## 3 Results and Discussion  
### Calibration of CR-39 detectors  
The CR-39 nuclear track detectors are frequently used to detect and characterize charged particles such as protons, alpha particles or neutrons [9; 20]. The analysis of laser-accelerated proton beams by means of CR-39 detectors was demonstrated [3; 7] to represent a powerful tool, as the shape and size of a track left by each proton into the detector can give useful information about their energy and incident angle. Figure 1: (**a**) General view of the experimental set-up; Detailed view of arrangement used: (**b**) for laser beam focal point profile analysis; (**c**) to visualize the reflected laser light on target; (**d**) SEM images of the magnetron sputtering produced Ag target. The region damaged by the protons can be revealed after the chemical etching of the detector. Thus, depending on the etching conditions like: etching solution concentration, etching time and temperature, the proton tracks can be enlarged and made visible through optical microscopy [7; 9]. The region damaged by protons stopped into the detector is more chemically active than the surrounding protons unaffected zone [7; 9]. A proton that hits the detector slab at normal incident angle will leave a circular track. An oblique incidence angle between the proton and the detector surface implies an elliptic shape of the track and the major axis will be larger than the minor axis. The first step in calibrating the CR-39 detectors consists in finding the material bulk etch rate, under very well-defined chemical and temperature conditions. The bulk etch rate of a CR-39 nuclear track detector is usually calculated both experimentally and theoretically. We used the weight loss method to calculate the bulk etch rate experimentally [21]. Several samples of CR-39 detectors were etched in 6.25 N NaOH solution at 70 \({}^{\circ}\)C, for different time intervals. The detector weights were measured before and after etching. Then, the bulk etch rate \(\rm{v_{b}}\) is determined using the following relation [21]:  
\[(\rm{M_{1}-M_{2}})D/2M_{1}=\rm{v_{b}}\ t \tag{1}\]  
where \(\rm{M_{1}}\) represents the initial detector weight, \(\rm{M_{2}}\) is the detector weight after chemical etching, while D stands for the initial thickness of the detector, and t is the etching time. The detectors weight was measured using an electronic balance, with a sensitivity of around \(10^{-4}\) g. The thickness of each detector was measured by means of an electronic device with an accuracy of 0.01 mm. Figure 2 shows a graphical representation of equation 1, which results from measurements (red points). By linear fitting (black line) of these experimental data with the analytical function \(\rm{y}=\rm{ax}\) (a = 1.65), the bulk etch rate of the CR-39 detectors was determined. A bulk etch rate of \(1.65\pm 0.05\)\(\rm{\mu m/h}\) over an etching time of 20 h was calculated (see Figure 2). Monoenergetic proton beams, produced in the TANDEM accelerator at the Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering ([[http://www.nipne.ro](http://www.nipne.ro)]([http://www.nipne.ro](http://www.nipne.ro))), were used to calibrate the CR-39 detectors with an aim to find a relation between the incident energy of the proton beam on a CR-39 detector, and the diameter of the proton tracks revealed after chemical etching. The CR-39 plastic nuclear track detectors were exposed to different proton energies, for beam fluencies of around 70,000 particles/cm\({}^{2}\). The proton beam energy dispersion at the TANDEM facility is \(\pm 5.5\) keV. The diameter of the proton beam spot is 7 mm, and the irradiation time value is about 1 s. The particles were normally incident to the surface of the plastic sheet. The particle beam fluency value was specially chosen to avoid overlapping of the proton tracks on the CR-39 detector during the optical microscopy  
Figure 2: Experimental (red points) and theoretical (black line curve) CR-39 detectors thickness evolution as a function of the etching time.