Electronic Supplementary Material
Evaluation of uncertainty budget
The uncertainty budget takes into account all possible sources of uncertainty starting from
sampling up to measurements. Recognition of the biggest contribution define the most
sensitive step in the elaborated procedure, and can initiate appropriate procedure corrections.
In the case of highly accurate RNAA methods, estimation of expanded uncertainty should
prove the significance of these methods from metrological point of view.
For radiochemical neutron activation analysis, the sources of uncertainty (u) are divided into
four groups [1]:

preparation of samples, standards and monitors to the irradiation in the reactor u1 ;

irradiation in the neutron flux in nuclear reactor u2;

radiochemical separations u3;

gamma-ray spectrometric measurements u4.
The standard uncertainties within particular categories connected with individual sources of
uncertainty can all be quantitatively evaluated and expressed in SI units [2,3].
In RNAA, when the samples are irradiated together with the standards, CRMs and blank in
one package in the neutron flux, measurements are carried out under the same geometric
conditions using the same HPGe detector, mass fraction wx of the element to be determined
(x) is given by the equation [1]:
wx =
Ax Dst C st mst

Ast Dx C x m x Yx
(1)
where symbols Ax, Dx, Cx, mx, Yx are for the sample, and Ast, Dst, Cst, mst for standard
respectively; and
-
D is the decay factor (D = exp(-λtd)), where td is the decay time;
-
C is the measurement factor (C = (1-exp(-λtm)/ λtm), where tm is the measurement
time).
-
Ax is the count rate of analytical gamma-ray of indicator nuclide (s-1, Ax = Np tc-1,
where Np is net number of counts in peak corrected for pulse losses and tc is the live
counting time);
-
mx is the sample mass (g);
-
Yx is the chemical yield of the separation.
The uncertainty sources taken into account within preparation of samples and standards to the
irradiation were: sample and standard mass determination, standard purity, sample mass
changing during weighing, determination of moisture content. The uncertainty in sample and
standard weighing was estimated according to the producer specification to be at maximum
0.1%. In the case of moisture determination, uncertainty has been estimated from
measurements of water content of the several samples (not used for analysis) accordingly to
CRMs producer recommendation. The relative uncertainty associated with moisture
determination, calculated from rectangular distribution ( u  a / 3 ) is almost negligible.
Similarly, in the case of standard purity; arsenic standard solution was prepared from highpurity As2O3 thus uncertainty associated with it is negligible. Also the uncertainties associated
with the other sources of uncertainty in the stage of preparation of the sample and standard i.e.
change of sample mass during weighing, stoichiometry, variation of isotopic abundance and
residual blank can be neglected.
Sources of uncertainty associated with the irradiation step are: differences in irradiation
geometry and neutron spectrum in space and time including neutron self-shielding and
scattering, differences in irradiation time, nuclear reaction interferences and volatilization
losses during irradiation. Differences of the neutron flux caused by the flux gradient in space
are determined and corrected for by use of sandwich elemental standards. The standard
uncertainty attached to this correction has been calculated from triangular distribution
( u  a / 6 ) and is equal to 0.1%. The standard uncertainty related to thermal neutron selfshielding and scattering is significant in the case of high density samples or for elements with
very high cross-section. For typical biological samples this component is usually negligible
and was evaluated to be less than 0.2% [1]).
In arsenic determination by NAA, interfering nuclear reactions should be taken into account:


75
Se(n, p)76As, 79Br(n, )76As and 74Ge(n, )75Ge 
As(n, )76As [4]. The possibility of
76
appearance of these reactions was checked, no corrections were needed. The uncertainty
connected with differences in irradiation time is zero due to simultaneous irradiation of
samples, standards, CRMs and blank. Uncertainty associated with the analyte losses during
irradiation was negligible. Irradiation of arsenic was done with using various irradiation
vessels: polyethylene capsules and sealed quarts ampoules; independently on the container
used, the recovery of irradiated arsenic was the same and quantitative.
Sources of uncertainty related to radiochemical separation are: quantitative separation of
determined element and standard, isotope exchange between analysed radionuclide and stable
carrier (or radioindicator). In the elaborated procedure, the chemical yield was evaluated by
several analyses of various biological materials spiked with
73
As radiotracer. The yield was
determined as 100%  1%. The uncertainty estimated from the rectangular distribution is
equal to 0.6% for both sample and standard. Uncertainty related to the isotope exchange
between isolated radionuclide 76As and stable carrier 75As is negligible, when carrier is added
before sample decomposition.
Sources of uncertainty associated with gamma-ray spectrometric measurement are: counting
statistics, blank correction, differences in counting geometry and time, pulse-up losses,
cascade summing, effects of dead-time and decay time, gamma-ray interferences, selfshielding and peak integration.
The uncertainty resulting from counting statistics of the samples and the standards is
calculated from the Poisson’s distribution, according to the equation: u=100(Np+2B)1/2/Np,
where B-background, Np-net peak area. For the elaborated method standard uncertainty for
sample is equal 1%, for standard-0.6%. Differences in these values results from differences in
number of counts for standard and for sample; this is connected with relatively short half-life
time of
76
As (26.3 h). In the case of long time measurements of several samples, counting
statistics for first samples are much better than for the last one. Uncertainty from the counting
geometry was evaluated using triangular distribution and was calculated to be 0.4%. In the
case of peak area evaluation, higher uncertainties are to be expected for small peaks (close to
detection limit) and for multiplets. In the case of the present method, the purity of isolated
76
As is very high-only energy peak of 559 keV is visible in the spectra. Increased background
the low energy region originated from beta-emitter 32PO43- does not influence the count rate
and peak shape of arsenic. Also, the high cross section of
75
As(n, )76As reaction results in
relatively high number of counts. Uncertainty associated with peak integration was calculated
to be 0.3%. The uncertainty related to other sources attached to this step is neglected.
The combined standard uncertainty calculated according to uncertainty propagation law
amounted to 1.7%.
The uncertainty budget for the arsenic determination in Oriental Tobacco Leaves CTA-OTL-1
is presented in Table 4. Obtained value for As determination in CTA-OTL-1 is 543 ng g-1,
combined standard uncertainty: 9.2 ng g-1, expanded uncertainty for coverage factor k=2 (a
level of confidence of approximately 95 %): 18.5 ng g-1. The final results with expanded
uncertainty is equal (543  19) ng g-1, where the certified value is (539  59) ng g-1.
1. Kucera J, Bode P, Stepanek V (2004) Uncertainty evaluation in instrumental and
radio-chemical neutron activation analysis in quantifying uncertainty in nuclear
analytical measurements. IAEA-TECDOC1401, IAEA Vienna
2. Tian W, Ni B, Wang P, Cao L, Zhang Y (2001) Metrological role of neutron
activation analysis. IA. Inherent characteristics of relative INAA as a primary ratio
method of measurement. Accred Qual Assur 6:488-492. doi 10.1007/s00769-0010407-1
3. Tian W, Ni B, Wang P, Cao L, Zhang Y (2002) Metrological role of neutron
activation analysis, IB Inherent characteristics of relative INAA as a primary ratio
method of measurement. Accred Qual Assur 7:7-12. doi 10.1007/s00769-001-0408-0
4. Koch RC (1960) Activation Analysis, Handbook, Academic Press
Table. The uncertainty budget for the arsenic determination in Oriental Tobacco Leaves CTAOTL-1 by highly accurate RNAA method.
term
Relative standard
value
Mass of sample
Ws
200 mg
0.1
Mass of standard
Wst
5 mg
0.1
Residue blank
Wb
0 mg
0.1
Neutron flux gradient

1.00  0.002
0.1
Neutron self-shielding/scattering

1.00
0.2
Sample counting statiscics
Ns
30000 counts
1.0
Standard counting statistics
Nst
50000 counts
0.6
Counting geometry of sample
Ns
1.00
0.4
Counting geometry of standard
Nst
1.00
0.4
Pulse pile-up losses of sample
Ns
0 (%)
0.3
Pulse pile-up losses of standard
Nst
0 (%)
0.3
Peak integration method for sample
Ns
1.00
0.3
Peak integration method for standard
Nst
1.00
0.3
Radiochemical separation of sample
Ys
1.00  0.1
0.6
Radiochemical separation of standard
Yst
1.00  0.1
0.6
Source of uncertainty
uncertainty (%)