- Email: [email protected]
Interpolated energy distributions of Hg203 gamma rays scattered in sand
NUCLEAR
INSTRUMENTS
AND
METHODS
34 (I965) 325-327; ©
NORTH-HOLLAND
PUBLISHING
CO.
INTERPOLATED ENERGY D I S T R I B I I r I O N S O F I-Igam G A M M A RAYS SCATTERED IN SAND A. SCHAARSCHMIDT Institut fiir angewandte Physik der Johann-Wolfgang-Goethe-Univer$1tlit, Frankfurt am Main, Germany
Received 7 January 1965 Using the moments-method spectra of Goldstein and Wilkinsl) the energy distributions of the number flux of multiple scattered ?-rays in quartz sand, starting from a point isotropic source of
Hg203, are evaluated by interpolation for 10, 20, 30 ... 110 cm distance from the source. Also the curves for the corresponsJing number, energy and dose build-up factors are Oven.
Recently, the energy distributions of y-rays from a Cs 137 source (initial energy Eo = 0.662 MeV) scattered in water were published2). For shielding and radiation protection installations, however, one usually employs sand or concrete, hence, the knowledge of the y-radiation fields in these media is of great importance, too. In the course of a comprehensive work on multiple y-ray scattering in media of low atomic number the author already gave theoretical and experimental spectra of y-rays scattered in sand for sources of Cs ts~ ( E o = 0 . 6 6 2 MeV) a n d Co ~° ( E o = 1 . 1 7 3 and 1.333 MeV), ref. 3). In order to complete this work in the direction towards lower initial energies, in this note the energy distributions of y-rays in quartz sand (silicon dioxyd) starting from a point isotropic source of Hg 2°s (initial energy of the quanta Eo =0.279 MeV) are presented, interpolated from the data of Goldstein and Wilkinsl). Fig. 1 shows the total mass attenuation coefficient of quartz sand for y-radiation, calculated according to
lsio==
0.02
1
0.14
018
'
0.10
i.5 ~u
0.09
).0
o" x
&08
3.5 ~ha
0.07
3.0
0.06
OD5 E (MeV)
32.00Zo + 28.09Zsi 60.09
E (MeV) 006 0.10
Fig. 1. Total mass attenuation coefficientZsio= of quartz sand for y-radiation vs energy E. The upper curve refers to the axes above and on the right, the lower one to the axes below and on the left.
'
without the contribution of coherent scattering, using the table of White-Grodstein4). Because of the low atomic numbers of oxygen and silicon, quartz sand belongs to those media, which like water and aluminium behave almost as a pure Compton scatterer for energies E > 0.2 MeV. Therefore the y-ray spectra are the same for these media in the upper energy range being of interest here, if the/zor-values are taken to be equal (Po = total linear attenuation coefficient at Eo, r = distance from the source). In the low energy region there is somewhat less absorption by photoelectric effect in sand compared to aluminium; therefore the spectra in sand ought to be increasingly a little bit higher t h a n in aluminium towards lower energies, but this fact is practically not significant except possibly near the maximum at about 80 keV. As starting point for the interpolation of the spectra
the well-known distribution curves and tables of Goldstein and Wilkins 1) were used. AS in 2.3) the interpolations were made graphically utilizing the carpet technique of YatesS). Of the scattering media, considered in 1), aluminium is the most similar to sand. Yet the lowest initial energy for which y-spectra were calculated by Goldstein and Wilkins in aluminium, is Eo = 0.5 MeV; hence, for Eo = 0.279 MeV the curves had to be extrapolated with respect to the initial energy. This extrapolation turned out to be very uncertain. Therefore, in addition the spectra in w a t e r , which are given in 1) down to Eo = 0.255 MeV, were i n t e r p o l a t e d for Eo = 0.279 MeV; this interpolation can be done quite reliable. Proceeding from these water spectra to the corresponding aluminium spectra the difficulty of correct consideration of the different
325
326
^. SCHAARSCHM1DT
photoelectric absorption arises in the low energy range. For this reason the ratio of t h e height of the spectra in aluminium and water for several scattering energies E and several distances #or, as taken from the data in J), were also extrapolated for the initial energy Eo = 0.279 MeV. This results in numerical factors depending on E and #0 r with which the interpolated water spectra were multiplied.-Thus another approximation for the spectra in alundnium is obtained, which as the former one contains one extrapolation. Therefore in the lower energy range the mean values between these two approximations were taken. In the upper energy region E > 0 . 2 MeV the curves were chosen to be near the interpolated water spectra because of the reasons mentioned above. These resulting curves were then interpolated with respect to the distance from the source, assuming a density of the sand of 1.59 g/cm 3 (#o = 0.175 c m - l ) and finally divided by E in order to get the n u m b e r flux spectra (the original spectra of Goldstein and Wilkins refer to the energy flux). The height of the cur~es~ at the initial energy Eo, the energy El =0,133 MeV, at which the discontinuity occurs and the height of the discontinuity itself have been calculated directly according to the formulae given inl'2). Fig. 2 shows the resulting energy distributions of the number flux. The interpolation uncertainty is assumed to be less than + 15~o for E > 0 . 1 MeV, in the low energy region it might be greater; especially one should not draw detailed conclusions from the decrease of the spectra on the left flank of the maximum. 10 OOC
,
z ], 7oc
L
I
'
'
.:.. iI O~
I
O.lO
I
I 0.15
~
I
-._._._______
020
I
,o,
I1 I ,I
3oc
/ti t
200[
.,
I/J 1, 1
,oJ °-o0'o 'o' , /i :l I
!
tl.,'1
60
/
!:
i/
l Y,,.I II
ft I '
"
/1 /,,'1/
10
15
20
30 40 r(cm)
50 60
80
100
F i 8. 3. B u i l d - u p f a c t o r s f o r a p o i n t i s o t r o p i c s o u r c e o f HB203 y - r a y s in q u a r t z sand as a f u n c t i o n o f t h e d i s t a n c e r f r o m t h e source, c a l c u l a t e d f r o m t h e spectra o f fig. 2. - - - - n u m b e r b u i l d up factor, e n e r g y b u i l d - u p f a c t o r , - - - dose b u i l d - u p f a c t o r .
~ !
1c
50£
0.25
I
E (MeV)
Fig. 2. Energy distributions of the number flux No(r,E) of multiple scattered y-rays in quartz sand, source Hg 203 (0.279
MeV) point isotropic, source normalisation one photon per second; density of the sand 1.59 g/cm3, linear attenuation coefficient at E0:/~o = 0.175 cm-l; r = distance from the source in cm. Spectra interpolated from the data of Goldstein and Wilkinsl).
Fig. 3 represents the curves for the number build-up, the energy build-up and the dose build-up factors as calculated from the spectra of fig. 2. The dose build-up factor calculated here from the interpolated spectra, agrees with the values, which can be taken directly from the data in 6) within a limit of better than 10%. The results of the moments-method calculations of the penetration of 7-rays through various media from point-isotropic sources have also been interpolated and fitted analytically for a larger set of initial and final energies by Babb et al.7). For further extension of the moments-method calculations of 1) see s). A treatise concerning the theory of multiple scattering of ?-rays will appear in Z. angew. Phys.9). References 1) H. Goldstein and J. E. Wilkins jr., USAEC Report NYO-3075 (1954). 2) A. Schaarschmidt, Nucl. Instr. and Meth. 27 (1964) 311.
INTERPOLATED ENERGY DISTRIBUTIONS OF H g 2°3 GAMMA RAYS 3) A. Schaarschmidt, Z. ang~-w.Physik, 18 (1964) 167. 4) G. White Grodstein, N. B. S. Circular 583 (1957). 5) A. H. Yates, Aircraft Eng. 18 (1946) 8. 6) M. J. Berger and L. V. Spencer, N. B. S. Techn. Note no. 11 (1959).
327
7) D. D. Babb, J. W. Keller and E. McGray, ANP-Report NARF-59-36T (1959). S) L. V. Spencer and J.~Lamkin, N. B. S. Report 5944 (1958); N. B. S. Report 6591 (1959). 9) A. Schaarschmidt, Z: angew..'Phys. (in press).
INSTRUMENTS
AND
METHODS
34 (I965) 325-327; ©
NORTH-HOLLAND
PUBLISHING
CO.
INTERPOLATED ENERGY D I S T R I B I I r I O N S O F I-Igam G A M M A RAYS SCATTERED IN SAND A. SCHAARSCHMIDT Institut fiir angewandte Physik der Johann-Wolfgang-Goethe-Univer$1tlit, Frankfurt am Main, Germany
Received 7 January 1965 Using the moments-method spectra of Goldstein and Wilkinsl) the energy distributions of the number flux of multiple scattered ?-rays in quartz sand, starting from a point isotropic source of
Hg203, are evaluated by interpolation for 10, 20, 30 ... 110 cm distance from the source. Also the curves for the corresponsJing number, energy and dose build-up factors are Oven.
Recently, the energy distributions of y-rays from a Cs 137 source (initial energy Eo = 0.662 MeV) scattered in water were published2). For shielding and radiation protection installations, however, one usually employs sand or concrete, hence, the knowledge of the y-radiation fields in these media is of great importance, too. In the course of a comprehensive work on multiple y-ray scattering in media of low atomic number the author already gave theoretical and experimental spectra of y-rays scattered in sand for sources of Cs ts~ ( E o = 0 . 6 6 2 MeV) a n d Co ~° ( E o = 1 . 1 7 3 and 1.333 MeV), ref. 3). In order to complete this work in the direction towards lower initial energies, in this note the energy distributions of y-rays in quartz sand (silicon dioxyd) starting from a point isotropic source of Hg 2°s (initial energy of the quanta Eo =0.279 MeV) are presented, interpolated from the data of Goldstein and Wilkinsl). Fig. 1 shows the total mass attenuation coefficient of quartz sand for y-radiation, calculated according to
lsio==
0.02
1
0.14
018
'
0.10
i.5 ~u
0.09
).0
o" x
&08
3.5 ~ha
0.07
3.0
0.06
OD5 E (MeV)
32.00Zo + 28.09Zsi 60.09
E (MeV) 006 0.10
Fig. 1. Total mass attenuation coefficientZsio= of quartz sand for y-radiation vs energy E. The upper curve refers to the axes above and on the right, the lower one to the axes below and on the left.
'
without the contribution of coherent scattering, using the table of White-Grodstein4). Because of the low atomic numbers of oxygen and silicon, quartz sand belongs to those media, which like water and aluminium behave almost as a pure Compton scatterer for energies E > 0.2 MeV. Therefore the y-ray spectra are the same for these media in the upper energy range being of interest here, if the/zor-values are taken to be equal (Po = total linear attenuation coefficient at Eo, r = distance from the source). In the low energy region there is somewhat less absorption by photoelectric effect in sand compared to aluminium; therefore the spectra in sand ought to be increasingly a little bit higher t h a n in aluminium towards lower energies, but this fact is practically not significant except possibly near the maximum at about 80 keV. As starting point for the interpolation of the spectra
the well-known distribution curves and tables of Goldstein and Wilkins 1) were used. AS in 2.3) the interpolations were made graphically utilizing the carpet technique of YatesS). Of the scattering media, considered in 1), aluminium is the most similar to sand. Yet the lowest initial energy for which y-spectra were calculated by Goldstein and Wilkins in aluminium, is Eo = 0.5 MeV; hence, for Eo = 0.279 MeV the curves had to be extrapolated with respect to the initial energy. This extrapolation turned out to be very uncertain. Therefore, in addition the spectra in w a t e r , which are given in 1) down to Eo = 0.255 MeV, were i n t e r p o l a t e d for Eo = 0.279 MeV; this interpolation can be done quite reliable. Proceeding from these water spectra to the corresponding aluminium spectra the difficulty of correct consideration of the different
325
326
^. SCHAARSCHM1DT
photoelectric absorption arises in the low energy range. For this reason the ratio of t h e height of the spectra in aluminium and water for several scattering energies E and several distances #or, as taken from the data in J), were also extrapolated for the initial energy Eo = 0.279 MeV. This results in numerical factors depending on E and #0 r with which the interpolated water spectra were multiplied.-Thus another approximation for the spectra in alundnium is obtained, which as the former one contains one extrapolation. Therefore in the lower energy range the mean values between these two approximations were taken. In the upper energy region E > 0 . 2 MeV the curves were chosen to be near the interpolated water spectra because of the reasons mentioned above. These resulting curves were then interpolated with respect to the distance from the source, assuming a density of the sand of 1.59 g/cm 3 (#o = 0.175 c m - l ) and finally divided by E in order to get the n u m b e r flux spectra (the original spectra of Goldstein and Wilkins refer to the energy flux). The height of the cur~es~ at the initial energy Eo, the energy El =0,133 MeV, at which the discontinuity occurs and the height of the discontinuity itself have been calculated directly according to the formulae given inl'2). Fig. 2 shows the resulting energy distributions of the number flux. The interpolation uncertainty is assumed to be less than + 15~o for E > 0 . 1 MeV, in the low energy region it might be greater; especially one should not draw detailed conclusions from the decrease of the spectra on the left flank of the maximum. 10 OOC
,
z ], 7oc
L
I
'
'
.:.. iI O~
I
O.lO
I
I 0.15
~
I
-._._._______
020
I
,o,
I1 I ,I
3oc
/ti t
200[
.,
I/J 1, 1
,oJ °-o0'o 'o' , /i :l I
!
tl.,'1
60
/
!:
i/
l Y,,.I II
ft I '
"
/1 /,,'1/
10
15
20
30 40 r(cm)
50 60
80
100
F i 8. 3. B u i l d - u p f a c t o r s f o r a p o i n t i s o t r o p i c s o u r c e o f HB203 y - r a y s in q u a r t z sand as a f u n c t i o n o f t h e d i s t a n c e r f r o m t h e source, c a l c u l a t e d f r o m t h e spectra o f fig. 2. - - - - n u m b e r b u i l d up factor, e n e r g y b u i l d - u p f a c t o r , - - - dose b u i l d - u p f a c t o r .
~ !
1c
50£
0.25
I
E (MeV)
Fig. 2. Energy distributions of the number flux No(r,E) of multiple scattered y-rays in quartz sand, source Hg 203 (0.279
MeV) point isotropic, source normalisation one photon per second; density of the sand 1.59 g/cm3, linear attenuation coefficient at E0:/~o = 0.175 cm-l; r = distance from the source in cm. Spectra interpolated from the data of Goldstein and Wilkinsl).
Fig. 3 represents the curves for the number build-up, the energy build-up and the dose build-up factors as calculated from the spectra of fig. 2. The dose build-up factor calculated here from the interpolated spectra, agrees with the values, which can be taken directly from the data in 6) within a limit of better than 10%. The results of the moments-method calculations of the penetration of 7-rays through various media from point-isotropic sources have also been interpolated and fitted analytically for a larger set of initial and final energies by Babb et al.7). For further extension of the moments-method calculations of 1) see s). A treatise concerning the theory of multiple scattering of ?-rays will appear in Z. angew. Phys.9). References 1) H. Goldstein and J. E. Wilkins jr., USAEC Report NYO-3075 (1954). 2) A. Schaarschmidt, Nucl. Instr. and Meth. 27 (1964) 311.
INTERPOLATED ENERGY DISTRIBUTIONS OF H g 2°3 GAMMA RAYS 3) A. Schaarschmidt, Z. ang~-w.Physik, 18 (1964) 167. 4) G. White Grodstein, N. B. S. Circular 583 (1957). 5) A. H. Yates, Aircraft Eng. 18 (1946) 8. 6) M. J. Berger and L. V. Spencer, N. B. S. Techn. Note no. 11 (1959).
327
7) D. D. Babb, J. W. Keller and E. McGray, ANP-Report NARF-59-36T (1959). S) L. V. Spencer and J.~Lamkin, N. B. S. Report 5944 (1958); N. B. S. Report 6591 (1959). 9) A. Schaarschmidt, Z: angew..'Phys. (in press).