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Effect of geometry on mass attenuation coefficient of β-particles
Int. J. Appl. Radial. /sot. VoL 35, No. I0, pp. 98[-982, 1984
Table 2. Comparison of estimated values of~/p obtained in various geometries End point ~ / p cm-'g-t) energy, F.0 (MeV) 2~ Gleason eta/: s) Good geometry
Pergamon Press Lid 1984. Printed in Great Britain. 0020-708X/84 $3.00+ 0.00
0.43 0.76
Effect of Geometry on Mass Attenuation Coefficient of #-Particles
1.545
1.697 2.284
S. R. THONTADARYA Department of Physics, Karnatak University, Dharwad 580
55.67 24.1 8.49 7.4 4.78
56.83 25.17
56.88 25.77
9.12
9.61
7.98 5.22
8.44 5.58
particles which do not undergo collision and are scattered at very small angles (~< 10°) will reach the detector. In 2~ geometry all the 'B-panicles are made to fall on the absorbers while all particles transmitted in all directions are collected and counted by the detector. This is achieved by keeping the source, absorbers and detector very close to each other. A radioisotope source prepared between two thin Mylar
003, India
(Received 16 April 1984)
The mass attenuation coefficient of 'B-panicles in aluminum is determined for five different 'B-emitters covering the end-point energy range from 0.4 to 2.3 MeV adopting two extreme geometries, namely the good geometry setup and the 2~ geometry setup. The experimental and estimated values obtained using these geometries are compared with those values obtained using an intermediate geometry by Nathuram et aL, (" and Gleason et al. (s) The effect of geometry on I~/p values is discussed.
films over an active area of less than 3 mm and activity of about 0.01/zCi is placed on the aluminum absorbers and both the source and absorbers are placed on top of the detector window. For such an arrangement, in spite of the presence of a small dead space in the G - M counter, we can assume that the effective solid angle subtended by the active area of the detector at the absorber and source is 2z. So the recorded transmitted intensity in 2~ geometry would be more and the "intensity-thickness'" curve would be less steep; hence Iz/p values would be smaller compared to the
Introduction
values obtained with good geometry. We have determined lz/p values for five different ~-¢mitters covering the endpoint energy range from 0.4 to 2.3 MeV, from the usual semilog graph of transmitted intensity vs thickness curve using the least squares fit (LSF) method. We found that for each source the experimental points lie close to the LSF straight line to 5~/~transmission in the case of 2~ geometry. The p/p values thus obtained are plotted as a function of end-point energy on a log-log graph. We found that the #/p values lie close to the LSF line yielding a relation ~/p = 16.1 E~"L~7. With good geometry we obtained the relationt3) #/p = 17.6 E~"L39.
It is well known that the mass attenuation coefficient pip (cm-'. g -I) of'B-particles is related to the end-point energy Eo (MeV) of that 'B-spectrum, as p/p ffi A E~ s where A and B are constants for a given material. Recently Nathuram et al. ") determined these constants as a function of Z of the absorber material to facilitate the estimation ofl~/p for any material. However I~/P values and hence A and B constants may also depend on geometry. (:) Since there is no systematic study available to estimate the extent of deviation of these values in various geometrical arrangements we attempt here to study the effect of geometry on p/p values for a given material
Results and Discussion
Experimental A r r a n g e m e n t and Procedure
In Table I, we give the experimental values of #/p obtained using 2~ geometry and good geometry for five different 'B-emitters along with the experimental values of Nathuram et a/.; (° Nathuram et al. adopted a geometry similar to the one adopted earlier by Gleason et al. 0) in which the incident beam is collimated while most of the transmitted 'B-particles are counted. This type of geometry lies between 27t geometry and good geometry. Hence their values o f ~ / p should fall within the values obtained by using extreme geometries. Gleason et al. obtained a similar empirical relation as ~/p = 17 Eo"k Table 2 gives the estimated values (fitted values) according to the relations obtained by us, along with that of Gleason et al. for those end-point
We have adopted two extreme geometries namely "good geometry" and 2~ geometry to measure the transmitted intensity of ,B-particles; these geometries cover the entire range of all the configurations adopted for the study of transmission of 'B-particles. The details of these and the results obtained using good geometry are discussed in our earlier papers, °') Here we shall quote only the essential points of these configurations and also describe the methods of determining /~/p values in 2~ geometry. In a good geometrical configuration both the incident and transmitted beams are well collimated and the absorbers are kept halfway between the source and detector. So only those
Table I. Comparison of exper/mental values of ~/p obtained in various geometries End point ~/p cm2g-I) Isotope ~SSW ~TI 91y 32p 9Oy
eIler~, ~o (MeV) 0.43 0.76 1.545 1.697 2.284
2n 57.32 23.5 87.37.3 4.94
Nathuram et al.[" -24.2 -8.4 5.0 981
Good geometry 57.85 24.82 9.48 8.9 5.57
982
Technical Note
energies which we used in our measurements. We see that both the experimental values of Nathuram et al. and estimated values of Gleason et al. lie between the values obtained by adopting extreme geometries as expected. The deviation in #/p values of extreme geometries is negligible at 0.43 and 0.76 MeV but is about 12% around 2 MeV. This clearly shows that the effect of geometry on g/p values is considerable at high end-point energies, say, above 1 MeV. Hence care should be taken with regard to geometry before any comparison of I~/P values is made or before using any empirical relation to estimate Iz/p values at higher end-point energies of ~-spectra.
References 1. Nathuram, Sundara Rao I. S. and Mehta M. K. Pramana 18, 12 ('1982). 2. Knop C. and Paul W. Alpha, Beta and Gamma Ray Spectroscopy (Ed. K. Siegbahn) Vol. 1 (North Holland, Amsterdam, 1965). 3. Thontadarya S. R. and Umakantha N. Phys. Rev. B 4, 1632 (1971). 4. Thontadarya S. R. and Umakantha N. Indian d. Pure Appl. Phys. 11, 629 (1973). 5. Gleason G. I., Taylor I. D. and Tabern D. L. Nucleonics 8, 12 (1951).
Table 2. Comparison of estimated values of~/p obtained in various geometries End point ~ / p cm-'g-t) energy, F.0 (MeV) 2~ Gleason eta/: s) Good geometry
Pergamon Press Lid 1984. Printed in Great Britain. 0020-708X/84 $3.00+ 0.00
0.43 0.76
Effect of Geometry on Mass Attenuation Coefficient of #-Particles
1.545
1.697 2.284
S. R. THONTADARYA Department of Physics, Karnatak University, Dharwad 580
55.67 24.1 8.49 7.4 4.78
56.83 25.17
56.88 25.77
9.12
9.61
7.98 5.22
8.44 5.58
particles which do not undergo collision and are scattered at very small angles (~< 10°) will reach the detector. In 2~ geometry all the 'B-panicles are made to fall on the absorbers while all particles transmitted in all directions are collected and counted by the detector. This is achieved by keeping the source, absorbers and detector very close to each other. A radioisotope source prepared between two thin Mylar
003, India
(Received 16 April 1984)
The mass attenuation coefficient of 'B-panicles in aluminum is determined for five different 'B-emitters covering the end-point energy range from 0.4 to 2.3 MeV adopting two extreme geometries, namely the good geometry setup and the 2~ geometry setup. The experimental and estimated values obtained using these geometries are compared with those values obtained using an intermediate geometry by Nathuram et aL, (" and Gleason et al. (s) The effect of geometry on I~/p values is discussed.
films over an active area of less than 3 mm and activity of about 0.01/zCi is placed on the aluminum absorbers and both the source and absorbers are placed on top of the detector window. For such an arrangement, in spite of the presence of a small dead space in the G - M counter, we can assume that the effective solid angle subtended by the active area of the detector at the absorber and source is 2z. So the recorded transmitted intensity in 2~ geometry would be more and the "intensity-thickness'" curve would be less steep; hence Iz/p values would be smaller compared to the
Introduction
values obtained with good geometry. We have determined lz/p values for five different ~-¢mitters covering the endpoint energy range from 0.4 to 2.3 MeV, from the usual semilog graph of transmitted intensity vs thickness curve using the least squares fit (LSF) method. We found that for each source the experimental points lie close to the LSF straight line to 5~/~transmission in the case of 2~ geometry. The p/p values thus obtained are plotted as a function of end-point energy on a log-log graph. We found that the #/p values lie close to the LSF line yielding a relation ~/p = 16.1 E~"L~7. With good geometry we obtained the relationt3) #/p = 17.6 E~"L39.
It is well known that the mass attenuation coefficient pip (cm-'. g -I) of'B-particles is related to the end-point energy Eo (MeV) of that 'B-spectrum, as p/p ffi A E~ s where A and B are constants for a given material. Recently Nathuram et al. ") determined these constants as a function of Z of the absorber material to facilitate the estimation ofl~/p for any material. However I~/P values and hence A and B constants may also depend on geometry. (:) Since there is no systematic study available to estimate the extent of deviation of these values in various geometrical arrangements we attempt here to study the effect of geometry on p/p values for a given material
Results and Discussion
Experimental A r r a n g e m e n t and Procedure
In Table I, we give the experimental values of #/p obtained using 2~ geometry and good geometry for five different 'B-emitters along with the experimental values of Nathuram et a/.; (° Nathuram et al. adopted a geometry similar to the one adopted earlier by Gleason et al. 0) in which the incident beam is collimated while most of the transmitted 'B-particles are counted. This type of geometry lies between 27t geometry and good geometry. Hence their values o f ~ / p should fall within the values obtained by using extreme geometries. Gleason et al. obtained a similar empirical relation as ~/p = 17 Eo"k Table 2 gives the estimated values (fitted values) according to the relations obtained by us, along with that of Gleason et al. for those end-point
We have adopted two extreme geometries namely "good geometry" and 2~ geometry to measure the transmitted intensity of ,B-particles; these geometries cover the entire range of all the configurations adopted for the study of transmission of 'B-particles. The details of these and the results obtained using good geometry are discussed in our earlier papers, °') Here we shall quote only the essential points of these configurations and also describe the methods of determining /~/p values in 2~ geometry. In a good geometrical configuration both the incident and transmitted beams are well collimated and the absorbers are kept halfway between the source and detector. So only those
Table I. Comparison of exper/mental values of ~/p obtained in various geometries End point ~/p cm2g-I) Isotope ~SSW ~TI 91y 32p 9Oy
eIler~, ~o (MeV) 0.43 0.76 1.545 1.697 2.284
2n 57.32 23.5 87.37.3 4.94
Nathuram et al.[" -24.2 -8.4 5.0 981
Good geometry 57.85 24.82 9.48 8.9 5.57
982
Technical Note
energies which we used in our measurements. We see that both the experimental values of Nathuram et al. and estimated values of Gleason et al. lie between the values obtained by adopting extreme geometries as expected. The deviation in #/p values of extreme geometries is negligible at 0.43 and 0.76 MeV but is about 12% around 2 MeV. This clearly shows that the effect of geometry on g/p values is considerable at high end-point energies, say, above 1 MeV. Hence care should be taken with regard to geometry before any comparison of I~/P values is made or before using any empirical relation to estimate Iz/p values at higher end-point energies of ~-spectra.
References 1. Nathuram, Sundara Rao I. S. and Mehta M. K. Pramana 18, 12 ('1982). 2. Knop C. and Paul W. Alpha, Beta and Gamma Ray Spectroscopy (Ed. K. Siegbahn) Vol. 1 (North Holland, Amsterdam, 1965). 3. Thontadarya S. R. and Umakantha N. Phys. Rev. B 4, 1632 (1971). 4. Thontadarya S. R. and Umakantha N. Indian d. Pure Appl. Phys. 11, 629 (1973). 5. Gleason G. I., Taylor I. D. and Tabern D. L. Nucleonics 8, 12 (1951).