## 2 Materials and Methods  
The sampling, performed in an area around a large incinerator in Central Italy, was 24-h long for each filter by means of a dual channel sampler, mod. Swam Dual Channel sampler (FAI Instruments, Fonte Nuova, Italy) (flux 16.7 L min\({}^{-1}\), i.e., 1 m\({}^{3}\) h\({}^{-1}\)), equipped with PM\({}_{10}\)/PM\({}_{2.5}\)/PM\({}_{1}\) sampling heads, alternatively: 45 samples (15 filters PM\({}_{10}\), 18 PM\({}_{2.5}\), and 12 PM\({}_{1}\)) were collected during the seasonal sampling campaign between the middle of May and the middle of October to also understand the element content and distribution. The sampling points were fixed and located in a radius of 20 m from the plant boarders, no residences were present in the area, few commercial activities were positioned over 50 m from the site. During all samplings, the incinerator operated. All the treatments of samplestorage and handling were carried out at the National Institute for Insurance against Accidents at Work's (INAIL) laboratory according to European Union (EU) regulations [33]. Samples (i.e., filter samples), blank and standards were put in nuclear-grade polyethylene cylinders (Kartell, Milan, Italy). The irradiation was performed in the rotatory rack \"Lazy Susan\" of the TRIGA nuclear reactor at R.C.-Casaccia ENEA: the irradiation time was 25 h at 1 MW. The rotatory rack was held at constant rotation for having a uniform thermal flux, \(2\times 10^{12}\) n \(\times\) cm\({}^{-2}\) x s\({}^{-1}\) (and relative fluency \(2.34\times 10^{17}\) n \(\times\) cm\({}^{-2}\)): the flux stability (\(>\)99.8%) was tested irradiating the Au standard as a monitor. For INAA analysis, primary and secondary standards were used. This procedure was followed to obtain good quality assurance and quality control (QA/QC): standard reference materials (SRMs) with high reproducibility and precision were used. These SRMs have been certified by several international proficiency tests, to which our laboratory routinely takes part. Primary standards ([PERSON], Milano, Italy) were Ag, As, Au, Ba, Ca, Cd, Co, Cr, Cs, Eu, Fe, Hg, Ir, K, Mo, Na, Ni, Rb, rare earth elements (REE, i.e., La, Sm, Yb, Nd, Gd, Dy, Er, Yb), Sb, Se, Sn, Sr, Tb, Th, U, W, and Zn whereas, as secondary standards, two SRMs such as GXR-3 from the U.S. Geochemical Survey (USGS), and coal fly ash (CFA 1633b) from the National Institute of Standards and Technology (NIST). It would be better to use a reference material with a matrix as similar as possible to the samples investigated: two SRMs (i.e., USGS-GXR-3 2709 and NIST 1633b), coal fly ash, along with 35 primary standards (at different concentrations, alone or in mixing standard solutions) were used for overcoming this issue. After irradiation, \(\gamma\)-ray spectrometry measurements of different durations were carried out using a Ge(HP) Canberra detector (Meriden, CT, USA) (full width at half maximum 1.75 keV at 1332 keV, relative efficiency 35%; peak/Compton ratio 60.2:1) connected to a multichannel analyzer equipped with software packages (Canberra Genie 2k) for a \(\gamma\)-spectra analysis. For the energy and efficiency calibrations, two sources were used (i.e., a multi-peak source, BML 1517B (\({}^{241}\)Am, \({}^{109}\)Cd, \({}^{57}\)Co, \({}^{51}\)Cr, \({}^{137}\)Cs, \({}^{88}\)Yr, \({}^{60}\)Co: 1 cc of this source was placed in the Kartell nuclear grade tube) and a \({}^{152}\)Eu source). The BML 1517B source was produced and certified by the ENEA National Institute of Ionizing Radiation Metrology (INMRI-ENEA) whereas the \({}^{152}\)Eu source was by the Centre Nationale pour l'Energie Atomique (CNEA), respectively. According to the half-life time of each radionuclide [34], two gamma measurements were performed.