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Correction of self-absorption effects in activation analysis for oxygen with 14-MeV neutrons
Atrdyticcc Cltiniicu Acts, 63 ( 1973) 359-367 Q Elscvier Scientific Publishing Company,
Amsterdam
- Printed in The Nctlterlnnds
359
CORRECTION OF SELF-ABSORPTION EFFECTS IN ACTIVATION ANALYSIS FOR OXYGEN WITH 14-MeV NEUTRONS* J. A. LEAL
HORTA
and A. N. DOS SANTOS
Itwrirwo & Pmquiscrs Ratliorrtivm. (Received
Belo Harizorlte-MG
(Btwzil)
1st August 1972)
In activation analysis for oxygen with L4-MeV neutrons’, use is made of the rGO(n,p)rGN reaction. The resulting radioisotope has a. half-life of 7.2 s and emits several radiations, the most important being 6.1-MeV y-rays (68’j/,) and 10.4MeV P-rays (26%). Owing to differences in the neutron, y-ray and P-ray selfabsorption effects in samples of different matrices, and the difficulty of providing standards of composition and density similar to the sample, an accurate method for the correction of these effects is highly desirable. Self-absorption does not follow a simple exponential behaviour and depends strongly on sample geometry, density and composition. The /3-contribution to the counts may amount to over 30”/0 and its effect cannot be neglected because it depends strongly on sample density. Because of the high energy of the P-particles, the use of an absorber for their removal is undesirable, for it leads to considerable counting losses. In this paper, a procedure is described by which the individual contributions to the self-absorption effect can be determined, and the appropriate correction factor obtained as a function of sample geometry, composition and density by means of a computer code. The entry data of the code are the sample and standard densities, compositions and geometry, and the code gives directly the correction factor to be applied to the results of the analysis. A method of measuring the relative j?-contribution is also described; this allows one to obtain appropriate correction factors for any particular system, since this contribution depends on parameters such as detector size, discriminator settings, etc. As extensively verified for accurately known samples of widely varying composition, the results fall within the predicted values with a precision of about lo/, even though the correction may amount to more than 2Oo/0. DETERMINATION
OF THE CORRECTION
FACTOk
The problem of self-absorption has been studied by several authors2-‘. According to some workers3-5, the attenuation follows a simple exponential law, which applies to a unidirectional beam traversing a slab. Because of the different * Based on part of the thesis prescntcd by J. A. Lea1 Horta to the University of Minas Gerais, under the sponsorship of the Brazilinn Nuclear Energy Commission (CNEN). in December 1971.
J. A. LEAL
360
NORTA,
A. N. DOS SANTOS
paths of the particles in the sample, it is difficult to define a parameter that corresponds to the thickness of a slab. In this paper, escape probabilities mathematically established for infinite cylinder and infinite slab6 are applied to cylindrical samples, as proposed by Gilat and Gurfinkel’, Escape probabilities are defined6 by the expression:
where P defines the point where a particle arises, qO(F) the source distribution (supposedly isotropic) and P(T) its probability of escaping from the body. The hypothesis of isotropic distribution has not been accurately verified, but is acceptable because the scope of the measurement is the determination of the ratio of activities (sample/standard) measured under identical geometrical conditions2. Escape probabilities are established as a function of the nondimensional parameter a/l, where a is a linear dimension of the absorber (radius for an infinite cylinder, thickness for an infinite slab) and 2 is the mean free path of the particle in the medium. The value l/1 represents the probability of a particle traversing a unit length in an infinite absorber, and is calculated from experimental data in the form of microscopical cross-sections (a) or mass-absorption coefficients (~/~). In the first case, it can be shown that:
(2) where p is the specific mass of the sample, NO is Avogadro’s number, nf is the relative number of atoms of element t in the sample, and MI is the atomic mass 1 of element i. If the experimental data are given as mass-absorption coefficients, (3) where (P/P)~ is the mass-absorption coefficient of element i. The above calculations are needed for neutron and y-ray attenuation, The j-ray attenuation is considered to depend only on the density of the absorber, according to the empirical formula’: 1 - = p’ l?/(Emnx)i’l*, 1
(4
E moxbeing the maximal energy of the P-radiation, If the following parameter is defined : x = a/l
the escape
(5)
probabilities
P,,(X)
in MeV.
= i[i
are given6 by -
1
Irn e-xuU-3du
for an infinite slab of thickness
a, and
1
(6)
SELF-ABSORPTION J%&)
IN N.A.A.
=3x
1 +
;
361
2(xCKt(x)It(x)+K*(x)lo(x)l--11+ C~tW1Hl
-&W*(x)
+w~ow)
(7)
for an infinite cylinder, K,(x) and In(x) being Bessel functions, and cz the radius of the cylinder. These expressions are applicable to a finite cylinder, if one uses the interpolated value7 : P(-J =
R-P,,-+d-P,, R -t’ d
(8)
where R and cfare, respectively, the radius and height of the cylinder. The parameter a is obtained from
Figure 1 shows the curves of Pas, PO,, the interpolated curve for a cylinder having d=4 R, and the exponential attenuation curve, as a function of x. In activation analysis for oxygen, the counted radiation from the ’ % isotope produced consists mainly of 6.1-MeV y-rays and 10.4-MeV P-rays; the 7.1-MeV y-rays *making a negligible contribution. The other radiations emitted by r6N are eliminated by discrimination. The y- and p-ray self-absorption must then be calculated for these energy values.
Fig. 1. Curves of escape probabilities and the decreasing exponential function. (1) Function exp (-cl/l); (2) escape probability for infinite cylinder of radius a; (3) escape probability for infinite slab of thicknks a; (4) interpolated curve for a cylinder having d==4R.
J. A. LEAi
362
MORTA, A. N. DOS SANTOS
Because of the high threshold of the (n,p) reaction producing 16N (above 9 MeV), neutron removal cross-sections are chosen3-5 for estimating neutron selfabsorption, since a neutron suffering any interaction becomes practically unable to cause such a reaction. The removal cross-sections used are those given by Avery et al 9 and Zoller’“. Mass-absorption coefficients for 6-MeV y-rays are taken from Allen”. ’ Considering the particles involved in activation and counting, the activity of a sample can be written, as regards self-absorption: A = KMPo,
(R, Pay 3- R, Pop)
The sample-standard
ratio of oxygen masses
(10) then becomes:
M A. P&l (PA, f r J%,) ---Y M = A’ Po,(Po,+rPOp) In eqns. (10) and (1 l), PO,, PO,, and Pop are the escape probabilities calculated eqn. (8) for neutrons, y- and P-rays, respectively; R, and R, the probabilities count arising from a y- or a P-ray, respectively; and I’ = R,fR,
W) from of a
(121 unprimed values refer to the sample and the primed ones to the standard. The value of r can be obtained experimentally by measuring the attenuation of 16N radiation emitted by a thin sample placed at a fixed point near the.counter surface, an absorber of variable thickness being used. The ratio between two measurements done in the presenceand the absence of an absorber can be written as:
The
C(X)
-
CO
=
R,&(X) -I- R&J(X)
(13)
where X is the thickness of the absorber. For absorber thicknesses greater than thl= range of the P-rays, the absorption curve is due to It-attenuation only and is, practically, exponential. This function is fitted to the data and its value at X =U gives R,. The parameter r is obtained from I- = ( 1 - R&R,, since R,-I- R,=
( 14)
1.
EXPERIMENTAL
Equipment nnd operating conditions The neutron source used in this work was a Sames electrostatic accelerator (300 kV, 1 mA), producing 14-MeV neutrons through the Q&T) reaction. The tritiated target had a useful diameter of 16 mm, and the deuteron beam could be controlled by means of rotating probes, in order to cover the target surface homogeneously. A pneumatic, single-transfer system positioned the cylindrical samples parallel to the target, and a typical sample (10 mm diameter, 20 mm lorig) stood 15 mm from the target backing. For the counting of 16N, a 5”x 5” NaI(T1) scintilIator was vertically mounted inside a cubic lead shield measuring 62 cm externally, on each side. Samples were placed horizontally over the crystal.
SELF-ABSORPTION
IN N.A.A.
363
The measurements were standardized through two alternative systems. The first utilized a Plexiglas comparator of the type described by Gilmore and Hull”, consisting of a plastic scintillator covered with 2 cm of Plexiglas, positioned near the accelerator target. The rGN activity induced in the Plexiglas was counted simultaneously with the sample, by means of an assembly of two single-channel analysers commanded by a common timer. The second standardization system consisted of a special neutron monitorr3 measuring the flux during the irradiation period in 2-s time intervals. This system was switched to count the sample when it arrived at the counting position, without disturbing the timing cadence. The series of counts thus obtained were computer-processed in order to standardize irradiation conditions (equivalent r6N activation) and decay time, by a procedure similar to that used by Morgan and Ehman 14, and to lit the 16N decay curve. Determirlation of the parameter r For the determination of C(X)/Co values in eqn. (13), the following method was employed: the timer commanded successive 4.1-s counting intervals. During the first interval the sample was counted with an absorber placed over the counter. During the second time interval the absorber was removed and the sequence continued. If A is termed the result of counting during the first interval, and B the sum of third, fourth and fifth counts, the ratio C(X)/& is given by: C(X) CO
-
K A B
(15)
The decay correction factor K was calculated from the ‘“N half-life value (7.2 s). The absorber consisted of stainless steel square plates totally covering the upper surface of the counter. The sample chosen for determination of r was a Plexiglas foil 20 mm x 10 mm and 1.5 mm thick. Alternatively, a standard cylindrical polyethylene capsule containing distilled water was used to observe the effect of sample self-absorption and give a better representation of the attenuation curve, given the improved counting statistics. Experimental measurement of snmple self-absorption This measurement utilized samples of different compositions with a precisely known oxygen content. The ratio of normalized activities for pairs of such samples was determined in the same manner as for an unknown sample and a standard in routine analysis. The measured activities were used in eqn. (1 l), and the results were compared with the ratios of oxygen content to test the accuracy of the correction factor. The samples were chosen from substances with a low moisture content and with fine granule size. The. polyethylene sample. vials were previously, analysed, giving a blank value of less than 0.6 mg of equivalent oxygen content. The sample materials were oven-dried and were placed in their vials in 4-mm layers, which were successively pressed in a stainless steel press of special design to a pressure of 7.6 kg cm-‘; the lilled vials were then heat-sealed. Water samples were injected with a hypodermic syringe into previously sealed vials. The Plexiglas sample consisted of.a Plexiglas cylinder totally filling the standard vial.
J. A. LEAL
364 TABLE
HORTA,
A. N. DOS
SANTOS
I
SAMPLE
CHARACTERISTICS
Muss (YJ
Ca,(P04)2
0.6789
TiO, Hz0 Fe,% C,H,COOH PbOr (I) PbOz (If) Plexiglas
1.7075 1.4900 0.9498 1.3629 7.052 7.267 1.5299
AND
ESCAPE
PROBABILITIES
Dettsirf
u.xygor
Cgcm")
content
0.4587 1.1537 1.oooo 1.9669 0.9209 4.7649 4.8769 1.1924
PO,
(%J
lb
IP
41.27 40.05 88.81 30.06 26.20 13.38 13.38 31.96
0.9915 0~9816 0.9546 0.98 16 0.9683 0.9652 0.9644 0.953 1
0.9905 0.9789 0.9536 0.9786 0.9645 0.9597 0.9589 0.9489
J%Yd
Pod
0.9915 0.9803 0.9826 0.9766 0.9849 0.8975 0.8954 0.9803
0.7692 0.5667 0.6030 0.5320 0.6232 0.2131 0.2087 0.5582
LISample geometry: 10 mm diameter, 20 mm IGng. b Escape probabilities for 14 McV neutrons, calculated with removal cross-section data from Avery et a1.9. taken from Avery et al.). c Idem, calculated with data from Zoller lo (hydrogen removal cross-section d Escape probabilities for 6-McV y-rays. I’ Escape probabilities for 10.4-McV p-rays.
The characteristics of the samples are shown in Table I. The irradiation times were between 8 and 15 s, depending on the sample composition. When the Plexiglas comparator was used, activities were calculated from a 30-s counting time which yielded between 10,000 and 50,000 counts, thus insuring good counting statistics, With the neutron flux monitor the sample decay curves were followed for SS s. The background was in all cases less than 3 c,p.s. Reproducibility of the results varied from 2.5% to 4.5x, depending on the beam stability. The activity ratio was obtained from the mean of a series of measurements having a standard error of the mean about 1%. To verify the validity of the proposed correction method with total P-absorp tion, some measurements were performed with Plexiglas absorbers of 10 cm total thickness placed over the counter. RESULTS
Figure 2 shows the attenuation curves obtained for the Plexiglas and water samples as a function of absorber thickness, Each point consists of the mean of 4-6 measurements. The exponential function R,e”‘X .representing y-ray attenuation was computer-fitted, for absorber thicknesses above 7 g cmB2, by means of Gauss-Seidel’s non-linear method of least squares. The fitting was made for all measurements considered individually. For the weighting of the least-squares fit, variances were estimated from Poisson’s distribution and eqn. (15):
SELF-ABSORPTION
365
IN N.A.A.
Fig. 2. Attenuation (0) Hz0 cylindrical
curves sample
PO
IS
IO
if
/ema
(between 4.5 and 8 MeV) in stainless steel. of 16N /3- and y-radiations (10 mm diam. x 20 mm long); (A) Plexiglas foil (10 mm x 20 mm x 1.5 mm).
where Y- C(X)/C, and E is the relative error from causes other than counting statistics. The weights were then estimated by: 1 p&z-= (17) Ai/[x’(l+ Y,/K+AiS2)] 02(r,) A total df 60 points was used in each fit. The results are shown in Table 13, with their corresponding standard deviations. In this Table, (18)
pi ~Si”
where N is the number of data and a1 is the deviation between the data x and the corresponding value of the fitted function. The experimental error 8 in eqn. (15) was taken equal to 0.9%, which gives the best values for S2, but its effect on the estimates for R, and p is less than 1% when it is made to vary from 0 to 2%. It can be seen that the estimates of p are not significantly different for the two samples. Differences between the estimates of R, are due to the larger P-radiation selfabsorption in the water sample. From the value of R, obtained for the Plexiglas foil, the value r= 0.22 was found for the constant to be used in the correction factor. TABLE
II
LEAST-SQUARES Sample H2O
Plexiglas
FIT OF R,e- fix ATTENUATION
R,
P
0.858 kO.007
3.118~Io.050
0.818&IO.012
3.180*0.087
OF ‘“N S2 1.0856
0.9797
y-RADIATION
366
J. A. LEAL
TABLE
A. N. DOS SANTOS
111
RESULTS ---._-__
OF ACTIWTY “--__-_.-
RATIO
MEASUREMENTS
A/n“*
-- ..-_._._CVir/llJctr lrhslJrher Ti02/Hz0 Fc,OJ/C,,HSCOOH Cu,(PO,)z/HzO C,H,COOH/k120 Ca,( PO,),,‘C,HSCOOH PbO, ( 1)/C, H &OO H PbOz ( f)/Cu,( PO,)2 Pb02 (Il)/Plcxiyl;w With
HORTA,
0.534 -I_0.005 1.64’ kO.03 0.43 1 * 0.004 0.278 CO.003 0.846 + 0.008 2.29 e0.02 2.G4 kO.03 1.68 kO.02
Cotrccfell
MIM’J
ih
II’
0.524 I.66 0.399 0.272 0.799 2.73 3.33 1.95
0.525
1.a 0.399 0.273 0.796 2.73 3.35
1.95
0.s 17 1.641 0.410 0.270 0.784 2.642 3.368 1.988
trhsorher
Pb02 (I)/C,H,COOH 2.42 f0.03 2.66 2.67 2.642 2.92 co.03 3.31 3.33 3.368 PbOt (W.&( PO& PbOl fll)/Plcxigtas 1.85 20.02 2.00 2.00 1.988 u Expcrimcntal activity ratio of the sampies and respective standard deviations, ’ Vuiucs of ,4//f’, corrected by means of neutron removal cross-sections from Avery ef trl.‘. ’ Values of A/A’, corrcctcd by mcuns of neutron removal cross-sections from Zollcr’“. ’ Oxygen muss ratio of the sumplcs (based on stoichiomctric volucs).
For the calculation of the correction factors a code for IBM-360 computers was written which includes atomic masses, cross-sections and mass-absorption coefficients. Alternatively, these factors can be calculated with the aid of tables of escape probabilities”. The results of relative measurements done with the samples referred in Table I are shown in Table III, in which the previously known M/M’ ratios can be compared with the experimental activity ratios A/A’ and the corrected values. It can’ be seen that the corrected values agree with the stoichiometric values to within two standard deviations. The in?portance of P-radiation self-absorption in samples with widely varying densities can be seen in Table XII, if one compares the values of the activity ratio A/A’ of sample/standard obtained in the absence and in the presence of the absorber. SUMMARY
A method of correcting sample self-absorption effects in activation analysis for oxygen by 14-MeV neutrons is described. The effects of neutron, y- and P-ray self-absorption are determined individually as a function of sample geometry and composition, by means of escape probabilities, and the overall correction factor is obtained by means of a computer code or through the use of tables. A procedure for measuring the &contribution to the counts, which may amount to over 30”/,, is described. Results of analyses for samples of composition widely different from
SELF-ABSORPTION
IN N.A.A.
the standard are presented; these agree with stoichiometric although the correction may amount to more than 20%.
367 values
within
l%,
RESUME
On propose une methode de correction des effets d’auto-absorption dans le dosage de l’oxygcne par activation neutronique. Les effets concernant les neutrons et les rayons gamma et beta sont determines separement en fonction de la geometric et de la composition des Cchantillons, et le facteur total de correction est obtenu au moyen d’un code Fortran. On determine la contribution relative des emissions beta aux comptages. Les resultats de dosages, effectues dans des Cchantillons qui presentent des compositions et densites tres diffcrentes, concordent avec les valeurs stoechiometriques a 1”/0pres, bien que la correction puisse se monter St plus de 20%. ZUSAMMENFASSUNG
Eine Methode zur Beriicksichtigung der Selbstabsorptionseffekte in der Probe bei der Bestimmung von Sauerstoff durch Aktivierungsanalyse mit 14 MeVNeutronen wird beschrieben. Die Einfliisse der Selbstabsorption von Neutronen, y- und j?-Strahlen werden als Funktion der Geometrie und Zusammensetzung der Probe mit Hilfe der Entweichungswahrscheinlichkeiten individuell ermittelt. Der Gesamt-Korrektionsfaktor wird mittels eines Rechenprogrammes oder unter Verwendung von Tabellen erhalten. Ein Verfahren zur Messung des P-Anteils an der Zlhlrate, der iiber 30”/, ausmachen kann, wird beschrieben. Die Analysenergebnisse von Proben, deren Zusammensetzungen sich stark vom Standard unterscheiden, werden vorgelegt. Sie stimmen mit den stiichiometrischen Werten innerhalb lo/, tiberein, obwohl der Korrektionsfaktor mehr als 20% betragen kann. REFERENCES 1 G. Auboin, P. Guazzoni and J. Lavcrlochcre, Rapport C.E.A. no. 2358. Saclay. 1963. 2 0. U. Andcrs and D. W. Briden, And. Cltem.. 36 (1964) 287.
3 4 5 6
7 8 9 10 11 12 13 14
S. S. Nargolwalla. M. R. Crambes and J. R. De Voe, .4&. Cl~e~n.,40 ( 1968) 666. S. S. Nargolwalla, M. R. Crambes and J. E. Sudduelh, Aural. Clrirrr. Actor, 49 (1970) 425. R. Gijbcls, A. Speecke and J. Hoste, Amd. Chim. Acta, 43 (1968) 183. K. M. Case, F. De Hoffman and G. Placzek, Iutrothrcviort to rhe Theory of Neutrort D#irsiott, Vol. I, Los Alamos Sci. Lab., Los Alamos, 1953. J. Gilat and Y. Gurfinkel, Nttcleort., 21 (1963) 143. R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955. A. F. Avery, D. E. Bendail, J. Butler and K. T. Spinney, AERE-R-3216, Harwell. 1960. L. K. Zoller, Nrtcfeor~., 22 (1964) 128. R. C. Weast (Editor), Handbook of Chemistry orzrlPhysics, The Chemical Rubber Co., Cleveland, 1967. J. T. Gilmore and D. E. Hull, Anc~l. C/rem., 35 (1963) 1623. C. A. Alvim and A. N. Santos, Nlrcl. Itzstrmr. Methods, 105 ( 1972) 289. J. W. Morgan and W. D. Ehman, Amd. C/h. Acru, 49 (1970) 287.
Amsterdam
- Printed in The Nctlterlnnds
359
CORRECTION OF SELF-ABSORPTION EFFECTS IN ACTIVATION ANALYSIS FOR OXYGEN WITH 14-MeV NEUTRONS* J. A. LEAL
HORTA
and A. N. DOS SANTOS
Itwrirwo & Pmquiscrs Ratliorrtivm. (Received
Belo Harizorlte-MG
(Btwzil)
1st August 1972)
In activation analysis for oxygen with L4-MeV neutrons’, use is made of the rGO(n,p)rGN reaction. The resulting radioisotope has a. half-life of 7.2 s and emits several radiations, the most important being 6.1-MeV y-rays (68’j/,) and 10.4MeV P-rays (26%). Owing to differences in the neutron, y-ray and P-ray selfabsorption effects in samples of different matrices, and the difficulty of providing standards of composition and density similar to the sample, an accurate method for the correction of these effects is highly desirable. Self-absorption does not follow a simple exponential behaviour and depends strongly on sample geometry, density and composition. The /3-contribution to the counts may amount to over 30”/0 and its effect cannot be neglected because it depends strongly on sample density. Because of the high energy of the P-particles, the use of an absorber for their removal is undesirable, for it leads to considerable counting losses. In this paper, a procedure is described by which the individual contributions to the self-absorption effect can be determined, and the appropriate correction factor obtained as a function of sample geometry, composition and density by means of a computer code. The entry data of the code are the sample and standard densities, compositions and geometry, and the code gives directly the correction factor to be applied to the results of the analysis. A method of measuring the relative j?-contribution is also described; this allows one to obtain appropriate correction factors for any particular system, since this contribution depends on parameters such as detector size, discriminator settings, etc. As extensively verified for accurately known samples of widely varying composition, the results fall within the predicted values with a precision of about lo/, even though the correction may amount to more than 2Oo/0. DETERMINATION
OF THE CORRECTION
FACTOk
The problem of self-absorption has been studied by several authors2-‘. According to some workers3-5, the attenuation follows a simple exponential law, which applies to a unidirectional beam traversing a slab. Because of the different * Based on part of the thesis prescntcd by J. A. Lea1 Horta to the University of Minas Gerais, under the sponsorship of the Brazilinn Nuclear Energy Commission (CNEN). in December 1971.
J. A. LEAL
360
NORTA,
A. N. DOS SANTOS
paths of the particles in the sample, it is difficult to define a parameter that corresponds to the thickness of a slab. In this paper, escape probabilities mathematically established for infinite cylinder and infinite slab6 are applied to cylindrical samples, as proposed by Gilat and Gurfinkel’, Escape probabilities are defined6 by the expression:
where P defines the point where a particle arises, qO(F) the source distribution (supposedly isotropic) and P(T) its probability of escaping from the body. The hypothesis of isotropic distribution has not been accurately verified, but is acceptable because the scope of the measurement is the determination of the ratio of activities (sample/standard) measured under identical geometrical conditions2. Escape probabilities are established as a function of the nondimensional parameter a/l, where a is a linear dimension of the absorber (radius for an infinite cylinder, thickness for an infinite slab) and 2 is the mean free path of the particle in the medium. The value l/1 represents the probability of a particle traversing a unit length in an infinite absorber, and is calculated from experimental data in the form of microscopical cross-sections (a) or mass-absorption coefficients (~/~). In the first case, it can be shown that:
(2) where p is the specific mass of the sample, NO is Avogadro’s number, nf is the relative number of atoms of element t in the sample, and MI is the atomic mass 1 of element i. If the experimental data are given as mass-absorption coefficients, (3) where (P/P)~ is the mass-absorption coefficient of element i. The above calculations are needed for neutron and y-ray attenuation, The j-ray attenuation is considered to depend only on the density of the absorber, according to the empirical formula’: 1 - = p’ l?/(Emnx)i’l*, 1
(4
E moxbeing the maximal energy of the P-radiation, If the following parameter is defined : x = a/l
the escape
(5)
probabilities
P,,(X)
in MeV.
= i[i
are given6 by -
1
Irn e-xuU-3du
for an infinite slab of thickness
a, and
1
(6)
SELF-ABSORPTION J%&)
IN N.A.A.
=3x
1 +
;
361
2(xCKt(x)It(x)+K*(x)lo(x)l--11+ C~tW1Hl
-&W*(x)
+w~ow)
(7)
for an infinite cylinder, K,(x) and In(x) being Bessel functions, and cz the radius of the cylinder. These expressions are applicable to a finite cylinder, if one uses the interpolated value7 : P(-J =
R-P,,-+d-P,, R -t’ d
(8)
where R and cfare, respectively, the radius and height of the cylinder. The parameter a is obtained from
Figure 1 shows the curves of Pas, PO,, the interpolated curve for a cylinder having d=4 R, and the exponential attenuation curve, as a function of x. In activation analysis for oxygen, the counted radiation from the ’ % isotope produced consists mainly of 6.1-MeV y-rays and 10.4-MeV P-rays; the 7.1-MeV y-rays *making a negligible contribution. The other radiations emitted by r6N are eliminated by discrimination. The y- and p-ray self-absorption must then be calculated for these energy values.
Fig. 1. Curves of escape probabilities and the decreasing exponential function. (1) Function exp (-cl/l); (2) escape probability for infinite cylinder of radius a; (3) escape probability for infinite slab of thicknks a; (4) interpolated curve for a cylinder having d==4R.
J. A. LEAi
362
MORTA, A. N. DOS SANTOS
Because of the high threshold of the (n,p) reaction producing 16N (above 9 MeV), neutron removal cross-sections are chosen3-5 for estimating neutron selfabsorption, since a neutron suffering any interaction becomes practically unable to cause such a reaction. The removal cross-sections used are those given by Avery et al 9 and Zoller’“. Mass-absorption coefficients for 6-MeV y-rays are taken from Allen”. ’ Considering the particles involved in activation and counting, the activity of a sample can be written, as regards self-absorption: A = KMPo,
(R, Pay 3- R, Pop)
The sample-standard
ratio of oxygen masses
(10) then becomes:
M A. P&l (PA, f r J%,) ---Y M = A’ Po,(Po,+rPOp) In eqns. (10) and (1 l), PO,, PO,, and Pop are the escape probabilities calculated eqn. (8) for neutrons, y- and P-rays, respectively; R, and R, the probabilities count arising from a y- or a P-ray, respectively; and I’ = R,fR,
W) from of a
(121 unprimed values refer to the sample and the primed ones to the standard. The value of r can be obtained experimentally by measuring the attenuation of 16N radiation emitted by a thin sample placed at a fixed point near the.counter surface, an absorber of variable thickness being used. The ratio between two measurements done in the presenceand the absence of an absorber can be written as:
The
C(X)
-
CO
=
R,&(X) -I- R&J(X)
(13)
where X is the thickness of the absorber. For absorber thicknesses greater than thl= range of the P-rays, the absorption curve is due to It-attenuation only and is, practically, exponential. This function is fitted to the data and its value at X =U gives R,. The parameter r is obtained from I- = ( 1 - R&R,, since R,-I- R,=
( 14)
1.
EXPERIMENTAL
Equipment nnd operating conditions The neutron source used in this work was a Sames electrostatic accelerator (300 kV, 1 mA), producing 14-MeV neutrons through the Q&T) reaction. The tritiated target had a useful diameter of 16 mm, and the deuteron beam could be controlled by means of rotating probes, in order to cover the target surface homogeneously. A pneumatic, single-transfer system positioned the cylindrical samples parallel to the target, and a typical sample (10 mm diameter, 20 mm lorig) stood 15 mm from the target backing. For the counting of 16N, a 5”x 5” NaI(T1) scintilIator was vertically mounted inside a cubic lead shield measuring 62 cm externally, on each side. Samples were placed horizontally over the crystal.
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363
The measurements were standardized through two alternative systems. The first utilized a Plexiglas comparator of the type described by Gilmore and Hull”, consisting of a plastic scintillator covered with 2 cm of Plexiglas, positioned near the accelerator target. The rGN activity induced in the Plexiglas was counted simultaneously with the sample, by means of an assembly of two single-channel analysers commanded by a common timer. The second standardization system consisted of a special neutron monitorr3 measuring the flux during the irradiation period in 2-s time intervals. This system was switched to count the sample when it arrived at the counting position, without disturbing the timing cadence. The series of counts thus obtained were computer-processed in order to standardize irradiation conditions (equivalent r6N activation) and decay time, by a procedure similar to that used by Morgan and Ehman 14, and to lit the 16N decay curve. Determirlation of the parameter r For the determination of C(X)/Co values in eqn. (13), the following method was employed: the timer commanded successive 4.1-s counting intervals. During the first interval the sample was counted with an absorber placed over the counter. During the second time interval the absorber was removed and the sequence continued. If A is termed the result of counting during the first interval, and B the sum of third, fourth and fifth counts, the ratio C(X)/& is given by: C(X) CO
-
K A B
(15)
The decay correction factor K was calculated from the ‘“N half-life value (7.2 s). The absorber consisted of stainless steel square plates totally covering the upper surface of the counter. The sample chosen for determination of r was a Plexiglas foil 20 mm x 10 mm and 1.5 mm thick. Alternatively, a standard cylindrical polyethylene capsule containing distilled water was used to observe the effect of sample self-absorption and give a better representation of the attenuation curve, given the improved counting statistics. Experimental measurement of snmple self-absorption This measurement utilized samples of different compositions with a precisely known oxygen content. The ratio of normalized activities for pairs of such samples was determined in the same manner as for an unknown sample and a standard in routine analysis. The measured activities were used in eqn. (1 l), and the results were compared with the ratios of oxygen content to test the accuracy of the correction factor. The samples were chosen from substances with a low moisture content and with fine granule size. The. polyethylene sample. vials were previously, analysed, giving a blank value of less than 0.6 mg of equivalent oxygen content. The sample materials were oven-dried and were placed in their vials in 4-mm layers, which were successively pressed in a stainless steel press of special design to a pressure of 7.6 kg cm-‘; the lilled vials were then heat-sealed. Water samples were injected with a hypodermic syringe into previously sealed vials. The Plexiglas sample consisted of.a Plexiglas cylinder totally filling the standard vial.
J. A. LEAL
364 TABLE
HORTA,
A. N. DOS
SANTOS
I
SAMPLE
CHARACTERISTICS
Muss (YJ
Ca,(P04)2
0.6789
TiO, Hz0 Fe,% C,H,COOH PbOr (I) PbOz (If) Plexiglas
1.7075 1.4900 0.9498 1.3629 7.052 7.267 1.5299
AND
ESCAPE
PROBABILITIES
Dettsirf
u.xygor
Cgcm")
content
0.4587 1.1537 1.oooo 1.9669 0.9209 4.7649 4.8769 1.1924
PO,
(%J
lb
IP
41.27 40.05 88.81 30.06 26.20 13.38 13.38 31.96
0.9915 0~9816 0.9546 0.98 16 0.9683 0.9652 0.9644 0.953 1
0.9905 0.9789 0.9536 0.9786 0.9645 0.9597 0.9589 0.9489
J%Yd
Pod
0.9915 0.9803 0.9826 0.9766 0.9849 0.8975 0.8954 0.9803
0.7692 0.5667 0.6030 0.5320 0.6232 0.2131 0.2087 0.5582
LISample geometry: 10 mm diameter, 20 mm IGng. b Escape probabilities for 14 McV neutrons, calculated with removal cross-section data from Avery et a1.9. taken from Avery et al.). c Idem, calculated with data from Zoller lo (hydrogen removal cross-section d Escape probabilities for 6-McV y-rays. I’ Escape probabilities for 10.4-McV p-rays.
The characteristics of the samples are shown in Table I. The irradiation times were between 8 and 15 s, depending on the sample composition. When the Plexiglas comparator was used, activities were calculated from a 30-s counting time which yielded between 10,000 and 50,000 counts, thus insuring good counting statistics, With the neutron flux monitor the sample decay curves were followed for SS s. The background was in all cases less than 3 c,p.s. Reproducibility of the results varied from 2.5% to 4.5x, depending on the beam stability. The activity ratio was obtained from the mean of a series of measurements having a standard error of the mean about 1%. To verify the validity of the proposed correction method with total P-absorp tion, some measurements were performed with Plexiglas absorbers of 10 cm total thickness placed over the counter. RESULTS
Figure 2 shows the attenuation curves obtained for the Plexiglas and water samples as a function of absorber thickness, Each point consists of the mean of 4-6 measurements. The exponential function R,e”‘X .representing y-ray attenuation was computer-fitted, for absorber thicknesses above 7 g cmB2, by means of Gauss-Seidel’s non-linear method of least squares. The fitting was made for all measurements considered individually. For the weighting of the least-squares fit, variances were estimated from Poisson’s distribution and eqn. (15):
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Fig. 2. Attenuation (0) Hz0 cylindrical
curves sample
PO
IS
IO
if
/ema
(between 4.5 and 8 MeV) in stainless steel. of 16N /3- and y-radiations (10 mm diam. x 20 mm long); (A) Plexiglas foil (10 mm x 20 mm x 1.5 mm).
where Y- C(X)/C, and E is the relative error from causes other than counting statistics. The weights were then estimated by: 1 p&z-= (17) Ai/[x’(l+ Y,/K+AiS2)] 02(r,) A total df 60 points was used in each fit. The results are shown in Table 13, with their corresponding standard deviations. In this Table, (18)
pi ~Si”
where N is the number of data and a1 is the deviation between the data x and the corresponding value of the fitted function. The experimental error 8 in eqn. (15) was taken equal to 0.9%, which gives the best values for S2, but its effect on the estimates for R, and p is less than 1% when it is made to vary from 0 to 2%. It can be seen that the estimates of p are not significantly different for the two samples. Differences between the estimates of R, are due to the larger P-radiation selfabsorption in the water sample. From the value of R, obtained for the Plexiglas foil, the value r= 0.22 was found for the constant to be used in the correction factor. TABLE
II
LEAST-SQUARES Sample H2O
Plexiglas
FIT OF R,e- fix ATTENUATION
R,
P
0.858 kO.007
3.118~Io.050
0.818&IO.012
3.180*0.087
OF ‘“N S2 1.0856
0.9797
y-RADIATION
366
J. A. LEAL
TABLE
A. N. DOS SANTOS
111
RESULTS ---._-__
OF ACTIWTY “--__-_.-
RATIO
MEASUREMENTS
A/n“*
-- ..-_._._CVir/llJctr lrhslJrher Ti02/Hz0 Fc,OJ/C,,HSCOOH Cu,(PO,)z/HzO C,H,COOH/k120 Ca,( PO,),,‘C,HSCOOH PbO, ( 1)/C, H &OO H PbOz ( f)/Cu,( PO,)2 Pb02 (Il)/Plcxiyl;w With
HORTA,
0.534 -I_0.005 1.64’ kO.03 0.43 1 * 0.004 0.278 CO.003 0.846 + 0.008 2.29 e0.02 2.G4 kO.03 1.68 kO.02
Cotrccfell
MIM’J
ih
II’
0.524 I.66 0.399 0.272 0.799 2.73 3.33 1.95
0.525
1.a 0.399 0.273 0.796 2.73 3.35
1.95
0.s 17 1.641 0.410 0.270 0.784 2.642 3.368 1.988
trhsorher
Pb02 (I)/C,H,COOH 2.42 f0.03 2.66 2.67 2.642 2.92 co.03 3.31 3.33 3.368 PbOt (W.&( PO& PbOl fll)/Plcxigtas 1.85 20.02 2.00 2.00 1.988 u Expcrimcntal activity ratio of the sampies and respective standard deviations, ’ Vuiucs of ,4//f’, corrected by means of neutron removal cross-sections from Avery ef trl.‘. ’ Values of A/A’, corrcctcd by mcuns of neutron removal cross-sections from Zollcr’“. ’ Oxygen muss ratio of the sumplcs (based on stoichiomctric volucs).
For the calculation of the correction factors a code for IBM-360 computers was written which includes atomic masses, cross-sections and mass-absorption coefficients. Alternatively, these factors can be calculated with the aid of tables of escape probabilities”. The results of relative measurements done with the samples referred in Table I are shown in Table III, in which the previously known M/M’ ratios can be compared with the experimental activity ratios A/A’ and the corrected values. It can’ be seen that the corrected values agree with the stoichiometric values to within two standard deviations. The in?portance of P-radiation self-absorption in samples with widely varying densities can be seen in Table XII, if one compares the values of the activity ratio A/A’ of sample/standard obtained in the absence and in the presence of the absorber. SUMMARY
A method of correcting sample self-absorption effects in activation analysis for oxygen by 14-MeV neutrons is described. The effects of neutron, y- and P-ray self-absorption are determined individually as a function of sample geometry and composition, by means of escape probabilities, and the overall correction factor is obtained by means of a computer code or through the use of tables. A procedure for measuring the &contribution to the counts, which may amount to over 30”/,, is described. Results of analyses for samples of composition widely different from
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the standard are presented; these agree with stoichiometric although the correction may amount to more than 20%.
367 values
within
l%,
RESUME
On propose une methode de correction des effets d’auto-absorption dans le dosage de l’oxygcne par activation neutronique. Les effets concernant les neutrons et les rayons gamma et beta sont determines separement en fonction de la geometric et de la composition des Cchantillons, et le facteur total de correction est obtenu au moyen d’un code Fortran. On determine la contribution relative des emissions beta aux comptages. Les resultats de dosages, effectues dans des Cchantillons qui presentent des compositions et densites tres diffcrentes, concordent avec les valeurs stoechiometriques a 1”/0pres, bien que la correction puisse se monter St plus de 20%. ZUSAMMENFASSUNG
Eine Methode zur Beriicksichtigung der Selbstabsorptionseffekte in der Probe bei der Bestimmung von Sauerstoff durch Aktivierungsanalyse mit 14 MeVNeutronen wird beschrieben. Die Einfliisse der Selbstabsorption von Neutronen, y- und j?-Strahlen werden als Funktion der Geometrie und Zusammensetzung der Probe mit Hilfe der Entweichungswahrscheinlichkeiten individuell ermittelt. Der Gesamt-Korrektionsfaktor wird mittels eines Rechenprogrammes oder unter Verwendung von Tabellen erhalten. Ein Verfahren zur Messung des P-Anteils an der Zlhlrate, der iiber 30”/, ausmachen kann, wird beschrieben. Die Analysenergebnisse von Proben, deren Zusammensetzungen sich stark vom Standard unterscheiden, werden vorgelegt. Sie stimmen mit den stiichiometrischen Werten innerhalb lo/, tiberein, obwohl der Korrektionsfaktor mehr als 20% betragen kann. REFERENCES 1 G. Auboin, P. Guazzoni and J. Lavcrlochcre, Rapport C.E.A. no. 2358. Saclay. 1963. 2 0. U. Andcrs and D. W. Briden, And. Cltem.. 36 (1964) 287.
3 4 5 6
7 8 9 10 11 12 13 14
S. S. Nargolwalla. M. R. Crambes and J. R. De Voe, .4&. Cl~e~n.,40 ( 1968) 666. S. S. Nargolwalla, M. R. Crambes and J. E. Sudduelh, Aural. Clrirrr. Actor, 49 (1970) 425. R. Gijbcls, A. Speecke and J. Hoste, Amd. Chim. Acta, 43 (1968) 183. K. M. Case, F. De Hoffman and G. Placzek, Iutrothrcviort to rhe Theory of Neutrort D#irsiott, Vol. I, Los Alamos Sci. Lab., Los Alamos, 1953. J. Gilat and Y. Gurfinkel, Nttcleort., 21 (1963) 143. R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955. A. F. Avery, D. E. Bendail, J. Butler and K. T. Spinney, AERE-R-3216, Harwell. 1960. L. K. Zoller, Nrtcfeor~., 22 (1964) 128. R. C. Weast (Editor), Handbook of Chemistry orzrlPhysics, The Chemical Rubber Co., Cleveland, 1967. J. T. Gilmore and D. E. Hull, Anc~l. C/rem., 35 (1963) 1623. C. A. Alvim and A. N. Santos, Nlrcl. Itzstrmr. Methods, 105 ( 1972) 289. J. W. Morgan and W. D. Ehman, Amd. C/h. Acru, 49 (1970) 287.