A graphical absolute method for range determination of β-particles

International Journal of Applied Radiation and Isotopes,

1957,Vol. 2, pp. 145-148. Pergamon Press Ltd., London

A Graphical Absolute Method for Range Determination of -Particles F. BARREIRA and M. LARANJEIRA Centros de Estudos da Energia Nuclear-Laborat6rio de Fisica Lisbon

(Received 4 March 1957)

A graphical method for range determination of fl-particles is described. No comparative isotope is used in its application. The absorption curve is plotted against a straight line. A transformed curve, obtained in this way, enables us to deduce the desired range, by a graphical extrapolation over the unknown region of the absorption curve.

UNE M E T H O D E G R A P H I O U E ABSOLUE DE D E T E R M I N A T I O N DU P A R C O U R S MOYEN DES P A R T I C U L E S fl On d~crit une m6thode graphique de d6termination du parcours moyen des particules /~. Cette m6thode ne n6cessite pas l'emploi d'isotope de comparaison. On construit la courbe d'absorption qui est projetfie sur une certaine droite. La courbe transform6e ainsi obtenue permet de calculer le parcours recherch6, par extrapolation graphique de la partie inconnue de la courbe d'absorption.

EINE G R A P H I S C H E ABSOLUTE M E T H O D E Z U R B E S T I M M U N G V O N fl-REICHWEITEN Es wird eine graphische Methode zur Bestimmung der Reichweite yon /~-Strahlern beschrieben, welche ohne Vergleich mit einem fl-Strahler bekannter Reichweite durchgeftihrt werden kann. Die gemessene Absorptionskurve wird in bestimmter Weise transformiert. Die so erhaltene neue Kruve gestattet durch graphische Extrapolation tiber den unbekannten tell der Absorptionskurve die Bestimmung der gew~inschten Reichweite.

1.

INTRODUCTION

BESIDES its o w n i n t r i n s i c v a l u e , d e t e r m i nations of maximum energy offl-particles and conversion electrons by absorption techniques have an immediate practical interest for the identification of radionuclides, in a d d i t i o n to o t h e r d a t a . HALLDEN (1) p u b -

lished a chart in which radionuclides were classified a c c o r d i n g to t h e i r h a l f - l i v e s a n d t h e i r m a x i m u m fl-energies. B a c k g r o u n d i n t e r f e r e n c e s s u c h as ) , - r a d i a tions, B r e m s s t r a h l u n g a n d n a t u r a l b a c k g r o u n d , v e r y o f t e n g i v e rise to s u c h difficulties 145

4--12 pp

F. Barreira and M. Laranjeira

146

that it is nearly impossible to obtain the fl range directly, by extrapolating the absorption curve. Furthermore, the form of this curve depends on various factors, such as geometrical arrangement of the counting system, the maximum energy of fl-particles, the atomic number of the absorber and the degree of "forbiddenness" of the transition, all of which make it sometimes difficult to employ comparative methods. In FEATHER'S method(2, a) it is frequently necessary to extrapolate lines with pronounced curvature, the forms of which depend strongly on geometrical counting conditions for the isotope as compared with the standard. In a method recently proposed by HARLEY and H A L L D E N , (~) w e discovered difficulties in application, for we could not reproduce 2. D E S C R I P T I O N

A simple absorption curve is plotted, using semi-logarithmic co-ordinates (Fig. 1), after subtracting normal backgrounds. A straight line AB is now drawn so that the absorption curve falls completely between it and the ordinate axis. The absorption Projected length A

lOOrk [

.

40 , i

I

L

i

iI

[ t

'

i

I

5o1-\',, , ,l: l i ,\\',

lO!

g

1.0

I

80

120

160

, I

the straight lines which were claimed by the authors, owing possibly, to our different geometrical counting conditions. The loss of the final part of the absorption curve, when dealing with radionuclides more energetic than the standard isotope, seems to be one of the weaker points of this method. In view of all the disadvantages in the comparative methods, we tried to find an available process in which range determinations should not depend on comparison with any other radionuclide. Since in such an absolute method a fixed geometry is no longer essential, it can be changed in order to obtain the best form for the absorption curve. This will be important for the accuracy of our method in each particular case, and also for the analysis of a complex spectrum into its components. OF THE

METHOD

curve is projected onto AB with horizontal lines as shown in Fig. 1. Now to every point on the absorption curve there correspond an absorber thickness (as measured on the abcissa in mg/cm ~) and a projected length AL along the line AB, which is itself a measure of percentage transmission of radiations. The absorber thickness, in mg/cm ~ is next plotted against the corresponding projected length AL, in arbitrary units, using log-log co-ordinates, as in Fig. 2. The curve thus obtained has small curvature and can be extrapolated easily to projected lengths E

160

t

5 loc

°5filiii L

u

¢ 2C .~,

O'0

0

.

200

0

1 ~ 600 1000 r a g / c r r l 2 (AI)

¢ ¢1

10

Absorption curve for p3~ a n d projection on straight line.

I

500

10OO

mg/crr~ (At) Absorber thickness

Absorber thickness

FIO. l.

/ 100 2 0 0

B

F

//

c

_~ 5C

0

/ P

FIG. 2.

T r a n s f o r m e d curve: absorber thickness vs. projected length.

Range determinationof fl-particles corresponding to any desired percentage transmission. In practice the maximum range to which fl-particles can penetrate is not sharply defined, depending as it does upon collision phenomena of a random nature. It is therefore taken as the thickness of absorber required to reduce the transmitted radiation to an arbitrary proportion of the incident radiation. We have adopted the level at which this proportion is 0.01 per cent to define the maximum range. This brings our

results into good agreement with other published data, (a) although we shall presently show that the level adopted is not very critical. Referring now to Fig. 1, the projected length corresponding to the maximum range is now the length AB to the point where the straight line reaches the 0.01 per cent ordinate. In Fig. 2 the level EF corresponds to this length and extrapolation of the curve to this level shows the corresponding maximum range.

3. E X P E R I M E N T A L

By using log-log co-ordinates for extrapolating the thickness-length curves, for fl-emitters with a wide range of maximum energies, we obtained small curvatures in all tests (Fig. 3). The direction of curvature was always the same and good extrapolations were obtained. In Table 1, the results of these tests are compared with those using FEATHER'S method and with the ranges obtained from GLENDENIN'S curve using the maximum fl-particle energies reported by HOLLANDER, PERLMAN, and SEABORG. (5) An attempt was also made to compare the present method with that of HARLEY and HALLDEN(4) but the straight lines reported by these workers were not obtained, either with p32, RaE, or UX2 as standard isotopes. As stated above, we have extrapolated to the level 0.01 per cent of the incident radiations to obtain the range. Table 2 shows

147

RESULTS I Cc~°

~o ,- lOO t - 50 o

I

_r

I

/i

/

iv"

{

/']Z!/" ,,

[

SrQ°IBRaE FF~Yg°ux,~ r

I/

,//I

i/7:v

.~. 2c a 10-10

40

100

400

1000

mg/crn2 (AI) Absorber thickness

Fro. 3. Thickness-length curves for various beta emitters (see Table 1).

that the difference in extrapolating to 0-1 per cent is small. Ranges given by GLEN9EmN'S curve are quoted for comparison and deviations of our method from GLENDENIN'S ranges for both extrapolations are shown.

TABLE 1

TABLE 2 Range Radionuclide

Coe0

Sr~O I131 RaE p3,

y~0 UX,

Range (mg/cm ~)

Mgx°

energy (MeV)

0.306 0.537 0.608 (80%) 1.17 1.712 2.18 2-32 (98%)

GLENAuthors' ~;lNo~t [ method (mg/cm2)i (mg/cm2) 81 173 205

82 4 - 2 1754-2 2054-5

485 790 1050 1130

4704-5 7904- 10 10504-20 11504-20

I~EATHER'S

method (mg/cm 2)

80 4-2 1804-5 2004-5 460 780 1070 I100

4444-

15 10 60 50

Deviations per cent i

Radionuclide

GLENDENIN

C o 60 S r 90 I131

81 173 205 485 790 1050 1130

RaE p 3 .o

yg0

UX2

plot

ExtraExtra- / ExtraExtrapolation polation polation polation to 0"1 to 0'01 to 0-01 to 0.1 per cent per cent[ per cent per cent 82 175 205 475 790 1050 1150

80 175 200 465 780 1030 1120

+ 1"2 +1"2 0-0 --2"1 0"0 0'0 +1'8

--1"2 +1"2 --2"4 --4.1 --1"3 --1"9 --0-9

148

F. Barreira and M. Lumrzjeira 4.

CONCLUSIONS

The most important feature of’our present method is the fact that comparison with a standard is unnecessary. Indeed, as is well known, the use of comparative methods is largely invalidated when the absorption curves differ greatly in their characteristics. An additional advantage is that the relative positions of the counter, absorber and sample are no longer fixed: the geometry can be adjusted to obtain the most convenient form of absorption curve. This is sometimes important for resolving a. complex spectrum into its /?-components. The method can then be applied separately to each

component. The accuracy of the method can be improved for particular nuclides by choosing the most suitable geometry to facilitate extrapolation of the thicknesslength curve. It can be inferred from Table 2 that the level of transmitted radiation chosen to determine the range is not critical below 0.1 per cent so that the arbitrary choice of 0.01 per cent is justified. We have obtained better results with the method described than with that of FEATHER. It is also quicker in its application.

REFERENCES 1. HALLDEN A.

Nuleonics 13, 6, 78 (1955). 2. FEATHERN. Proc. Camb. Phil. Sot. 34, 599 (1938) ; COOK G. B. and DUNCAN J. F. Modern Radiochemical Practice University Oxford Press, (1952).

3. GLENDENINL. E. Aiicleonics 2, 1, 12 (1948). 4. HARLEY J. H. and HALLDEN N. Nxleonics 13, 1, 32 (1955). 5. HOLLANDERJ. M., PERLMAN I., and SEABORG G. T. Rev. Mod. Phys. 25, 469 (1953).