Determination of Carbon-12, Carbon-13 Isotopic Abundances and NitrogenKarbon Ratios in Biological Substances by Proton-Reaction Analysis Enzo Ricci Analytical Chemistry Diuision, Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830 Counting of prompt gamma rays from the reactions W(p,r)l3N and %(p,r)14N, induced with 0.7 MeV protons was successfully applied to the determination of the isotopic abundances of 1% and I3C in biological materials. The method allows rapid determinations in biomedical and environmental tracer studies; this stable isotope provides an interesting alternative to IC, whose use i s limited by its radioactivity. Nitrogen-15 could be simultaneously determined by the reaction lSN(p,cur)lzC; thus the elemental ratio N/C, proportional to the isotopic ratio ljN/lZC in natural biological samples, was also studied. Samples of human lung, brain, and Escherichia coli were analyzed against urea, benzamide and graphite standards. Relative standard deviations were 4.8-8.6% and 4.89.0% for the determinations of 13Cisotopic abundances and of ratios N/C, respectively. Therefore, a 20% variation is observable and the method can, for example, determine an increase in the I3C abundance from the natural 1.11% (average) to only 1.33%. An accuracy check of the 1% determination-with reference to mass spectrometric “true” results-gave a relative error of only -1.8% for proton reaction analysis. Ease and speed are important advantages of this technique over mass spectrometry and nuclear magnetic resonance, and its error i s compatible with the natural variation of biological results.
THEUSEFULNESS of carbon and nitrogen tracer experiments is well established in biomedical and ecological studies, t o understand the pharmacology and metabolism of natural and synthetic substances in living organisms. Carbon-I4 is the most extensively used tracer, despite its counting difficulties-only low-energy (0.1 56 MeV) beta emission. Because of its long half-life (5730 years), however, I4C is a serious radiological hazard for humans. Even its use in plants and animals is often open to questions regarding influence of its radiation on the very processes being traced with it; for example, I4C tagging would be a self-defeating approach to the current controversy about biological effects of long-term exposure to low-level radiation o n local ecosystems (1). Radioactive I3N does not present this problem because its half-life is only 9.96 minutes, but this very fact limits its use t o very short experiments. The logical alternative, then, has been to use stable I3C and ‘jN tracers. Nuclear magnetic resonance (NMR) and mass spectrometry (MS) have been the classical methods to follow these isotopes-by determining the ratios 13C/12Cand 15NI l 4 Nduring stable-tracer experiments. The N M R sensitivity is low ( 2 , 3) for these tracers and nil for 12C; moreover, as the samples must generally be liquid, previous acid destruction of organic matter is necessary. Whereas MS is very (1) S. I. Auerbach, Nucl. Safety, 12, 25 (1971). (2) N. F. Chamberlain in “Treatise on Analytical Chemistry,” I. M. Kolthoff, P. J. Elving, and E. B. Sandell, Ed., Part 1 , Vol.
4, Interscience, New York, N. Y., 1963, p 1944. (3) F. A. Bovey, “Nuclear Magnetic Resonance Spectroscopy,” Academic Press, New York, 1969, pp 228, 236. 1866
sensitive and precise ( 4 ) , it also requires unavoidable and tedious sample preparation steps; the specimens must be quantitatively converted into gas before analysis-a cumbersome operation when many successive samples are taken during a long tracer experiment, As the sample is destroyed in N M R and MS, all information about spatial distribution of the stable tracer is lost. Finally, considering the natural variability of tracer results for different individuals of the same species, it appears that neither biomedical nor environmental research can take full advantage of the excellent accuracy and precision of MS. In all these regards, charged-particle reaction analysis appears as an advantageous alternative. Use of this method has greatly expanded over the last few years (3, because it is fast and free from tedious sample-preparation steps; moreover, it may be amenable to sample surface scanning, as an actual microprobe (6-8). The purpose of this paper is to report the successful application of proton bombardment-with simultaneous gamma spectrometry-as an alternative t o conventional methods for measuring carbon and nitrogen isotopic ratios in biological materials. It should be stressed that no effort was made t o match the precision of MS, because the need was felt for a complementary technique-i.e., a sufficiently precise method that may provide, simply and rapidly, results relevant t o biomedical and environmental stable-tracer studies, and that could be eventually elaborated into a scanning microprobe. NUCLEAR REACTIONS AND BASIC EQUATIONS The most abundant elemental constituents of biological substances are carbon, nitrogen, oxygen, hydrogen, sulfur, and phosphorus. We observed that 0.7 MeV protons can induce nuclear reactions on the isotopes of the first two elements, without appreciably interacting with the others. At this energy, the most prominent proton reactions with light elements have positive Q values and proceed by formation of a n intermediate, highly excited “compound nucleus,” which immediately loses energy by emission of prompt gamma rays. Table I lists the nuclear reactions and parameters that are pertinent to this work. As only thick targets were used, the 0.7 MeV protons could only reach-by energy degradation in them-the 457, 554, and 429 KeV resonances (4) F. W. Melpolder and R. A. Brown in “Treatise on Analytical Chemistry,” I. M. Kolthoff, P. J. Elving, and E. B. Sandell, E d , Part 1 , Vol. 4, Interscience, New York, N. Y.,1963, p 2010. (5) W. S. Lyon, E. Ricci, and H. H. Ross, ANAL.CHEM., 38, 251 R (1966): 40, 168 R (1968); 42, 123 R (1970). (6) R. L. Macklin, J. H. Gibbons, and T. H. Handley, U. S. A t . Enprgy Conim. Repf., ORNL-TM-2238 (1968). (7) T. B. Pierce, P. F. Peck, and D. R. A. Cuff, Nucl. Zmtrun?. Methods, 67, 1 ( I 969). (8) P. B. Price and J. R. Bird, ibid., 69, 277 (1969).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
Table I. Significant Parameters for Proton-Reaction Determination of Carbon and Nitrogen Isotopic Ratios.
Reaction *C(P,Y)3N
Q,MeV
Proton energy, KeV
1.941
456.8 i 0.5 1697 f 12 554 f 2 1160 1747.3 f 0.8 429 f 1 898 f 1 1210 f 3 1640 f 3
13C(~,y)14N
7.546
l6N(p,ay)1*C
4.964
Q
Resonance Width I-, KeV 39.5 =k 1.0 74 f 9 32.5 jz 1 6 12 0.075 0.9 2.2 f 0 . 2 22.5 i 1 68 f 3
u,
mb
Excitation energy, MeV
Prominent prompt gamma rays, MeV
2.363 3.507 8.060 8.62 9.17 12.505 12.955 13.247 13.651
2.363 3.507 8.060 2.92, 2.39, 2.31 9.17, 6.44, 2.73 4.433 4.433 4.433 4.433
0.127 0.035 1.44 0.56 340 200 800
600 340
Data presented directly as given in Reference 9.
of the reactions 12C(p,y)13N,13C(p,y)14NN, and 15N(p,ay)1zC, respectively; thus, the intensities of the corresponding 2.363, 8.060, and 4.433 MeV gamma rays were correlated with the contents of lZC, 13C, and l5N, respectively, in the samples. Though original plans did not call for determination of 15N, this isotope was also included because its very intense prompt gamma rays were always found in the spectra. Unfortunately, 4 N cannot be determined by proton-reaction analysis ; thus the elemental ratio N/C-proportional to the isotopic ratio 15N/12C-was investigated, rather than lsN/14N. Changes in the N/C ratio may be useful in biomedical work-either with or without administering stable tracer 1SN-to observe relative concentration changes of nitrogenous compounds (proteins, etc.). Charged-particle reaction analysis calculations are naturally involved because, unlike neutrons and photons, these particles readily lose energy when they penetrate matter and, therefore, the nuclear-reaction cross section earies with sample depth. The reaction prompt gamma-ray yield-or photon count rate-is thus
T o obtain the elemental ratio N/C-proportional to the isotopic ratio 15N/12Cin natural substances-the yield ratio r = Y(1SN)/Y(12C)is experimentally determined (10) for sample (nonprime) and standard (prime) and used in (Ratio N/C)
=
C
=
C' r/r'
(3)
An analogous equation could determine the isotopic ratio lsN/lZC itself, in natural and tagged specimens, also in terms of r/r'; but Equation 3 was used here because only natural samples were analyzed. EXPERIMENTAL
(2) is the abundance ratio for the sample, and F' that for the standard. Also, R = Y(*3C)/Y(12C) is the corresponding experimental yield ratio for the sample, and R' the analogous experimental result for the standard.
Standards were first bombarded at various proton energies to determine gamma-ray yields-and, thus, sensitivitiesfor the reactions of interest; the spectra provided information about the interplay between these yields and interferences from unwanted reactions. Also, the accuracy for the determination of the per cent 13Cabundance was checked, and the precision with which this value and the ratios laC/12C and N/C may be obtained was established, during a number of repetitive analyses of biological samples. Finally, the performance of different standards in these determinations was assessed. Samples and Standards. One of the advantages of the proton-reaction method in biological determinations is the great ease of its sample preparation procedures. The samples used in this work were simply freeze-dried and directly pressed into 2-mm thick disks of 2.5-cm diameter; the pressing step added very little complication but-by compacting the samples-it improved their heat dissipation characteristics. Typical samples of human lung, brain, and Escherichia coli were chosen to test directly the applicability of the method in biomedicine and environmental research. The human samples were from two different individuals, killed by violent death in the same geographical area. Benzamide, urea, and graphite were considered adequate standards (10); a piece of nuclear grade graphite and pressed disks-analogous to the samples-of the organic reagents were used for this purpose. Among these standards, benzamide has good thermal properties and contains all the isotopes of interest, while graphite is satisfactory for carbon isotopic ratios. Urea is also useful, but precautions should be taken to prevent its decomposition into biuret (160 "C); benzamide boils-wirhout decomposition-at a much higher temperature. Though no melting was observed during any of these experiments ( I I ) , it is not expected that nondestructive melting-or even slow evaporation-might change the usefulness of any of these standards, because their composi-
(9) F. Ajzenberg-Selove and T. Lauritsen, N u d . Phys., 11, 1 (1959). (IO) E. Ricci, Nucl. Ztistrum. Merhods, 94, 565 (1971)..
(1 1) E. Ricci, J . Radioarral. Chem., in press.
u(E) d E A I:'~-< S(E) where a is the sought isotope's fractional abundance, A the corresponding element's atomic weight, c its concentration in a target of stopping power S ( E ) , I the beam intensity, N o Avogadro's number, and X the counting efficiency; the reaction cross section a(E)-or rather the ratio u(E)/S(E)-is integrated over the span 2e of the resonance E,. Calculations become very complex when yield ratios are first determined for samples and then dioided by ratios from standards. It has been shown elsewhere (IO), however, that because of stoppingpower characteristics of biological substances for low-energy protons, very simple basic equations may be derived for the comparator technique in this case. In particular, the carbon per cent isotopic abundances-for both carbon-tagged and natural samples-are - acXNoI J''Otf
( l Z C C ) = 100/(F where F
=
+ l), and (13CC) = 100F/(F+ l),
F' R/R'
=
(1)
('3C73/(12C73
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
1867
COLD P L U N G T
0-1
(
12.7crn x 1 2 . ? c r n \ W , No1 ( T I ) DETECTOR
\
GAMMA-RAY ENERGY, MeV
0
2
4
R
R
LIQUID N, 30 crn3 G e ( L i )
DETECTOR
E QUARTZ VIEWER
PROTONS
Figure 1. Bombardment and counting system
'I
BENZAMIDE
(0.49 P A )
2
tions will remain unchanged. I n fact, even the decomposition of urea cannot alter significantly its carbon isotopic ratio and, thus, its value as a standard in this particular determination. Irradiation. A 3-MV Van de Graaff accelerator was used for the experiments and the general arrangement of the bombardment-counting assembly is shown schematically in Figure 1. The sample o r standard was tightened flat-to facilitate thermal contact-against the aluminum target holder by a tantalum washer and screws. To minimize target heating, the beam was defocused as much as was compatible with the 1.9-cm diameter opening of this washer. Also, the target holder was welded to a n aluminum plunger submerged in a cold mixture of acetone and dry ice (-78.5 "C). The beam spot was visually monitored on a quartz viewer which could be rotated in front of the target, and the latter was insulated by a quartz pipe, also a part of the viewer assembly. To prevent recoil electrons from introducing errors in the current measurements by escaping from the target, the latter was connected to the positive terminal of a 300-V battery-not shown in the figure-introduced in series in the Faraday cup circuit. No current leaks were observed when this circuit was tested with the battery connected and the cold plunger submerged in the Dewar. To avoid residual pump oil and other impurities in the beam pipe, a liquid nitrogen trap was placed 1 m from the target. Counting. The prompt gamma rays were detected by a pair of 12.7 cm x 12.7 cm NaI(T1) detectors positionedas shown in Figure 1-with the line of their centers passing by the irradiated spot of the target, perpendicular to the beam; this spot was a t 5.7 cm, perpendicularly, from the center of the face of either detector. The detector multiplier phototubes were powered by one high voltage supply through a high voltage divider box. The pulses from each detector were boosted by a standard preamplifier and merged into a fast amplifier, whose output fed finally into a multichannel analyzer. A 30 cm3 Ge(Li) detector-shown in the figure-was used in some of the experiments. However, not only was its high resolution found unnecessary for this work, but its efficiency (sensitivity) much too low to be useful. The intensities of the photopeaks of interest were calculated in each of the spectra-with the help of the program GABA3 D (E. Schonfeld, N.A.S.A., unpublished)-at a IBM 360 computer. The program first subtracted background, and then computed the area--i.e., the net total count rate-under each peak, by the method of the tangent to the valleys. Figure 2 shows a typical benzamide spectrum; the photopeaks corresponding to the 2.363, 4.433, and 8.060 MeV prompt photons-from the proton reactions o n I C , lrN, 1868
L
'0
J 40
I
I
I
I
I
I
I
I
I
120 CHANNEL NUMBER
80
I 160
\,,,I 200
Figure 2. Typical prompt gamma-ray spectrum of benzamide under 0.7-MeV proton bombardment and lac,respectively (Table 1)-clearly stand out, as well as the first escape peaks corresponding to the last two, at 3.922 and 7.549 MeV. The areas under these escape peaks were added to those of the corresponding photopeaks to compute the l5N and 13Ccount rates. RESULTS AND DISCUSSION
The background was measured both with the accelerator
off and with 0.3-1.0 pA beams of 0.7-0.9 MeV protons on blank tantalum and quartz targets; also, 0.7-1.8 MeV protons were stopped at the accelerator cup, about 4 m from the detectors. No significant variations were observed, so that the background was attributed to the accelerator building rather than to the machine operation. The 1.46 and 2.61 MeV gamma rays, respectively, from 40Kand 208TI(232Th decay chain) in the concrete walls, were always present, in addition to a n unidentified peak a t 1.8-1.9 MeV. Background spectra to be subtracted were always counted shortly before or after the corresponding sample or standard spectra. Yields and Sensitivities. Graphite and urea standards were irradiated with protons of 0.7, 0.8, 0.9, 1.0, 1.2, and 1.8 MeV, in view of the resonance energies of interest (Table I); yield and sensitivity results are presented in Table 11. The first group of data gives yields per unit beam current for the reactions 12C(p,y)13N, 13C(p,y)14N,and 15N(p,ay)12C,represented by their respective reacting nuclides; data for 1,2 and 1.8 MeV protons were seldom useful, because unwanted reactions at these energies caused reduction of the yields of interest and increased interference, particularly from oxygen. The second group of results presents the corresponding analytical sensitivities-ie., yields per unit beam current, per unit concentration of stable isotope in the standard. The detection limits in the third group were obtained by dividing the minimum measurable count rate per unit beam current, in each case, by the corresponding sensitivity. For each peak or peak combination, and for each bombarding energy, the minimum measurable count rate was defined to be equal to the corresponding area ufider the line of the valleys in a urea spectrum--i.e., the assumption was made that the overall area of a peak, or peak combination, should be
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
Table 11. Gamma-Ray Yields from the Reactions 1 2 C ( p , ~ ) ~ ~laC(p,r)14N, N, 15N(p,cuy)12C, and Related Analytical Parameters Proton bombarding energy, MeVd DeterReacting 1 .o 0.8 0.9 0.7 mination" Unitsb nuclidec 7297 =k 72 7431 + 65 7771 i 61 7573 f 54 Yield cpm/d '2C 639 + 46 678 f 41 635 f 44 6 4 5 It 36 1 3 c 13,580 f 263 2146 f 114 1186 f 105 936 i 48 16N 7.38 f 0.07 7.51 =k 0.07 7.86 i 0.06 7.66 i 0.05 Sensitivity cpm/(ppt pA) 12C 57.7 =k 4.2 61.2 i 3.7 57.3 k 4 . 0 58.2 + 3.2 1 3 c 1974 f 154 1260 f 67 696 f 62 566 f 28 16N Detection ppt 1 2 6 309 f 3 98.8 i 0.8 136f 1 86.2 f 0 . 6 5.07 f 0.36 4.01 i 0.24 3.33 k 0.23 3.17 i 0.18 limit 13 c .0.768 f 0.015 0.889 i 0.047 0.985 i 0.087 1.01 31 0.05 15N Assume minimum determinable cpm per pA given by backDetection limit = (Minimum determinable cpm per MA) + (Sensitivity). ground under line between valleys for corresponding peak in typical urea standard spectrum. b 1 ppt = 1 part per thousand. Natural graphite (l*C, 988.92 ppt, 13C, 11.08 ppt) and urea (15N, 1.703 ppt) were used for carbon and nitrogen isotopes, respectively. Error of beam-intensity measurement considered comd Errors represent counting statistical uncertainties from GABA-3D program. paratively insignificant, and that of arbitrary minimum determinable cpm per PA, nil.
GAMMA-RAY ENERGY 4 6 ~
.o
2
UREA
0
40
80 i20 CHANNEL NUMBER
GAMMA-RAY ENERGY, MeV
MeV
8
\ 1 60
2 00
Figure 3. Typical prompt gamma-ray spectra of urea, under bombardment with 0.7- and 1.0-MeV protons twice the area under the corresponding valley line for urea, to be detectable. Table I1 shows little energy dependence of the gamma-ray yields for 12C and 13C. In agreement with the resonance parameters of Table I, instead, the sensitivity for 15N increases by a factor of 14 from 0.7 t o 1.0 MeV, and it reaches 229 and 166,260 i 2294 cpm/(ppt MA) for 1.2 16,600 and 1.8 MeV protons, respectively. Though these values are not given in the table, they were easily determinedbecause of the outstanding l5N yield-despite interferences a t high proton energies. Figure 3 supports this by showing an impressive intensity increase of the 15N peaks from 0.7 t o 1.0 MeV. However, the background under the peak increases at 1.0 MeV, and the 13Cpeaks become less clearly defined and inconveniently close-in energy and intensity--to interfering radiation; this is reflected in the cor-
4
' 0
40
80 '20 CHANNEL NUMBER
'60
200
Figure 4. Typical prompt gamma-ray spectra of human lung, brain, and E. coli, under bombardment with 0.7-MeV protons responding detection limits, which increase by factors of 3.6 and 1.6, respectively, for 12Cand I3C,from 0.7 to 1.O MeV. I n conclusion, bombardment with 0.7 MeV protons yields satisfactory sensitivities for 12C, 13C, and 15N, without including significant interference. If only ljN, o r the ratios N / C and/or 15N/12C, were sought, a higher bombarding be considered more adenergy-up t o 1.0 MeV-might vantageous, but certainly not mandatory. Isotopic Abundances and Elemental Ratios. Ratios 3C/12C
ANALYTICAL CHEMISTRY, VOL. 43, NO. 13, NOVEMBER 1971
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Table 111. Determinations of ISotopic Abundances and Elemental Ratios Carbon resultsa N/C results* IsotoDic ratio Elemental ratio Yield ratio 13c/11C 13C isotopic Yield ratio DeterN/C abundance, Sample minationc ( R , cpm/cpm) (F,atom/atom) (C, g/g) ( r , cpm/cpm) 0.2344 1.124 Human lung 1 0.08751 0.01137 0.05396 2 0.1934 0.08638 0.01 122 1.110 0.04452 3 0.07666 0.00996 0.986 0.05453 0.2369 4 0.05111 0.09483 0.01232 1.217 0.2221 17 i s 0.08635 i.0.00744 0.01122 f 0.00096 1.109 i 0.095 0.05103 f 0.00458 0.2217 f 0.0199 8.6 8.6 9.0 8.6 9.0 0.09442 0.05936 0.01226 1.212 0.2579 Human brain 0.05989 0.08690 1.116 0.01129 0.2602 0.08766 0.01139 1.126 0.05987 0.2601 0.08454 0.05347 0.01086 1.086 0.2323 0.08838 zk 0.00424 0.01145 f 0.00057 1.135 f 0.054 0.05815 f 0.00313 0.2526 f 0.0136 4.8 5.0 4.8 5.4 5.4 1 0.3189 E. coli 0.08139 0.01057 1.046 0.07340 0.3249 2 1.100 0.07479 0.08567 0.01113 0.3365 0.08873 1.139 0.07744 3 0.01152 0.2997 0.06897 0.07657 0.985 0.00995 4 0.08309 f 0.00528 0.01079 f 0.00068 1.068 f 0.067 0,07365 f 0.00354 0.3200 f 0.0154 a i s 4.8 6.4 6.3 6.3 4.8 s% 2.632 0.3417 25.47 Enriched C 1 2.573 0.3341 25.04 2 0.3379 f 0.0054 25.26 i 0.31 2.603 f 0.042 8 f S 1.6 1.6 1.3 Graphite (F‘ = 0.01065 a Calculated by comparison with benzamide standard; i.e., F‘ = 0.01082 and R’ = 0.08327 in Equations 1 and 2. and R’ = 0.08203) was used as standard for enriched carbon. b Calculated by Equation 3 against benzamide staniard with C’ = 0.1667 and r‘ = 0.03837. c Mean, 3; standard deviation, s; ( s z ) = 100 s / X .
and N/C, and l3C isotopic abundances, were determined for the three natural samples, by comparison with the three standards. Each sample was bombarded four successive times with a 0.33-0.48 pA beam of 0.7-MeV protons; it is shown elsewhere (11) that the organic targets can stand a total 30-50 minute bombardment in these experimental conditions and setup, without observable chemical decomposition. Figures 2 and 3 show typical spectra for the standards and Figure 4 illustrates analogous data for the samples. The three sample spectra are qcite similar and also resemble those of benzamide and urea. I n all spectra the peaks of interest are well defined and free from interferences, thus being quite suitable for count-rate comparisons. The ratio (13Cz)/(12Cx)-equal t o 13C/12C,in atoms per atom-is given by Equation 2, where it appears as F, in terms of the corresponding ratio F‘ for the standard. The values R and R’ in Equation 2 are simply the ratios, for sample and standard, respectively, between the experimental net count rates for 13C (8.060 MeV plus escape peak) and for 12C(2.363 MeV photopeak). With F , the per cent 13C abundance was immediately obtained by Equation 1. Table I11 displays the final four results per sample, for the ratio I3C/12C and the 13C per cent isotopic abundance-obtained against a benzamide standard-in columns four and five, respectively ; two determinations-against a graphite standard-on a carbon pellet, containing a n unknown amount of enriched l3C, are added for the sake of completeness. F o r benzamide it is F‘ = 1.07/98.93 = 0.01082, obtained independently by MS; for graphite, F’ = 0.01065, determined by proton-reaction analysis against benzamide. Results for 12Cabundances are not listed because they can be obtained by simply substracting the 13Cabundances from 100 (Equation l). The elemental ratio N/C (gram per gram) was calculated 1870
by Equation 3, where C’ is the analogous, known ratio for the benzamide standard, [.e., C’ = 11.57/69.40 = 0.1667. Again in this equation, r and r’ are the ratios, for sample and standard, respectively, between the experimental net count rates for 15N (4.433 MeV plus escape peak) and for 12C (2.363 MeV photopeak). Final results for elemental ratios N/C are presented in the last column of Table 111. The higher values of this ratio for E. coli suggest greater concentrations of protein in these bacteria-largely consisting of protoplasm matter-than in the more specialized and complex human tissues. The errors s assigned t o mean values -7 in the table are standard deviations, and are taken t o represent the precision of these determinations; it is then apparent that precision values for biological samples are 4.8-8.6% for I3C per cent for ratios abundances and 13C/*C ratios, and 4.8-9.0 N/C. Because of Equations 1-3 and of the definition of standard deviation (12), these precision values are independent of the nature of the standard used to determine the last two ratios; moreover, this extends here to the 13Cper cent abundance results because F
