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ATTENUATION COEFFICIENTS OF GASES FOR 4.5 TO 145 keV PHOTONS
J. Mccrary
To cite this version:
J. Mccrary. ATTENUATION COEFFICIENTS OF GASES FOR 4.5 TO 145 keV PHOTONS. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-21-C4-25. �10.1051/jphyscol:1971404�. �jpa-00214605�
ATTENUATION COEFFICIENTS OF GASES FOR 4.5 TO 145 keV PHOTONS (*)
J. H. McCRARY
EG & G, Inc., Las Vegas, Nevada, U. S. A.
Rbumk. - Nous avons mesure des coefficients d'absorption massique pour I'air, I'hydrogkne, I'hBlium, le neon, I'argon, le krypton et le xBnon. Des photons d'energie 4,508-5,895-9,243-27,380- 44,229-88,09 et 145,43 keV ont Bte obtenus a I'aide de sources a radioisotopes. Pour I'hydrogkne et l'helium les mesures sont effectubs seulement a 5,895 keV. Les erreurs experimentales sont infkrieures a 2 % pour la plupart des mesures.
Abstract. - Narrow beam mass attenuation coefficients were measured for air, hydrogen, helium, neon, argon, krypton and xenon. Radioisotope sources were used to provide photons whose energies were 4.508, 5.895, 9.243, 27.380, 44.229, 88.09 and 145.43 keV. Hydrogen and helium measurements were made only at 5.895 keV. Experimental errors were less than 2 % for most of the measurements.
Introduction. - In the energy region of 1 to 20 key, extensive measurements have been made of the attenuation coefficients of neon and argon [l-91.
Above 20 keV very few experimental results are available [8], [9]. For photon energies greater than 3 keV relatively few attenuation coefficients have been measured for air [S], [6], [7], 1101, hydrogen [2], helium [2], krypton [g], [ll], [l21 and xenon [12]. Rau and Fano [l31 suggest that irregularities in photon cross sections are likely to occur with the interpolation of these cross sections with respect to Z for the noble gases. In an attempt to improve the present knowledge of gas photon cross sections, an experiment was designed wherin the narrow beam mass attenuation coefficients of air, neon, argon, krypton and xenon would be measured with an accuracy of + 1 to 2 %
at seven energies between 4.5 and 145 key. Hydrogen and helium measurements would be made at 5.895 keV.
The narrow beam mass attenuation coefficient pip, with units of cm2/g is defined by the relation
where I/I, is the gas transmissivity and x is the sample thickness in g/cm2.
Apparatus. - The experimental arrangement is shown schematically in figure l. Since the measured mass attenuation coefficients ranged through four orders of magnitude, many different sample lengths and sample densities were required. Sample lengths
(*) This work was performed under the auspices of the United States Atomic Energy Commission. This work is to be published in PIzys. Rev., 1970 and J. Appl. Phys., 1970.
PRESSURE G A U G E
G A S
-
BOTTLE
0s W I N D O W
COUNTER
3-
FIG. l. - Schematic diagram of typical experimental arrangement.
of 10 cm to 733 cm and sample pressures of 30 torr to 3 600 torr were used. The solid angle subtended by the detector at the source varied between 7 X 1 0 - ~ sr and 1.5 X 10a5 sr.
The gas chamber shown in figure 1 was made from sections of brass pipe which were 5 114 in. ID 5 112 in.
OD. Several one, two, and four ft lengths of this pipe were equiped with 0-ringed end flanges which could be bolted together to provide the needed gas sample length. The pipes were cleaned and leak checked prior to use.
From one to three collimators were spaced at equal intervals between the source and the detector to minimize scattering from the walls of the pipe and from the gas. The collimators were made from Pb sufficiently thick to stop virtually all of the source radiation. The collimator apertures were in every case slightly larger than the cone subtended by the detector a t the source. The number of collimators was determined by the sample length. Longer sample lengths were used with the higher energy :photon
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971404
C4-22 J. H. McCRARY
sources. Thus in the energy region where scattering contained less than 100 ppm of impurities. Hydrogen is more important, more collimation was used. contained 0.20 + 0.02 % (weight) of water and kryp-
One of the 2 ft sections of pipe was equipped with ton contained from 0.01 % to 0.03 % of xenon. A gas handling and gas sampling apparatus. Experi- few of the samples contained detectable quantities of ments involving sample lengths of less than 2 ft were air. None of the noble gases contained sufficient performed by placing the source, detector, and col- impurities to necessitate corrections to the measured limator on a track inside the gas handling section of attenuation coefficients.
pipe. A large mechanical pump was used to evacuate The measurement of the air attenuation coefficient the chamber. The vacuum condition was read on a at 4.508 keV made use of atmospheric air. As discus- thermocouple vacuum gauge. All vacuum counts sed in Ref. 10, no impurity corrections were required were taken at pressures of Jess than 5 x 10~3 torr. in this measurement. The higher energy air measure-
Gas pressures of less than one atmosphere were ments required pressures greater than one atmosphere.
measured with a closed end Hg manometer and Pressurized bottles of air were acquired from a local cathetometer. The accuracy of these measurements diver's supply vendor. Air processed for this purpose was ± 0 . 3 torr. Pressures greater than one atmosphere is filtered in order to remove moisture and oil vapors.
were measured with a Heise Bourdon tube pressure Mass spectrometric analyses of air samples taken gauge whose accuracy was ± 5 torr. Room air (and from the diver's bottles revealed that the relative thus sample) temperature was measured with a Hg quantities of the major constituents of the compressed thermometer which was checked against two Weather air were the same as those of atmospheric air. There Bureau secondary standard thermometers. The accu- were no detectable impurities present in the bottles racy of the temperature measurements was + 0.2 °C. of compressed air. As a final check on the air purity, Sample temperatures ranged from 21 °C to 27 °C. the experiment reported in Ref. 10 was repeated using Measurements of sample lengths greater than 60 cm compressed air. The measured attenuation coefficient were made with a steel tape whose accuracy was of air at 5.895 keV using the compressed air was checked with a precision cathetometer. The accuracy 24.50 cm2/g compared with 24.55 ± 0.25 cm2/g of these measurements was + 0.5 mm. The shorter reported in Ref. 10, well within quoted experimental lengths were set with metal measuring bars whose errors. The errors introduced into the present measu- lengths were known with an accuracy of + .03 mm. rements due to the composition and purity of the Source and detector end corrections were known to compressed air were negligible.
within + 0.25 mm. In order to calculate the mass attenuation coeffi- The detection of photons and the techniques cient from the measured count rates, the gas sample employed in maintaining acceptable spectral purity thickness in g/cm2 is required. This thickness is the were different for the different photon sources. The product of the sample length and density. The gas source-detector arrangements are summarized in density was obtained by applying pressure and tern- Table I. perature corrections to handbook [17] values of the
STP densities. These corrections were applied assu- Samples. — Samples of « Research Grade » noble ming the validity of the perfect gas law as follows : gases were purchased commercially. Mass spectro-
metric analyses of samples of the gases taken during _ | — ) / 273.15 \ . ^ these experiments revealed that most of the gases \Po) \273.15 + Tj
TABLE I
Summary of source-detector parameters
Energy Source and source Method of discriminating (keV) strength (mCi) Half-life (14) Detector against spectral impurities
4.508 (15) 4 9V - 0.2 330 d Nal KI Kfi filter
5.895(15) 55Fe - 0.1 ; 150 (*) 2.6 y Nal Cr K$ filter 9.243(15) 7 1G e - 1 5 11.4 d Nal Zn ^ f i l t e r
27.380(15) 1 2 5I - 3 0 60 d Ge(Li) Single channel analyzer adjusted on resolved Koc photopeak 44.229(15) 1 5 9Dy - 30 144 d Ge(Li) Single channel analyzer adjusted
on resolved Koc photopeak 88.09 (16) 1 0 9Cd - 100 453 d Nal Mo filter for Ag X-rays
145.43 (14) 141Ce - 30 33 d Nal Mo filter for P particles and Pr X-rays
(*) The moie intense source was used in the He — H2 experiments.
where p is the density of the gas at the pressure P where p/p is the mass attenuation coefficient in and temperature T (°C). P0 is atmospheric pressure cm2/g, / is the attenuated count rate, I0 is the unatte- (760 torr), and p0 is the density of the gas at standard nuated count rate, p is the sample density in g/cm3, temperature and pressure. The values of p0 used in and / is the sample length in cm. I0 is the mean of analyzing the data were 0.089 88 x 10"3 g/cm3 five vacuum counts from which was subtracted the for hydrogen, 0.178 5 x 10"3 g/cm3 for helium, mean of the background counts taken before and 0.899 90 x 10~3 g/cm3 for neon, 1.783 7 x 10"3g/cm3 after the vacuum counts. / is a single sample count for argon, 3.733 x 10"3 g/cm3 for krypton, 5.887 x from which was subtracted the mean of the background
10"3 g/cm3 for xenon, and 1.292 9 x 10"3 g/cm3 for counts taken before and after the set of five sample air. For the pressures and temperatures used in these counts containing /. p was calculated from Eq. (2) experiments, the error introduced by assuming the using the values of P and T measured during the validity of the perfect gas law was negligible. sample count /. The value of I0 used in Eq. (3) was
the one measured nearest in time to the value of / Experimental procedure. — In addition to the being used. Thus in the data taking sequence the sample thickness, other quantities required for the first measure of I0 was used with the first five values calculation of p/p are the unattenuated photon beam of /, etc.
intensity, the attenuated photon beam intensity, A single sequence of counts resulted n ten measure- and the background count rate. Unattenuated count ments of p/p. Due to the data taking sequence, errors rates varied from 30 counts/s (49V source at 15 cm) due to source decay tend to cancel. The only source to 5 000 counts/s (71Ge source at 10 cm). Dead time whose decay rate could have introduced error was 7 1Ge.
in the Nal counter was shown to be negligible for This source was sufficiently strong so that a single these count rates. Except for the Xe measurement at data sequence required less than an hour, during 4.5 keV all unattenuated count rates were measured which time error in p/p due to the linear approxima- with the gas chamber pressure below 5 x 10"3 torr. tion to the source decay rate was negligible.
Background count rates were measured by placing T h e o m y deviation in the data taking and in the a Pb plate over the source. For most of the experi- data analysis procedures occured in the xenon expe- ments the background count rate was much less than r r m en t at 4.5 keV. In this instance Xe gas was used
1 % of the unattenuated count rate. The only excep- a s a n additional Kfi filter. The unattenuated count tions were the air, neon and argon measurements r a t e jo w a s measured with a pressure of 35 torr of made with the 141Ce source where the background Xe in the gas chamber. The Xe pressure was increased count rates were between 1 % and 3 % of the unatte- before the attenuated count rate was measured.
nuated count rates. The value of p used in Eq. (3) was calculated from Counting times, depending upon the count rate, Eq. (2) where P was the increase in pressure between varied from 100 s to 2 000 s. For each data point, t n e t w o c o u n t r a t e measurements.
counts were taken in the following sequence : back- T n e r e s m t s obtained at 4.508 keV were the only ground, five vacuum counts, background, five sample o n e s t o w h i c h c o r r e c ti o n s due to spectral impurities counts, background, five sample counts, background, w e r e a p piied. For the air, Ne, Ar and Kr experiments five vacuum counts, background. All of the counting t h e m e a s u r ed Ka/Kfi intensity ratio of the filtered times were the same during a given sequence. During 49y s o u r C e w a s 30. For the Xe measurement, the each sample count the sample pressure and tempera- r a t i o w a s 7 0 U s i n g t h e c o m pi ied attenuation coef- ture were measured. Sufficient counts were taken ficients f r o m R e f 1 5 ; factors were calculated by during most of the experiments so that the value of w h i c h t h e m e a s u r ed coefficients were multiplied to p/p calculated from each individual sample count c o r r e c t f o r t h e presence of the K$ radiation. This fac- contained a statistical error of one percent or less. t o r w a s x 0 0 8 x f o r a i r j j 0 0 7 8 f o r N e j 1 00 8 5 for Ar, The above data taking sequence was carried out from x 0 Q 7 7 for K r a n d 0.989 for Xe. The corrections are two to five times for each gas-energy experiment. s m a l l a n d a r e n o t s e n sitiv e to an accurate determina- Between these sequences the sample length and/or t i o n o f t h e Xa/Kfi intensity ratio.
sample pressure were changed. Whenever possible, S a m p l e i m p u ri t i e s represent the most important transmissrvities of 0.5 or less were used. Constraints s o u r c e o f e r r o r -n t h e h e l i u m a n d h y d r og e n measure- imposed by maximum sample length and pressure, m g n t s C o r r e c t i o n s t o ^p d u e to the presence of however, made this imposSlble for some of the expe- h impUrities were applied as follows :
riments.
(p/p) corr = [(p/p) meas - £ 0V/>),/,]/(l - 1ft) (4) Data analysis. — From the data taken in the above
mentioned sequence, the measured values of p/p where (p/p)l is the attenuation coefficient for the ith were calculated as follows : impurity element and ft is the weight fraction of the z'th impurity element in the sample. Since the values p _ - log I/I0 .,. of ft were small, accurate values of (p/p)t were not p pi required.
C4-24 J. H. McCRARY
TABLE II
Measured attenuation coefficients in cm2/g
Energy Air Ne Ar Kr Xe (keV)
4.508 54.0 + . 9 125 + 2 558 + 8 466 ± 8 278 ± 5 5.895 24.55 ± .25 (") 57.0 + .7 274 ± 3 227 ± 3 672 + 8 9.243 6.34 + . 0 8 15.0 + .2 79.7 + 1 . 0 66.0 + .8 210 ± 3 27.380 0.406 + .005 0.713 ± .008 3.46 ± .04 23.9 + .3 11.25 + .13 44.229 0.227 + .003 0.296 + .003 0.936 + .012 6.26 + .07 17.2 + .2 88.09 0.160 + .002 0.169 ± .002 0.237 + .003 0.992 + .012 2.79 ± .03 145.43 0.137 + .002 0.138+ .002 0.146+ .002 0.315 + .004 0.763 ± .010
(") From Reference 10.
The correction to the hydrogen data due to its finite geometry. These errors and estimates of their water impurity lowered the value of fi/p by 12 %. magnitude will be discussed separately below.
Since it is possible that the gas-handling system intro- ,,. _, „ „ . x
, , j * * 1.1 X- c • *• (1) COUNTING STATISTICS. — Sufficient counts were
duced undetectable quantities of air, corrections , . „ „ , • , , . , , , , . j t j j * <• *i. taken in all of the experiments to assure that the
were made to the helium and hydrogen data for the , , A *" . A . . , , „ „„ / i \ r • T-i-- random error due to counting statistics was less than assumed presence of 25 ppm (volume) of air. This n c 0/ -a u « • * • *u ,n n, m . ..
A * u if c *u M.- •* e tu 0.5 %. Each coefficient is the mean of 20 to 50 mdi- corresponds to one-half of the sensitivity of the gas . , ? , ™ , , , - . -
. . , . . - 1 j It. vidual measurements. The standard deviation for a mass spectrometer. These corrections lowered the . . x , , n/ _
i c i x. ^ o/ c t. J j i o / i - i-i- single measurement was approximately 1 % for most values of up by 2 % for hydrogen and 1 % for helium. „ ~ . T ^ • J .
„ , u- j - A . i c i A i 4.1. of the experiments. In the air and neon experiments The combined errors in the values of up due to the ^ 0 0 , ,T , , . , , _. , . i t , , , , ,.
c , .. , , 4 , , at 88 kev and 145 keV and in the hydrogen and helium corrections for both known and possible unknown . x . . . ._,. ^ , • , , ,,
. . , . 0 / , experiments, the transmissivities were high and the sample impurities is + 3 % or less. , , , , - , • ^ - i J.
— standard deviation for a single measurement ran as high as 1.5 %. For all of the experiments, however, Results. — The results of the experimental measure- t h e standard deviation of the mean (<r/Nv*) was less ments are listed in Table II and Table III. The quoted ^ n Q.5 °/.
errors include random errors due to counting statis-
tics and estimates of other possible random and sys- (2) B E A M INTENSITY MEASUREMENTS. — Systematic tematic errors. Each coefficient is the mean of from e r r o r s i n c o u n t r a t e measurements cancel since count 20 to 50 individual measurements. Most of the coeffi- r a t e s e n t e r o n lY a s a r a t i o [Eq- (3)]- E r r o r s i n M/P due cients were measured at more than one sample pres- t o s o u r c e d e c aY a n d electronic variations are negligi- sure and length. There were no differences in the values b l e ( < 0.1 %) due primarily to the data taking sequence of the measured coefficients which could be attribu- u s e d m t n e measurements.
ted to these changes in geometry and sample thickness. ( 3 ) P R E S S U R E ; TEMPERATURE, AND LENGTH MEASURE- MENTS. — For most of the measurements, errors in
TABLE III nip due to errors in P-T-L measurements were negli- gible. For experiments involving low pressure and Measured and calculated values of the helium and s h o r t s a m p I e l e n g t h S j s y s t e m a t i c errors in fi/p could hydrogen attenuation coefficients at 5.895 keV (these h a v e b e e n a s h i g h a s 1 % d u e t Q c o m b i n ed pressure values contain sample impurity corrections) and length measurements. Error in ^/p due to tempera-
T ,. , ture measurement was negligible.
Helium Hydrogen
Cross section (cm2/g) (cm2/g) (4) GAS PURITY. — Errors in nip due to sample
— — — impurities were + 3 % for the hydrogen and helium Hip (meas) 0.416 + 0.017 0.400 + 0.016 measurements and were less than 0.1 % for the other
measurements.
Errors. — Possible sources of error in the experi- (5) PHOTON BEAM SPECTRAL PURITY. — The only mental measurements include the following: (1) photon source whose spectrum contained apprecia- counting statistics, (2) beam intensity measurements, ble impurities was the 4 9V source. A small correction (3) pressure, temperature and length measurements, was applied to the measured coefficients to remove (4) gas purity, (5) photon beam spectral purity, and (6) the effect of the Ti Kp X-rays. The effect of spectral
impurities on the measured attenuation coefficients was less than + 0.2 %.
(6) FINITE GEOMETRY. - Small angle scattering of photons into the detector, and multiple Compton scattering by the chamber walls, collimators, and gas would tend to lower the measured attenuation coeffi- cients. For the higher energy measurements, where this effect could be non negligible, the beam geometry
was much tighter and the number of collimators was larger. Because of the narrow beam geometry used in these experiments, errors in the measured values of p/p due to finite geometry were < 0.05 % and were neglected.
An estimate of the combined errors is listed in Table I1 and Table I11 with the measured coefficients.
They vary from 1 % for most of the measurements to 4 % for the hydrogen and helium measurements.
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