## 3 Results and Discussion
### Calibration of CR-39 detectors
analysis after chemical etching. Reference [7] shows that proton beams with fluencies in the range of 10\({}^{5}\) particles/cm\({}^{2}\) are suited for counting proton beam tracks by visible light microscopy, avoiding any difficulties owing to track overlapping. After irradiation, the CR-39 samples were chemically etched using a 6.25 N NaOH solution at 70 \({}^{\circ}\)C for 6 hours in an etching bath container under conditions of fine temperature control. The temperature shift during the etching time was about 1 \({}^{\circ}\)C. After chemical etching all detectors are washed in distilled water. The diameters of the proton tracks on the post etched CR-39 detectors were analyzed by means of a EUROMEX IS.1053- PLPOLRi polarized microscope (Euromex Microscopen BV, Arnhem, Netherlands), fitted with a CMEX-5000 USB-2 DIGITAL CAMERA -EUROMEX DC.5000 (Euromex Microscopen BV, Arnhem, Netherlands). Figure 3 show the images of the tracks left by protons within the detector, for proton energies of 2, 3 and 5 MeV. The corresponding measured track diameters of the protons are 5.5 \(\upmu\)m, 4.5 \(\upmu\)m and 3 \(\upmu\)m, respectively. Besides circular proton tracks, in Figure 3a-c, some traces with irregular shapes and sizes attributed to the chemical etching of the detector material unmarked by protons, can be observed. Similar values for the proton track diameters are obtained after the analysis of the post-etched CR-39 detectors using atomic force microscopy. The data that connect the proton track diameters with respect to the proton beam energies, are in good agreement with those reported by [PERSON] et al. [8], in case of CR-39 detectors etched in 6.25 N NaOH solution at 70 \({}^{\circ}\)C, for different etching times. Figure 3 from Reference [8] presents the proton track diameters and the stopping power evolution in CR-39 detectors, as a function of the incident energy and etching time. By extrapolating these data, the proton track diameter values for 6 h etching time are shown to be \(\sim\)6.8 \(\upmu\)m, 5 \(\upmu\)m, 4 \(\upmu\)m, 3.5 \(\upmu\)m and 3 \(\upmu\)m, for proton incident energies of 1, 2, 3, 4 and 5 MeV, respectively. Figure 3 in [8] also shows that within the 1-6 MeV energy range, the proton track diameter decreases following the evolution of the stopping power as a function of energy. Recently, Reference [22] reported on a computer software, TRACK-P, used to compute the proton range and the proton track diameters in a post-etch CR-39 detector, as a function of: the incident proton energy, the bulk etch rate of the detector material, the incident angle of the protons on the detector, and the chemical etching time. It also computes the proton range using the SRIM 2003 software [23]. For a bulk etch rate of 1.65 \(\upmu\)m/h, and proton energies of 1, 2, 3, 4 and 5 MeV, for a 6 h etching time value and a 90\({}^{\circ}\) proton incident angle, the proton track diameters computed with TRACK-P are found to be 9.4 \(\upmu\)m, 7 \(\upmu\)m, 5.7 \(\upmu\)m, 4.5 \(\upmu\)m and 3.2 \(\upmu\)m, respectively. By using the SRIM code of [PERSON] et. al. [23] to calculate the energy loss dE/dx (keV/\(\upmu\)m) of protons with energies up to 15 MeV into the detector stack, we find the proton range, as illustrated in Figure 4a (black line). Protons with energy ranging between 1.1-10.4 MeV are stopped in the first CR-39 detector, while protons with energies between 10.5-14.8 MeV are stopped within the second CR-39 detector. Figure 3: Images of proton tracks on the CR-39 detectors, obtained for a 40\(\times\) optical microscope magnification: (**a**) 2 MeV; (**b**) 3 MeV and (**c**) 5 MeV proton beam energy. The proton range can also be computed using the TRACK-P software, but only for 1 mm thick CR-39 detectors and maximum incident proton energy up to 11 MeV [22]. The results on the proton range calculated with the TRACK-P software using as input data a bulk etch rate of 1.65 \(\upmu\)m/h, a 6 h etching time value, and a 90\({}^{\circ}\) proton incidence angle on the detector, are presented in Figure 4a (red points).