Loss of charged particles by nuclear interactions in scintillators

N U C L E A R INSTRUMENTS AND METHODS 42 (t966) 26-28; © NORTH=HOLLAND P U B L I S H I N G CO.

L O S S O F C H A R G E D P A R T I C L E S BY N U C L E A R I N T E R A C T I O N S I N S C I N T I L L A T O R S D. F. MEASDAY* Cyclotron Laboratory, Harvard University, Cambridge, Massachusetts

and R. J. SCHNEIDER Tufts University, Medford, Massachusetts

Received 22 November 1965 Some particles, when detected by total energy counters, undergo inelastic collisions. These particles are lost from the full energy

peak. This loss has been calculated for deuterons and alpha particles of up to 160 MeV, for NaI and plastic scintillators.

For scattering experiments involving charged particles it is convenient to use the pulse height in sodium iodide or plastic scintillators to specify the scattered particles. Since the pulse height will be smaller for a particle which has undergone a nuclear interaction in the scintillator, it is necessary to make a correction for particles lost from the peak of the pulse height spectrum. This correction has been calculated previously for protons below 160 MeV in sodium iodide and plastic1). We have repeated it for protons in sodium iodide, making use of more recent range-energy data. We have also extended the calculation to deuterons and alpha-particles below 160 MeV, in sodium iodide and plastic. The calculation is based on range-energy relations and inelastic scattering cross sections. The number of nuclear interactions was f o u n d by dividing the path of the decelerating particle into 20 MeV segments. The number of atoms per square centimeter needed to slow a particle from 120 to 100 MeV, for example, was computed and f r o m this n u m b e r one could obtain the n u m b e r o f interactions undergone by an initial 100 particles entering the scintillator. Allowance was made for the reduction in number of particles which had not yet reacted. It was assumed that no reactions took place below 10 MeV. Range-energy tables were c o m p u t e d for sodium iodide (Nal) f r o m the tables of Williamson and Boujot2), extrapolating between 150 and 160MeV. The range-energy tables for plastic (CH) were computed f r o m Rich and Madey 3) in the deuteron case, and Williamson and Boujot in the case of alpha-particles. The p r o t o n inelastic cross sections for sodium and iodine were taken f r o m ref. 1). Deuteron inelastic cross sections for sodium, iodine and carbon were interpolated f r o m published data at 22.4 MeV4), 26.5 MeV 5) and 160 MeV6). For hydrogen, the inelastic cross sec* Present address: CERN, Geneva 23, Switzerland.

tions were obtained from experiments where deuterium was the target and protons the projectiles. For equivalent centre of mass energy, one must use the relation adp(2E ) = apd(E ). The inelastic cross section is known at a proton energy of 77 MeV7). Other values were obtained by subtracting elastic cross sections 8 - 1o) from the total cross sectionll.12). We assumed that the neutron-deuteron and proton-deuteron interactions TABLE 1

Proton inelastic cross sections (rob). MeV

30-40 MeV

40-50 MeV

> 50 MeV

450 1700

520 1800

400 1550

350 1240

10-30

Sodium Iodine

TABLE 2

Deuteron inelastic cross sections (rob).

Hydrogen Carbon Sodium Iodine

10-20 MeV

20-40 MeV

40-60 MeV

60-80 MeV

> 80 MeV

200 920 [ 1180 1620

206 850 1100 1860

187 667 1000 2100

148 667 900 2300

108 667 930 2590

TABLE3 Alpha-particle inelastic cross sections (mb). 10-20 MeV Hydrogen Carbon Sodium Iodine 26

0 1000 1080 760

20-40 MeV

40-60 MeV

60-80 MeV

> 80 MeV

0 900 1050 I 1030 1300.__ ~ 1830

0 770 1000 2400

40 640 980 2900

950

LOSS

27

OF C H A R G E D P A R T I C L E S BY N U C L E A R I N T E R A C T I O N S IN S C I N T I L L A T O R S TABLE 4 Calculated loss corrections (tail as a percentage of the peak).

Particle energy (MeV)

Protons in NaI

Deuterons in NaI

Alphas in NaI

Deuterons in CH

Alphas in CH

20 40 60 80 100 120 140 160

0.52 2.36 4.38 6.60 10.2 13.8 18.2 23.0

0.34 1.73 3.99 6.97 10.9 16.1 22.2 29.1

0.04 0.21 0.51 0.96 1.61 2.29 3.11 4.10

0.88 3.89 7.74 12.8 19.1 26.9 36.5 48.2

0.11 0.51 1.05 1.69 2.35 3.15 4.13 5.22

were identical, apart from Coulomb effects. Alphaparticle inelastic cross sections for sodium, iodine and carbon were interpolated from published data at 40 MeV 13) and 240 MeV6). For hydrogen the inelastic cross sections were found from experiments on the proton bombardment of helium using the relation ff,,p(4E) = ap~,(E). We used the data summarized by Horikawa and Kanada 14). Tables 1-3 show the inelastic cross sections used. We estimate that these are correct to 15%. Table 4 gives the calculated loss corrections. The 100

I

I

I

I

I

I

II

I

I

I

I

I

t

]

values for protons in sodium iodide represent an improved fit to the experimental data of ref. t). The values for deuterons in both sodium iodide and plastic are in reasonable agreement with published experimental data at 26.8 MeVtS). One does not expect exact agreement at low energies because of the assumptions made in the calculation. For example, some of the reactions included in the total cross section may increase the energy deposited in the scintillator. At higher deuteron energies however, the stripping reaction predominates and half of the particle energy is lost. 10

t

i

PLASTIC ( C H ) - No I

S O x v

i

i

i

i ~ ii

I

i

PLASTIC (CH) - -

/

No I

tO

O O x

1.0

O tJ

O H-

t-

.J F-

0 1.O t-¢Y

/

b

/

0.~

/

O t-

/

/

I:E

/

/

/

O.tO

I

I

I

I

I

~o DEUTERON

I

I1[

I

too ENERGY

I

I

I

I

I

IOO, MeV)

Fig. 1. Deuteron loss correction in sodium iodide and plastic (CH) scintillators.

0,ito

I

I

I

I

I II1[

f

I

I

I

I II

100 ALPHA

PARTICLE

10oo ENERGY ( M e V )

Fig. 2. Alpha-particle loss correction in sodium iodide and plastic (CH) scintillators.

28

D. F. MEASDAY AND R. Jo S C H N E I D E R

We do not expect the results for alpha-particles to represent more than a guideline. Sodium iodide, and to a greater extent plastic, has a non-linear response to heavily ionizing particles. When a reaction takes place in the scintillator and a less heavily ionizing particle is emitted, then it is possible that just as much light will be produced as when the alpha-particle stops without an interaction. We therefore emphasize that the alpha-particle results must be considered as upper limits. The results for deuterons and alpha-particles are given graphically in figs. 1 and 2. They are plotted on a log-log scale.

We wish to acknowledge the support of the U.S. Atomic Energy Commission and the U.S. Office of N a v a l Research.

References 1) 2) 3) 4) 5)

D. F. Measday, Nucl. Instr. and Meth. 34 (1965) 353. C. Williamson and J. P. Boujot, CEA 2189 (Saclay). M. Rich and R. Madey, U C R L 2301. B. Wilkins and G. Igo, Phys. Lett. 3 (1962) 48. S. Mayo, W. Schimmerling, M. J. Sametband and R. M. Eisberg, Nucl. Phys. 62 (1965) 393. 6) G. P. Millburn, W. Birnbaum, W. E. Crandall and L. Schecter, Phys. Rev. 95 (1954) 1268. 7) M. Davison, H, W. K. Hopkins, L. Lyons and D. Shaw, Nucl. Phys. 45 (1963) 423. 8) J. H. Williams and M. K. Brussel, Phys. Rev. 110 (1958) 136. 9) D. O. Caldwell and J. R. Richardson, Phys. Rev. 98 (1955) 28. 10) J. D. Seagrave, Phys. Rev. 97 (1955) 757. 11) R. A. J. Riddle, A. Langsford, P. H. Bowen and G. C. Cox, Nucl. Phys. 61 (1965) 457. 12) J. D. Seagrave and R. L. Henkel, Phys. Rev. 98 (1955) 666. 13) G. Igo and B. D. Wilkins, Phys. Rev. 131 (1963) 1251. 14) N. Horikawa and H. Kanada, J. Phys. Soc. Jap. 20 (1965) 1758. 15) R. M. Eisberg, S. Mayo and W. Schimmerling, Nucl. Instr. and Meth. 21 (1963) 232.