## 3 Results and Discussion
### Validation of the \(k_{0}\)-INAA Method Using NIST SRM 1648a Urban PM  
To validate the \(k_{0}\)-INAA method for elemental analysis in airborne PM at JSI, we analyzed the NIST SRM 1648a urban PM, which provides certified and reference values for mass fractions of several elements. Figure 3 shows the gamma-ray spectra of short-lived nuclides irradiated for 2 min after cooling times of \(\sim\)11 and \(\sim\)35 min and those of long-lived nuclides irradiated for 12 h after a cooling time of \(\sim\)3, \(\sim\)10, and \(\sim\)28 days. The corresponding nuclide and gamma-ray energy of several isotopes are indicated in each spectrum for reference. Multiple measurements at different cooling times were conducted to measure the elements with different half-lives, with minimum influence of spectral interferences. Isotopes such as \({}^{52}\)V (T\({}_{1/2}\) = 3.75 m), \({}^{28}\)Al (T\({}_{1/2}\) = 2.2414 m), and \({}^{51}\)Ti (T\({}_{1/2}\) = 5.76 m) have a short half-life time of less than 10 min and should be measured as soon as possible after irradiation. The distance between the detector and the sample should be adjusted so that the dead time is less than 10%. Isotopes with a half-life of 10 min or more are measured after isotopes with a shorter half-life have sufficiently decayed and the background signal has decreased. For example, \({}^{27}\)Mg and \({}^{56}\)Mn emit gamma-rays at energies very close to each other upon nuclear activation (E\({}_{\gamma}\) = 843.8 keV, E\({}_{\gamma}\) = 846.8 keV, respectively), which may interfere with each other. However, their influence can be reduced by measuring them at different cooling times, as they have different half-life times (\({}^{27}\)Mg, T\({}_{1/2}\) = 9.462 m; \({}^{56}\)Mn, T\({}_{1/2}\) = 2.579 h). The HyperLab software helps further resolution of residual overlaps of gamma peaks of \({}^{27}\)Mg and \({}^{56}\)Mn in this energy interval. For the \({}^{27}\)Mg isotope, different gamma-ray emissions at 170.7 keV and 1014.4 keV can be used alternatively. However, their emission rates (I\({}_{\gamma}\) = 0.8% and I\({}_{\gamma}\) = 28%, respectively) are relatively lower than 843.8 keV (I\({}_{\gamma}\) = 71.8%), resulting in a significantly weak signal with a concomitant increase of measurement uncertainty. Depending on the specific gamma-ray interferences experienced by different analyte isotopes, such as \({}^{75}\)Se (T\({}_{1/2}\) = 119.781 d, E\({}_{\gamma}\) = 264.7 keV, E\({}_{\gamma}\) = 279.5 keV) and \({}^{203}\)Hg (T\({}_{1/2}\) = 46.61 d, E\({}_{\gamma}\) = 279.2 keV), the data obtained at different cooling times have been used to calculate the mass fractions of each element. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**El.** & **Mass Fraction \(\pm\) Expanded** & **LOD** & **El.** & **Mass Fraction \(\pm\) Expanded** & **LOD** \\  & **Uncertainty (mg/kg, \(k\) = 2)** & **(mg/kg)** & **Uncertainty (mg/kg, \(k\) = 2)** & **(mg/kg)** \\ \hline Ag & & 0.030 & La & 0.002 \\ Al & \(1.63\pm 0.42\) & 0.09 & Mg & \(1.74\pm 0.651\) & 1.07 \\ As & & 0.0063 & Mn & \(0.0387\pm 0.0036\) & 0.0045 \\ Au & \(0.00014\pm 0.00011\) & 0.00005 & Mo & & 0.023 \\ Ba & & 0.68 & Na & \(16.4\pm 3.1\) & 0.1 \\ Br & \(0.175\pm 0.024\) & 0.008 & Nd & & 0.04 \\ Ca & & 32.9 & Rb & & 0.23 \\ Cd & & 0.05 & Sb & \(0.0025\pm 0.0004\) & 0.0010 \\ Ce & & 0.03 & Sc & & 0.001 \\ C1 & \(28.2\pm 3.8\) & 0.4 & Se & & 0.03 \\ Co & & 0.009 & Sm & \(0.00017\pm 0.00005\) & 0.00015 \\ Cr & \(0.232\pm 0.050\) & 0.056 & Sn & & 1.4 \\ Cs & & 0.006 & Sr & & 2.5 \\ Cu & & 0.27 & Ta & & 0.002 \\ Dy & & 0.002 & Tb & & 0.002 \\ Eu & & 0.0007 & Th & & 0.0041 \\ Fe & \(3.77\pm 0.669\) & 3.76 & Ti & & 0.85 \\ Ga & & 0.037 & U & & 0.0014 \\ Hf & & 0.005 & V & & 0.0070 \\ Hg & & 0.017 & W & & 0.013 \\ I & & 0.028 & Yb & & 0.0021 \\ In & & 0.0005 & Zn & \(0.190\pm 0.050\) & 0.059 \\ K & & 3.3 & Zr & & 3.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Elemental mass fractions (above LODs) of cellulose paper analyzed by \(k_{0}\)-INAA and their LODs.