎𝑡𝑒 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠 𝑒𝑛𝑡𝑒𝑟𝑖𝑛𝑔 𝑑𝑒𝑡𝑒𝑐𝑡𝑜𝑟

Method to develop DRF

• Gamma spectroscopy experiment (with 1”X1” LaBr3 detector and various sources)

• MCNP simulation with same setups of experiment

• Find Gaussian fitting curve equations at different energy (Fitting program)

• Writing code for DRF

Goal for this project

• Understand all events inside of the

detector

• Improve fitting and code writing technic

• Compare between simulation results and

experiment results for every gamma

interactions

• Accurate and practical spectrum analysis

Experiment setup

1”X1” LaBr3 Detector

Source position

Ba133(keV)

81

303

356

Cs137(keV)

661.7

Eu152(MeV)

121.7817

244.697

344.2785

778.9040

964.079

1085.869

1112.074

1408.006

Energy calibration

Channel Original

(keV)

First order

(keV)

Second order

(keV)

46 81 78.7057 81.01108

171 303 302.4182 302.0373

202 356 357.8989 356.9969

373 661.7 663.9376 661.1974

788 1408 1406.663 1406.757

Measured spectra

0.001

0.01

0.1

1

10

100

count ra

te (

CPS)

3500300025002000150010005000keV

0.01

0.1

1

10

100

count ra

te (

CPS)

3500300025002000150010005000keV

0.01

0.1

1

count ra

te (

CPS)

3500300025002000150010005000keV

0.001

0.01

0.1

1

10

count ra

te (

CPS)

3500300025002000150010005000keV

Background

Ba-133

Cs-137

Am241+Eu152

Gaussian fitting 1/3

fit_wave1= W_coef[0]+W_coef[1]*exp(-((x-W_coef[2])/W_coef[3])^2)

W_coef={1.3028,11.643,80.869,4.8246}

V_chisq= 1.47046;V_npnts= 15;V_numNaNs= 0;V_numINFs= 0;

V_startRow= 0;V_endRow= 14;

W_sigma={0.168,0.27,0.0818,0.152}

Coefficient values ± one standard deviation

y0 =1.3028 ?0.168

A =11.643 ?0.27

x0 =80.869 ?0.0818

width =4.8246 ?0.152

12

10

8

6

4

2

9085807570

fit_wave3= W_coef[0]+W_coef[1]*exp(-((x-W_coef[2])/W_coef[3])^2)

W_coef={0.18242,1.4176,302.97,7.9149}

V_chisq= 0.0108718;V_npnts= 15;V_numNaNs= 0;V_numINFs= 0;

V_startRow= 0;V_endRow= 14;

W_sigma={0.0365,0.0341,0.0748,0.258}

Coefficient values ± one standard deviation

y0 =0.18242 ?0.0365

A =1.4176 ?0.0341

x0 =302.97 ?0.0748

width =7.9149 ?0.258

1.6

1.4

1.2

1.0

0.8

0.6

0.4

310305300295290

Ba-133

81 keV

Ba-133

303 keV

Gaussian fitting 2/3

fit_wave5= W_coef[0]+W_coef[1]*exp(-((x-W_coef[2])/W_coef[3])^2)

W_coef={0.14211,3.6111,355.9,8.5697}

V_chisq= 0.0193398;V_npnts= 15;V_numNaNs= 0;V_numINFs= 0;

V_startRow= 0;V_endRow= 14;

W_sigma={0.06,0.0552,0.0412,0.165}

Coefficient values ± one standard deviation

y0 =0.14211 ?0.06

A =3.6111 ?0.0552

x0 =355.9 ?0.0412

width =8.5697 ?0.165

fit_wave7= W_coef[0]+W_coef[1]*exp(-((x-W_coef[2])/W_coef[3])^2)

W_coef={0.77311,98.552,662.29,11.871}

V_chisq= 1.16801;V_npnts= 19;V_numNaNs= 0;V_numINFs= 0;

V_startRow= 0;V_endRow= 18;

W_sigma={0.475,0.435,0.012,0.0597}

Coefficient values ± one standard deviation

y0 =0.77311 ?0.475

A =98.552 ?0.435

x0 =662.29 ?0.012

width =11.871 ?0.0597

3.5

3.0

2.5

2.0

1.5

1.0

0.5

365360355350345

80

60

40

20

675670665660655650645

Cs-137

661.7 keV

Ba-133

356 keV

Gaussian fitting 3/3

fit_wave9= W_coef[0]+W_coef[1]*exp(-((x-W_coef[2])/W_coef[3])^2)

W_coef={-0.053832,2.034,1407.2,18.779}

V_chisq= 0.0120882;V_npnts= 23;V_numNaNs= 0;V_numINFs= 0;

V_startRow= 0;V_endRow= 22;

W_sigma={0.102,0.0972,0.0714,0.758}

Coefficient values ± one standard deviation

y0 =-0.053832 ?0.102

A =2.034 ?0.0972

x0 =1407.2 ?0.0714

width =18.779 ?0.758

1.8

1.6

1.4

1.2

1.0

0.8

0.6

1420141014001390

Eu-152

1408 keV

Energy resolution for LaBr3

80

60

40

x10

-3

140012001000800600400200

*CurveFit/M=2/W=0 Power, wave3/X=wave0/D

Fit converged properly

fit_wave3= W_coef[0]+W_coef[1]*x^W_coef[2]

W_coef={0.013247,2.7356,-0.78751}

V_chisq= 7.46812e-008;V_npnts= 5;V_numNaNs= 0;V_numINFs= 0;

V_startRow= 0;V_endRow= 4;

W_sigma={0.000448,0.107,0.0099}

Coefficient values ± one standard deviation

y0 =0.013247 ?0.000448

A =2.7356 ?0.107

pow =-0.78751 ?0.0099

Resolution function

The resolution function was expressed by a power law

relation (Berger and Seltzer, 1972):

𝑟 𝐸 = 𝐹𝑊𝐻𝑀

𝐸

𝑟 𝐸 = 𝑎 × 𝐸𝑏

𝑟 𝐸 = 0.013247 + 2.7356 × 𝐸−0.78751

LaBr3 Detector MCNP6 Simulation

Differences between Monte Carlo modeling and experiment

0.01

0.1

1

10

100

1000

3500300025002000150010005000

3

2

1

4

1. Intensity

2. Gaussian broadening(Energy resolution)

3. Coincidence counting(Sum effect)

4. Background

MCNP6 simulation

Experiment result

Algorithm for DRF

Input

(Simulation Result)

Gaussian Broadening

Add Coincidence

Counting

Multiply by Intensity

Add Background

Output Check the reduced

Chi-square with

experiment spectrum

Good Bad

Check

the parameters

Cs-137 decay mode

DRF result

Sum peak(1323.4keV)

K-40 (background)

Cs-137 peak(661.7keV)

Backscatter peak

0.01

0.1

1

10

100

Count ra

te(n

/s)

3500300025002000150010005000Energy(keV)

- Experiment- DRF

References

[1] Glenn F. Knoll, Radiation Detection and Measurement, John Wiley and Sons, Fourth Edition, 2010.

[2] Truong Thi Hong Loan, Study on the HPGe Detector Response Function by the Monte Carlo Method with

Using MCNP Code, Doctoral special subject report, UNS-VNU-HCMC, 2006.

[3] Gardner R. P. and Sood A. (2004) : A Monte Carlo simulation approach for generating NaI detector response

functions (DRFs) that accounts for non-linearity and variable flat continua. Nucl. Instr. and Meth. B 213, 87-99.

[4] Response Function of a 3×3 in. NaI Scintillation Detector in the range of 0.081 to 4.438 MeV Hashem Miri

Hakimabad, Hamed Panjeh* and Alireza Vejdani-Noghreiyan, Physics Department, Faculty of Science,

Ferdowsi University of Mashhad, Mashhad, Iran

[5] CALIBRATION OF THE HIGH AND LOW RESOLUTION GAMMA-RAY SPECTROMETERS*

AURELIAN LUCA, BEATRIS NEACSU, ANDREI ANTOHE, MARIA SAHAGIA

“Horia Hulubei” National Institute for Physics and Nuclear Engineering, IFIN-HH Bucharest,

P.O. Box MG-6, RO-077125 Bucharest-Magurele, Romania, E-mail: beatris.neacsu@gmail.com

Received March 22, 2912

Questions?