## 3 Results and Discussion
### Validation of the \(k_{0}\)-INAA Method Using NIST SRM 1648a Urban PM
JSI has been accredited to the \(k_{0}\)-INAA method in accordance with ISO/IEC 17025 (General requirements for the competence of testing and calibration laboratories, International Organization for Standardization, Vernier, GE, Switzerland) since 2009 (Accreditation Certificate LP-090) for analysis of various matrices samples based on concentration range, detection limit, and uncertainty. The elemental mass fraction values labeled # in Table 2 represent non-accredited activities, in accordance with LP-090, beyond the scope of the range of testing or the specified uncertainty. All details of uncertainty evaluation of \(k_{0}\)-INAA method is explained in our previous studies [13; 38] and the literature [32]. The expanded uncertainties for mass fraction values represented in Tables 1 and 2 have a coverage factor \(k\) = 2 at 95% confidence level. The combined standard uncertainties (typically, 3.5%) were calculated based on the quadratic summation of a number of parameters such as \(k_{0}\) constant (-1%), \(Q_{0}\) (-1%), \(f\) (-1%), \(\alpha\) (-1.5%), \(\varepsilon_{\mathrm{p}}\) measurement (-2%), and true coincidence correction (-1.5%) of \(k_{0}\)-INAA method and the standard deviation of the replicates of each sample. The results obtained by \(k_{0}\)-INAA are given in Table 2, where the E\({}_{\mathrm{n}}\) score [38; 47] of NIST SRM 1648a was used to evaluate the quality of the data. By definition, the E\({}_{\mathrm{n}}\) score is a ratio between the difference of the lab result and the assigned value and the square root of the quadratic summation of the expanded uncertainties (\(k\) = 2) of the lab and assigned value. According to the literature, satisfactory results are when \(-1.0<\) E\({}_{\mathrm{n}}\) \(<\) 1.0. Scores of E\({}_{\mathrm{n}}\)\(\geq\) 1.0 or E\({}_{\mathrm{n}}\)\(\leq\) -1.0 could indicate possible problems in the uncertainty estimations and measurement models, which need to be corrected and evaluated. As can be seen in Table 2, there is good agreement between the data obtained by \(k_{0}\)-INAA and certified values by NIST except for Hg (E\({}_{\mathrm{n}}\) = 1.07). The slightly higher value of Hg, obtained by \({}^{203}\)Hg (E\({}_{\mathrm{Y}}\) = 279.2 keV), can be explained by a large subtraction due to the interference of Se (26.1 mg/kg, \({}^{75}\)Se E\({}_{\mathrm{Y}}\) = 279.5 keV), whose contribution was about 75%. In Table 2, we also calculated the E\({}_{\mathrm{n}}\) score for reference values given by NIST (marked green), but this is given for information only. NIST established certified values using at least two different analytical techniques, while reference values were established by only a single method [35]. It should be mentioned that NIST established certified value for Ce (the only certified value among rare earth elements (REEs)) using INAA and PAA (photon activation analysis) techniques which is potentially influenced by fission of \({}^{235}\)U. Unfortunately, mass fraction data of U in NIST SRM 1648a is not available, but we found the content of U to be about 5.4 mg/kg (see Table 2) and Ce data obtained by \(k_{0}\)-INAA were corrected for about 3% of U contribution. This may explain a slightly lower value of the E\({}_{\mathrm{n}}\) score of Ce (-0.88) obtained by \(k_{0}\)-INAA. According to [PERSON] [48], INAA procedure at NIST uses multi-elemental solution dried on filter paper (10 \(\upmu\)L or 20 \(\upmu\)L standard solution on 5 mm diameter filter paper) as a calibration standard. Hence, it may not compensate for  
Figure 3: Gamma-ray spectra of NIST SRM 1648a urban PM irradiated for (a) 2 min and (b) 12 h.  
the interference of fission products of \({}^{235}\)U, if the multi-elemental standard does not include a similar amount of U as in the sample. However, the contribution of fission of \({}^{235}\)U may be ignored if only a low amount of U is present in the sample, which is not the case of NIST SRM 1648a.