The etched cones of vertically incident beam particles and the fragments are of circular shape and completely black in direct illumination. The background objects are shallow and appear as black circular objects with a brighter centre are not considered. Target fragments can be resolved based on their short range. The central brightness can be used to separate particle tracks from background. Figure 1 shows the distribution of cone height for beam ions and the fragments registered in a detector placed after the target. The ionizing particles traversing through an insulating material create a narrow path of intense damage on an atomic scale [12].

The damaged region in the detector can be revealed and enlarged by treating with a proper chemical reagent to become visible under an optical microscope. During the etching process, the track etch rate v_T exceeds the bulk etch rate v_B producing a conical etch-pit at the point

of entrance and exit of the particle. The size and shape of such cones depend on the energy loss of the incident particle; the measurement of the cone base area or heights allows, through an appropriate calibration, to determine the characteristics of the particle.

The focused surface of the opening of the etch-pits looks like a dark, circular of well defined diameter. The CR-39 detectors, placed upstream the targets registered the total number of incident Pb ions and detectors placed after the target recorded both the survived Pb ions and the fragments produced in the interaction of Pb ions with the target. Since the beam exposure is normally incident to the detector surface, the beam ions and the fragments produced as a result of fragmentation almost maintain their longitudinal velocity along the direction of beam ions and a sequence of etch cones is produced on the subsequent detector surfaces.

At relativistic energies the base area of the post etching cones depends only on charge Z, therefore peaks of measured etched cone heights correspond to different charges. This method is applicable as long as the projectile peak and the fragment peaks are clearly separated. It is reported in [13] that the etched cone diameter is sensitive to low Z ions, and cone height to high Z ions. The average values of the cone heights distribution observed in both the detectors is displayed in the form of well separated peaks, which are assigned to a charge value 63 £ Z £ 82 by counting downward beginning with the beam peak Z = 82 (we assume the charge assigned to the fragment as the atomic number of the fragment. In reality, charge of the fragment can be lower than the atomic number Z in a particular case when fragments have lowered their energy and collected electrons from the target which reduces their charge from the maximum possible charge. For the simplicity the atomic number of fragments is shown in Figure 1.

The charge resolution is related to cone height resolution. In view of different units of these quantities relative charge resolution is equated to relative length resolution using the relation

where is the standard deviation in the length of individual peaks assigned to charge value. The plot of charge Z verses cone lengths L is shown in Figure 2. The ratio is the slope of the plot.

The energy deposited by the charged particle to form the latent track is the Restricted Energy Loss (REL).The response of the detectors to relativistic ions is characterized by the correlation of parameter, and REL from the calibration curve. Since track etch rate v_T is a function of REL ,which depends on the charge and energy of the incident projectile ion, for relativistic energy ions the REL remains approximately constant therefore, it is considered that the diameter and length of etched cone are function of ion charge only as reported by [14].

The cylindrical cone length L is related to etch rate ratio ‘p’ through the equation

where‘t’ is etching time. The track etch rate () of the

cones produced in the detector can be calculated from the relation,

where L is the cone height, t is the etching time and is the bulk etch rate of the detector measured by the change in the thickness of the detector before and after etching of the detector. The refractive index of the CR-39 was experimentally determined and was used for the determination of the total height of cones.

For the resolution of higher charges the cone heights are associated with different charges. The charge values of fragments with almost identical are associated with specific REL values while the lengths are converted to ‘p’ values using Equation (3).

The relation between REL and ‘p’ is specific to the etching condition, because the value of ‘p’ is experimentally measured for the given etching conditions when unknown ion interacts on the detector, it is, therefore, possible to assign it an REL value. The REL vs. p graph as shown in Figure 3 constitute a calibration curve. The function REL defined as

For particles with ßc > 10^–2 c, the REL is a fraction of the electronic energy loss, leading to δ rays with energies lower than E_max, with E_max= 200 eV for CR-39 [15]. If the REL of a particle passing through a stack of detectors

is constant along its trajectory and the same etching conditions are applied to all the detectors in the stack, the track etching rate v_T is constant and identical cones are formed on all crossed detector surfaces.

Figure 4 shows the track length and charge resolutions for the fragments of 158 A GeV Pb projectiles produced in collisions of the projectile beam with Al target. The dotted horizontal line shows the mean values of track length and charge resolutions. We have also analyzed the distributions of track length (Figure 5(a) and charge resolutions (Figure 5(b)). Values of and squared regression coefficients R² for the Gaussian fits on both distributions are given in the respective plots in Figure 4. Peak values of the Gaussian fits on track length and charge resolutions in Figure 4 agree well with the respective arithmatic mean values in Figure 4.