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>.
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JOURNAL DE PHYSIQUE
Colloque C4, supplkment au no 10, Tome 32, Octobre 1971, page C4-21
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 4,508-5,895-9,243-27,38044,229-88,09 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
3COUNTER
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 at 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
is more important, more collimation was used.
One of the 2 ft sections of pipe was equipped with
gas handling and gas sampling apparatus. Experiments involving sample lengths of less than 2 ft were
performed by placing the source, detector, and collimator on a track inside the gas handling section of
pipe. A large mechanical pump was used to evacuate
the chamber. The vacuum condition was read on a
thermocouple vacuum gauge. All vacuum counts
were taken at pressures of Jess than 5 x 10~ 3 torr.
Gas pressures of less than one atmosphere were
measured with a closed end Hg manometer and
cathetometer. The accuracy of these measurements
was ± 0 . 3 torr. Pressures greater than one atmosphere
were measured with a Heise Bourdon tube pressure
gauge whose accuracy was ± 5 torr. Room air (and
thus sample) temperature was measured with a Hg
thermometer which was checked against two Weather
Bureau secondary standard thermometers. The accuracy of the temperature measurements was + 0.2 °C.
Sample temperatures ranged from 21 °C to 27 °C.
Measurements of sample lengths greater than 60 cm
were made with a steel tape whose accuracy was
checked with a precision cathetometer. The accuracy
of these measurements was + 0.5 mm. The shorter
lengths were set with metal measuring bars whose
lengths were known with an accuracy of + .03 mm.
Source and detector end corrections were known to
within + 0.25 mm.
The detection of photons and the techniques
employed in maintaining acceptable spectral purity
were different for the different photon sources. The
source-detector arrangements are summarized in
Table I.
Samples. — Samples of « Research Grade » noble
gases were purchased commercially. Mass spectrometric analyses of samples of the gases taken during
these experiments revealed that most of the gases
contained less than 100 ppm of impurities. Hydrogen
contained 0.20 + 0.02 % (weight) of water and krypton contained from 0.01 % to 0.03 % of xenon. A
few of the samples contained detectable quantities of
air. None of the noble gases contained sufficient
impurities to necessitate corrections to the measured
attenuation coefficients.
The measurement of the air attenuation coefficient
at 4.508 keV made use of atmospheric air. As discussed in Ref. 10, no impurity corrections were required
in this measurement. The higher energy air measurements required pressures greater than one atmosphere.
Pressurized bottles of air were acquired from a local
diver's supply vendor. Air processed for this purpose
is filtered in order to remove moisture and oil vapors.
Mass spectrometric analyses of air samples taken
from the diver's bottles revealed that the relative
quantities of the major constituents of the compressed
air were the same as those of atmospheric air. There
were no detectable impurities present in the bottles
of compressed air. As a final check on the air purity,
the experiment reported in Ref. 10 was repeated using
compressed air. The measured attenuation coefficient
of air at 5.895 keV using the compressed air was
24.50 cm2/g compared with 24.55 ± 0.25 cm2/g
reported in Ref. 10, well within quoted experimental
errors. The errors introduced into the present measurements due to the composition and purity of the
compressed air were negligible.
In order to calculate the mass attenuation coefficient from the measured count rates, the gas sample
thickness in g/cm2 is required. This thickness is the
product of the sample length and density. The gas
density was obtained by applying pressure and ternperature corrections to handbook [17] values of the
STP densities. These corrections were applied assuming the validity of the perfect gas law as follows :
_
| — ) / 273.15 \
\Po) \273.15 + Tj
.^
TABLE I
Summary of source-detector parameters
Energy
(keV)
4.508 (15)
5.895(15)
9.243(15)
27.380(15)
44.229(15)
88.09 (16)
145.43 (14)
Source and source
strength (mCi)
49
V - 0.2
Fe - 0.1 ; 150 (*)
71
Ge-15
125
I -30
55
Half-life (14)
Detector
330 d
2.6 y
11.4 d
60 d
Nal
Nal
Nal
Ge(Li)
Ge(Li)
159
Dy - 30
144
109
Cd - 100
Ce - 30
453 d
33 d
141
d
Nal
Nal
Method of discriminating
against spectral impurities
KI Kfi filter
Cr K$ filter
Zn ^ f i l t e r
Single channel analyzer adjusted
on resolved Koc photopeak
Single channel analyzer adjusted
on resolved Koc photopeak
Mo filter for Ag X-rays
Mo filter for P particles and
Pr X-rays
(*) The moie intense source was used in the He — H 2 experiments.
ATTENUATION COEFFICIENTS OF GASES FOR 4.5 TO 145 keV PHOTONS
where p is the density of the gas at the pressure P
and temperature T (°C). P0 is atmospheric pressure
(760 torr), and p0 is the density of the gas at standard
temperature and pressure. The values of p0 used in
analyzing the data were 0.089 88 x 10" 3 g/cm3
for hydrogen, 0.178 5 x 10" 3 g/cm3 for helium,
0.899 90 x 10~ 3 g/cm3 for neon, 1.783 7 x 10" 3 g/cm 3
for argon, 3.733 x 10" 3 g/cm3 for krypton, 5.887 x
10" 3 g/cm3 for xenon, and 1.292 9 x 10" 3 g/cm3 for
air. For the pressures and temperatures used in these
experiments, the error introduced by assuming the
validity of the perfect gas law was negligible.
Experimental procedure. — In addition to the
sample thickness, other quantities required for the
calculation of p/p are the unattenuated photon beam
intensity, the attenuated photon beam intensity,
and the background count rate. Unattenuated count
rates varied from 30 counts/s ( 49 V source at 15 cm)
to 5 000 counts/s ( 71 Ge source at 10 cm). Dead time
in the Nal counter was shown to be negligible for
these count rates. Except for the Xe measurement at
4.5 keV all unattenuated count rates were measured
with the gas chamber pressure below 5 x 10" 3 torr.
Background count rates were measured by placing
a Pb plate over the source. For most of the experiments the background count rate was much less than
1 % of the unattenuated count rate. The only exceptions were the air, neon and argon measurements
made with the 141 Ce source where the background
count rates were between 1 % and 3 % of the unattenuated count rates.
Counting times, depending upon the count rate,
varied from 100 s to 2 000 s. For each data point,
counts were taken in the following sequence : background, five vacuum counts, background, five sample
counts, background, five sample counts, background,
five vacuum counts, background. All of the counting
times were the same during a given sequence. During
each sample count the sample pressure and temperature were measured. Sufficient counts were taken
during most of the experiments so that the value of
p/p calculated from each individual sample count
contained a statistical error of one percent or less.
The above data taking sequence was carried out from
two to five times for each gas-energy experiment.
Between these sequences the sample length and/or
sample pressure were changed. Whenever possible,
transmissrvities of 0.5 or less were used. Constraints
imposed by maximum sample length and pressure,
however, made this imposSlble for some of the experiments.
where p/p is the mass attenuation coefficient in
cm2/g, / is the attenuated count rate, I0 is the unattenuated count rate, p is the sample density in g/cm3,
and / is the sample length in cm. I0 is the mean of
five vacuum counts from which was subtracted the
mean of the background counts taken before and
after the vacuum counts. / is a single sample count
from which was subtracted the mean of the background
counts taken before and after the set of five sample
counts containing /. p was calculated from Eq. (2)
using the values of P and T measured during the
sample count /. The value of I0 used in Eq. (3) was
the one measured nearest in time to the value of /
being used. Thus in the data taking sequence the
first measure of I0 was used with the first five values
of /, etc.
A single sequence of counts resulted n ten measurements of p/p. Due to the data taking sequence, errors
due to source decay tend to cancel. The only source
whose decay rate could have introduced error was 7 1 Ge.
This source was sufficiently strong so that a single
data sequence required less than an hour, during
which time error in p/p due to the linear approximation to the source decay rate was negligible.
T h e o m y deviation in the data taking and in the
d ata analysis procedures occured in the xenon exper r m e n t at 4.5 keV. In this instance Xe gas was used
a s a n additional Kfi filter. The unattenuated count
r a t e j o w a s measured with a pressure of 35 torr of
X e in the gas chamber. The Xe pressure was increased
before the attenuated count rate was measured.
The value of p used in Eq. (3) was calculated from
Eq. (2) where P was the increase in pressure between
t n e t w o c o u n t r a t e measurements.
T n e r e s m t s obtained at 4.508 keV were the only
o n e s t o w h i c h c o r r e c t i o n s due to spectral impurities
w e r e a p p iied. For the air, Ne, Ar and Kr experiments
t h e m e a s u r e d Ka/Kfi intensity ratio of the filtered
49y s o u r C e w a s 30. For the Xe measurement, the
r a t i o w a s 7 0 U s i n g t h e c o m p i i e d attenuation coefficients
from
Ref
1 5 ; factors were calculated by
w h i c h t h e m e a s u r e d coefficients were multiplied to
c o r r e c t f o r t h e presence of the K$ radiation. This fact 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 0 0 8 5 for Ar,
x 0 Q 7 7 for K r a n d 0 .989 for Xe. The corrections are
s m a l l a n d a r e n o t s e n s i t i v e to an accurate determinat i o n o f t h e Xa/Kfi intensity ratio.
S a m p l e i m p u r ities represent the most important
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 o g e n measuremgnts
C o r r e c t i o n s t o ^p
d u e to the presence of
h i mpU rities were applied as follows :
(p/p) corr = [(p/p) meas - £ 0V/>),/,]/(l - 1ft)
Data analysis. — From the data taken in the above
mentioned sequence, the measured values of p/p
were calculated as follows :
p _ - log I/I0
p
pi
.,.
C4-23
(4)
where (p/p)l is the attenuation coefficient for the ith
impurity element and ft is the weight fraction of the
z'th impurity element in the sample. Since the values
of ft were small, accurate values of (p/p)t were not
required.
C4-24
J. H. McCRARY
TABLE II
Measured attenuation coefficients in cm 2 /g
Energy
(keV)
4.508
5.895
9.243
27.380
44.229
88.09
145.43
Air
54.0
24.55
6.34
0.406
0.227
0.160
0.137
+.9
± .25 (")
+.08
+ .005
+ .003
+ .002
+ .002
Ne
Ar
Kr
125
+ 2
57.0 + .7
15.0 + .2
0.713 ± .008
0.296 + .003
0.169 ± .002
0.138+ .002
558
+8
274
±3
79.7 + 1 . 0
3.46 ± .04
0.936 + .012
0.237 + .003
0.146+ .002
466
227
66.0
23.9
6.26
0.992
0.315
Xe
±8
±3
+ .8
+ .3
+ .07
+ .012
+ .004
278
672
210
11.25
17.2
2.79
0.763
±5
+8
±3
+ .13
+ .2
± .03
± .010
(") From Reference 10.
The correction to the hydrogen data due to its
water impurity lowered the value of fi/p by 12 %.
Since it is possible that the gas-handling system intro,
,
j * * 1.1
Xc •
*•
duced undetectable quantities of air, corrections
, . , , , , .
j t j
j * <• *i.
were made to the helium and hydrogen data for the
,
„ „„
/ i
\ r • T-i-assumed presence of 25 ppm (volume) of air. This
A *
u if c *u
M.- •* e tu
corresponds to one-half of the sensitivity of the gas
.
.
,.
. - 1
j It.
mass spectrometer. These corrections lowered the
i
c i x. ^ o/ c t. J
j i o / i - i-ivalues of up by 2 % for hydrogen and 1 % for helium.
„,
u- j
-A.
i
c i A
i 4.1.
The combined errors in the values of up due to the
, .. ,
,
4,
,
c
corrections for both known and possible unknown
. .
, . 0/
,
sample impurities is + 3 % or less.
—
Results. — The results of the experimental measurements are listed in Table II and Table III. The quoted
errors include random errors due to counting statistics and estimates of other possible random and systematic errors. Each coefficient is the mean of from
20 to 50 individual measurements. Most of the coefficients were measured at more than one sample pressure and length. There were no differences in the values
of the measured coefficients which could be attributed to these changes in geometry and sample thickness.
finite geometry. These errors and estimates of their
magnitude will be discussed separately below.
,,. _,
„ „ . x
(1) COUNTING STATISTICS. — Sufficient counts were
,
.
„ „ ,
•
,
taken in all of the experiments to assure that the
,
, A
*" .
,
A . .
random error due to counting statistics was less than
-a u
« • * • *u
, n n , m . ..
n c 0/
0.5 %. Each coefficient is the mean of 20 to 50 mdi., ?
, ™
, , , - . vidual measurements. The standard deviation for a
. .
, , n/ _
x
single measurement was approximately 1 % for most
„~
.
•
J
.
T ^
of the experiments. In the air and neon experiments
^ 0 0 , ,T
, , . , , _.
, . it , ,
, , ,.
at 88 kev and 145 keV and in the hydrogen and helium
.
.
. . ._,. ^
,•,
, ,,
x
experiments, the transmissivities were high and the
, , , , - , •
^
- i
J.
standard deviation for a single measurement ran as
high as 1.5 %. For all of the experiments, however,
v
t h e standard deviation of the mean (<r/N *) was less
^ n Q.5 °/.
(2)
BEAM
MEASUREMENTS. — Systematic
measurements cancel since count
r a t e s e n t e r onl
Y a s a r a t i o [ E q- ( 3 )]- E r r o r s i n M/P due
t o s o u r c e deca
Y a n d electronic variations are negligible
( < 0.1 %) due primarily to the data taking sequence
used m tne
measurements.
INTENSITY
errors in c o u n t rate
( 3 ) P R E S S U R E ; TEM PERATURE,
AND LENGTH MEASURE-
— For most of the measurements, errors in
nip due to errors in P-T-L measurements were negligible. For experiments involving low pressure 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
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 e d pressure
and length measurements. Error in ^/p due to temperature measurement was negligible.
MENTS.
TABLE
III
Measured and calculated values of the helium and
hydrogen attenuation coefficients at 5.895 keV (these
values contain sample impurity corrections)
,
T ,.
Helium
Hydrogen
Cross section
(cm2/g)
(cm2/g)
—
—
—
Hip (meas)
0.416 + 0.017
0.400 + 0.016
Errors. — Possible sources of error in the experimental
measurements
include
the following:
(1)
(3)
counting
(4)
gas
pressure,
purity,
statistics,
temperature
(5) photon
(2) beam
beam
andintensity
spectral
length
measurements,
purity, and (6)
(4) GAS PURITY. — Errors in nip due to sample
impurities were + 3 % for the hydrogen and helium
measurements and were less than 0.1 % for the other
measurements.
(5) PHOTON BEAM SPECTRAL PURITY. — The only
4spectrum
9
photon
source
whose
contained
appreciathe
was
ble effect
impurities
applied
of the
towas
the
Tithe
Kp
measured
X-rays.
V source.
coefficients
The
A effect
small of
to
correction
spectral
remove
ATTENUATION COEFFICIENTS OF GASES FOR 4.5 TO 145 keV PHOTONS
impurities on the measured attenuation coefficients
was less than
0.2 %.
+
(6) FINITEGEOMETRY. - 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 coefficients. For the higher energy measurements, where
this effect could be non negligible, the beam geometry
W25
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.
References
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2 to 200 A Region n, Advances in X-Ray Analysis,
Volume 13, Plenum Press, New York (1970).
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[3] WUILLEUMIER
(F.), J. Physique (Paris), 1965, 26, 776.
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(A. P.) and ZIMKINA
(T. M.), IZV.Akad.
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(S. A.) and ORTON
(L. H. H.), Phil. Mug.,
[5] CROWTHER
1930, 10, 329 ; 1932, 13,505.
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(R. G.), Phys. Rev., 1931,38,1932.
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(B.), Ann. Physik, 1930,5,475.
[S] COLVERT
(W. W.), Phys. Rev., 1930, 36, 1619.
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(J. H.), ZIEGLER
(L. H.) and LOONEY
(L. D.),
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(I. A.) and ZIMKINA
(T. M.),
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[l21 WUILLEUMIER
(F.), cc Contribution a l'ktude de la
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[l31 RAU (A. R. P.) and FANO(U.), Phys. Rev., 1968,
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(C. M.), HOLLANDER
(J. M.) and PERLMAN
(I.), Table of Isotopes, 6th Edition, John Wiley
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(E.) and ISRAEL
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