The response function of large NaI detectors to high energy photons

Nuclear Instruments and Methods 185 (1981) 291-297 North-Holland PuNishing Company

THE RESPONSE

FUNCTION

291

OF LARGE NaI DETECTORS

TO HIGH ENERGY

PHOTONS

P. CORVISIERO, M. TAIUTI, A. ZUCCHIATT1 and M. ANGHINOLFI Istituto di Scienze Fisiehe dell'Universitdz, Genova, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Italy

Received 22 December 1980

The response function of large Nai crystals to high energy photons (E7 ~<300 MeV) has been evaluated using a Monte Carlo code. All the involved electromagnetic processes, including radiation energy losses, annihilation in flight and multiple scattering have been taken into account. The numerical and physical approximations have been tested by a detailed comparison of the Monte Carlo predictions with the available experimental response functions of NaI crystals to high energy monochromatic photon beams.

1. Introduction Sodium iodide crystals are widely used in several areas of science and technology [1] and in particular large NaI scintillators are employed as good resolution high efficiency photon detectors in nuclear and particle physics [ 1 - 4 ] . The accurate knowledge of the response function is very important in these experiments, since the presence of background and continu6us spectra generally inhibits the experimental determination of the low energy tail following the total absorption peak. This effect is particularly important at photon energies above 10 MeV where energy escape due to electromagnetic radiation losses decreases the total absorption efficiency, enhancing the tail contribution to the observed spectra. A large number of Monte Carlo calculations as well as a considerable amount of measurements has been performed for the response function and the detection efficiency of NaI scintillators [5-11]. The photon energy in these works is generally below 20 MeV; in this range an accurate evaluation of ionization energy losses and geometrical effects is done, while radiative losses are generally treated introducing drastic approximations. These procedures give poor results at higher energies, where radiation losses become dominant and the simulation of the electron random walk requires a detailed description of all the involved electromagnetic processes. The aim of this work, a Monte Carlo method to simulate the history of the electron photon shower, is a complete calculation of the NaI 0 029-554)(/81/0000-0000/$02.50 © North-Holland

response function for photon energies up to 300 MeV. Three points have been emphasized in the description of the physical processes: - ionization energy losses and the multiple scattering effect on the electron and positron trajectories; - bremsstrahlung energy losses, treated by means of electromagnetic cross sections approximated in the infrared region; - positron annihilation.

2. Outline of the program Photons are randomly generated with angular distribution P(07)inside the detection solid angle A~ and given energy spectrum n(ET); "end on" or "side on" incidence on a cylindrical NaI detector is allowed. Geometrical routines update at any interaction, the position and the flight direction of photons and electrons and propagate them up to the next interaction point or to escape from the crystal edges. A cut-off energy is fixed (30 keV in all our predictions) below which photons and electrons are considered completely absorbed. The photon is converted after a path length Xo with probability P(E~) = 1 - exp [-Xo(Zph + E c + ~ p p ) ]

.

Photoelectric effect (ph), Compton scattering (c) or pair production (pp) is selected according to the rela-

P. Corvisiero et aL /Response function of NaI detectors

292

tire macroscopic cross section [12] while energy and emission angle of the final products are chosen using the differential cross sections do/dE and do/dr2. In the case of a Compton event, the photon scattering angle is sampled from the Klein-Nishina cross section [13] do/dr2 and the energies of the scattered photon and electron as well as the electron polar emission angle 0e are computed. When the photoelectric conversion is selected, the photon energy is completely transferred to an electron whose flight direction is isotropically chosen. When the pair production occurs, the photon energy is randomly divided between the positron and the electron and their emission polar angle 0+ is sampled from the approximated probability distribution:

radiation (BS) component: dE+ d~-

dx

ion

0± dO_+ [0~ + (1/ae)2] 2 '

where A = 2(zr2a~ + 1)/zr2a4_+, and a_+ =E+/moc2. The azimuthal angles are always opposite and uniformly selected between 0 and 27r. All the interactions involve photon-electron conversion and the final electron path has to be followed. Radiation energy losses of positive and negative electrons (dominant in Nal above 20 MeV) are described, for the ith atom of the scintillator, by the BetheHeitler cross section dokJi [14], which gives the emission probability of a bremsstrahlung photon in the energy interval k-k + dk by an incident electron of energy E_+. The emitted photon energy should be selected through the probability function

2(? 0

i=l

~:ta

2

P(K, E ±)=

(1)

required by the Monte Carlo technique, numerically underfined due to the infrared divergency at K ~ 0. We have therefore assumed discrete photon emission above a threshold energy Eta and continuous radiation energy loss at lower energies. Being for our

2f

dE+- BS = N ~ th dx i=1 0

(2)

"

?±_toO c2

~]BS(E±) = N ~

dak [i Eta

is reported in fig. 1. Positrons annihilate at rest creating a photon pair with 0.511 MeV each, isotropically emitted in opposite directions. The annihilation probability is assumed to be 1 in this case. Annihilation in flight is instead selected according to its macroscopic cross section: 2 ~Ar(E+) = N

~

z;~(E+),

i=I

where o(E+) is the Dirac cross section [15]. The photons are emitted at angles 01, 02 with energies Ka, K2 given by sin 0cm(1 -- 132)1/2 01 = arctg -- , 2 ~ +- cos 0cm K1 2

doel

I

~-BS

The term -dE+/cL'c[ion is the Bethe-M¢ller specific ionization energy loss [13] which accounts for the interaction with the atomic Coulomb field. The integrals in eq. (1) are now convergent above Eth and the Monte Carlo random number generation can be performed. The macroscopic cross section for the discrete emission of a bremsstrahlung photon of energy above

i=l

P(O+_)dO±=A

dE+

I

•+ +mo c2 2

(1 -+~cOS0cm),

where the photon emission angle in the center of mass system 0era, is sampled from an isotropic angular distribution. The electron path has been computed assuming between two subsequent radiation points linear trajectories where the initial electron energy E+_ is slowed down by continuous losses [2]. After a path length x the emission probability of a bremsstrmhlung or annihilation photon by a negative or positive electron of energy E + - f~ (dE_+/dx)dx in the interval x-x + dx is given by: r

K dOkli ,

medium the total continuous energy loss has been defined as the sum of an ionization (ion) plus a soft

P(x'E±):exp l- yP(E~o

xp

-+-d o

dx' dx'

-o? ~dE+ dx') dxt

,

(3)

P. Corvisieroet al. / Response function of NaI detectors

293

3p/

Eth = 0.05

4

'7

E o

E t h= 0.1

E ~

2

N

i

i

i

i

I

i

i

L

L

50

I

i

i

I

[

100

~

I

I _

~

150

I

I

I

t

I

I

200

P

250 E +(MeV )

Fig. 1. Integrated macroscopic bremsstrahlung cross section for photon energies above a selected threshold Eth.

where obviously E+ X
= f-

(dE+/d.x)

-1 dE_+

and

.8

u(E_+) = XBs(L:_+) + ~ A ~ ( E + ) . .6

it, can be shown that

Since

RI

f

P(x, E±) dx

30 MeV

~

o

15 MeV

~

10 MeV

o xI

=l-expE-?t/~(E±-?

~,dx")dx

t

I 1

i.u

i _

I 2

i

I

i

3

__

x(cm)

>4 ~2

the sum of radiation and non-radiation probability results correctly normalized over the ionization range RI. The path lengths can now be determined by a unique random number qx generation in the 0-1 interval: - if qx > P(RI, E+), all the energy is released for continuous losses and the electron path is coincident with RI; - i f qx<~P(RI,E+_), a photon is emitted by bremsstrahlung or annihilation in flight after a path x given by the usual Monte Carlo rule: X

qx = f P(x', E.) dx' =R(x, E+). 0

(4)

300 MeV

1,

50 MeV

100 MeV

.8

I

_ _ 1

I

1

[

2

i

I _ _

3

r

x(cm)

Fig. 2. Bremsstrahlung plus annihilation in flight probability R(x, E+~ as a function of the electron path length at different E± energies.

294

P. Corvisiero et aL / Response function of Nal detectors

Numerical values of the probabilities R ( x , E+_) at various E_+ energies are reported in fig. 2. In all cases for computing convenience the Monte Carlo integral (4) has been put in the form:

flight direction of each secondary emitted photon are temporarily stored and the electron history followed again up to total energy loss, annihilation at rest, or escape from the crystal boundary. Then the program recalls the secondary photon parameters and follows the photon-electron shower by the same procedure.

R(x, E+) = 1 - exp[-p(E+)x] ,

where the energy dependence of p(Ee) has been adjusted to reproduce R(x,E+) to better than 10 -2 accuracy; this affords analytical solution of eq. (4) leading to a path length x-

3. Discussion and results

The approximations introduced in the bremsstrahlung cross section should strongly affect the interaction probability (3) and, through it, the total electron range. We have therefore checked our calculation by the comparison of the computed electron mean ranges with the predictions obtained by other methods. The computed range distribution function in NaI and the energy dependence of the Monte Carlo mean range (R) = f R "P(R) dR and straggling (computed without multiple scattering) S = [f (R - (R)) 2 • P(R) dR]U~-are reported in figs. 3 and 4. Our (R} values are coincident, up to 50 MeV, with the continuous slowing down approximation results Ray [18]; above this limit the range Ray is higher since it ignores large bremsstrahlung losses. Range calculations performed using shower theory and the Monte Carlo method by Wilson [19] give (R) values about 20% lower than our estimates with a straggling S/(R) still around 40%. The intrinsic response function/"n(~, E-r) i.e. the

ln(1 - qx)

p(E_+)

As mentioned before, multiple scattering makes the actual electron trajectory between two radiation points a sort of random path length to be exactly followed. We have approximated it by a straight line segment of length x making, with respect to the previous electron flight direction, an angle 0eff given by

S+

2 1 0eee=~

S+-

<0%E dE,

where the multiple scattering angle (02)E is described in refs. 16 and 17 and Ei+_,El+_are the initial and final electron energy. By this procedure the electron is followed up to the subsequent radiation point (bremsstrahlung or annihilation); the emission point, the energy and the

E..j:~20 ieV~

E± =10MeV

13z0 ~3

,

~J

~



II

._1

E:

2 R(cm)

J ,

1

,

2

~

V

,1

,

3

,

4 R(crn)

~,=250MeV


Ii

I

I

I

I T

5

I

I

1

I

I--L-~

I

I

10 R(cm)

5

10

15

Fig. 3. Range distribution functions P(R) at different electron energies.

20 R(cm)

P. Corvisieroet al. / Response function of NaI detectors 8~- ( c m ) ,

--

R AV

7

o



61

x

S

/

/

/

295

o o

5

/o 4

3

/ #

2

/o

1

x

x

I

~

x

x x l l i J I

I

I

I

100

I

I

I

I

I

150

I

I

I

I

I

200

/

I

I

I

I

250

E ± (MeV)

Fig. 4. Monte Carlo mean range {R), continuous slowing'down range Ray, and stragglingS vs. electron energy E_+.

pulse height A distribution corresponding to n monochromatic photons of energy E3' incident in the scintilator volume and the percent efficiency e(ET) have been evaluated by this code at different photon energies and detector geometries. The comparison of the observable response function Sn(A,ET) with the experimental data requires a folding of Fn(A, ET) with the experimental resolution

Sn(A, E.r) = f Fn(A', E,r) G(A' - A) dA' ,

0.05

E~, = 9 MeV = 0,81

g 0.04 "~ ~ 0.03

~.t t t~

...... Exper. Monte Carlo

g 0.02

~]e /

Q~ 0.01 .....

where the resolution function G is assumed to be Gaussian. The dispersion given consistently with statistical arguments by a(A) = a~/2~ + bA, only affects above Ev = 2 0 MeV the high energy side of the absorption peak, the remaining features being mainly fixed by the energy escape probability. The parameters a and b have been determined by a simultaneous analysis of a set of measurements from the same crystal [20,24] and assuming [22] a reasonable 10% resolution for the 0.662 MeV ISTCs peak. In the energy range between 9 and 60 MeV, we have analysed a set of measurements [20,22,23] performed on NaI crystals by means of monochromatic and polarized photons [21], capture photons from the 3H(p, 7)4He reaction [22] or with annihilation tagged photons [23]. The measured response functions are compared with our predictions in figs. 5,6,

3

4

5

6

7

0.041 E~, = 30 MeV

8

9 Enemy,

r5~

MeV

2"

1 10 r.

15 -

20

25

30 Energy, MeV

Fig. 5. Experimental [20] and computed response functions at E~/= 9 MeV and E~ = 30 MeV normalized to the detection efficiency (NaI = 12.7 cm ~ X 12.7 cm; beam spot = 1 cm; A ~ = 2.5 X 10 - s st).

P. Corvisiero et al. / Response function o f NaI detectors

296

O.020t

E~, = 60 MeV £=0.86

"~"r~" f

U

L~

g 0.015 Exper.

.....

o

-TIf i °

E

E

0.010

0

n-

0.005

•

""

I

L

]

r

12

24

36

48

60 Energy, MeV

Fig. 6. E x p e r i m e n t a l [20] a n d c o m p u t e d r e s p o n s e f u n c t i o n a t E 3, = 60 MeV. (NaI = 15 c m ~ × 10.2 cm; b e a m spot = 1 cm; zM2 = 2.5 X 10 -8 st).

a? 0.1;

tO oc-

E ~, = 20.6 MeV 0.09

°°l

f,, = 0 . 9 9

E~, = 46.5 MeV ~. = 0.99

0.0751-

g =o

i

o2 ¢- 0.06

o

.....

Exper.

.J-L

Monte

T[

..... Exper. _m_ Monte Carlo ".,. ,

0.050

0.03 O9

£C

0.025 1

r

10

15

20 Ener{~y,MeV 20

103

25

30

35

40

45 50 Energy, MeV

Fig. 8. E x p e r i m e n t a l [23] a n d c o m p u t e d r e s p o n s e f u n c t i o n a t E.y = 46.5 MeV (NaI = 20.3 cm ~5 X 30.5 cm; b e a m s p o t = 12.5 c m ; 2xa2 = 5 X 10 .6 sr).

g I0 2

7a and 8. The results show in any case a completely satisfactory agreement between the experimental and the Monte Carlo calculation over the whole A region;

0

o

101 I~U

~U

DU

~iU

Channels

IL~J

Fig. 7. (a) E x p e r i m e n t a l [22] a n d c o m p u t e d r e s p o n s e f u n c t i o n at E,y = 20.6 MeV (NaI = 24 c m ¢ X 30 cm; b e a m s p o t = 12 c m ; AS2 = 1.9 X 10 -2 st). (b) U n f o l d e d r e s p o n s e f u n c t i o n at the same p h o t o n e n e r g y for t w o d i f f e r e n t E t h values.

P. Corvisiero et al. /Response function o f NaI detectors the dependence from the assumed Eth threshold investigated for the 20.6 MeV case (fig. 7b) appears to be practically negligible. We can conclude from the quoted results that our Monte Carlo program, with the assumptions discussed before, is adequate to reproduce the complete response of a large NaI scintillator to high energy photons with a good degree of reliability. We are indebted to Prof. G. Ricco for stimulating discussions and continuous support during this work, and to the LADON Group for having provided us with the response function measurements at their new facility.

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297

[7] M.J. Berger and S.M. Seltzer, Nucl. Instr. and Meth. 104 (1972) 317. [8] T. Nakamura, Nucl. Instr. and Meth. 105 (1972) 77. [9] M. Belluscio, R. De Leo, A. Pantaleo and A. Vox, Nucl. Instr. and Meth. 118 (2974) 553. [10] S.M. Seltzer, Nucl. Instr. and Meth. 127 (1975) 293. [11] B. Grosswendt and E. Waibel, Nucl. Instr. and Meth. 133 (1976) 25. [12] E. Storm and N.I. Israel, Nucl. Data Tables A7 (1970) 565. [13] L. Marton, Methods of experimental physics, vol. 5A (Academic Press, New York, 1963). [14] H.W. Koch and J.W. Motz, Rev. Mod. Phys. 31 (2959) 920. [15] W. Heitler, The quantum theory of radiation (Clarendon, Oxford, 1954). [16] G. Moli~re, Z. Naturforsch 2a (1947) 133. [17] W.T. Scott, Rev. Mod. Phys. 35 (1963) 231. [18] M.J. Berger and S.M. Seltzer, Nuclear Science Series report 39 (1964) p. 205. [19] R.R. Wilson, Phys. Rev. 84 (1951) 100. [20] G. Matone and D. Prosperi, private communication. [21] R. Caloi, L. Casano, M.P. De Pascale, L. Federici, S. Frullani, G. Giordano, B. Girolami, G. Matone, M. Mattioh, P. Pelfer, P. Pieozza, E. Poldi, D. Prosperi and C. Sehaerf, Lecture Notes Phys. 108 (1979) 234. [22] G. Kernel, W.M. Mason and N.W. Tanner, Nucl. Instr. and Meth. 89 (1970) 1. [23] A. Veyssi~re, H. Beil, R. Berg~re, P. Carlos, J. Fagot and A. Lepr~tre, Nucl. Instr. and Meth. 265 (1979) 417. [24] A. Veyssi6re, private communication.