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Charge identification in CR-39 nuclear track detector using relativistic lead ion fragmentation
Nuclear Instruments and Methods in Physics Research A 453 (2000) 525}529
Charge identi"cation in CR-39 nuclear track detector using relativistic lead ion fragmentation S. Manzoor , I.E. Qureshi *, M.A. Rana , M.I. Shahzad , G. Sher , M. Sajid , H.A. Khan , G. Giacomelli, M. Giorgini, G. Mandrioli, L. Patrizii, V. Popa, P. Serra, V. Togo Radiation Physics Division, PINSTECH, P.O. Nilore, Islamabad, Pakistan University of Bologna and INFN, V. Berti Pichat 6/2, Bologna I-40127, Italy Received 19 January 2000; accepted 4 March 2000
Abstract Three stacks of plastic CR-39 Nuclear Track Detectors (NTD) were exposed to 158 A GeV Pb ions at the CERN-SPS beam facility. The main purpose of this experiment was the calibration of the CR-39 for the search of atmospheric magnetic monopoles. Di!erent targets (Al, Cu and Pb) were used to produce a large spectrum of charge ions for the purpose of calibration as well as the study of ultrarelativistic lead ion fragmentation. The exposure of each stack was performed at normal incidence with a #uence of about 1500 ion/cm. The total number of lead ions in each spill was about 7.8;10 and there were eight spills incident on each stack. For the stack with the Cu target, the lengths of etched cones on one face of the CR-39 were measured. From this measurement procedure, a new calibration curve has been generated for the extended charge region 63)Z)83. The charge resolution (p ) achieved by this technique is 8 &0.18e}0.21e. 2000 Elsevier Science B.V. All rights reserved.
1. Introduction For the registration of heavy ions with wide angular coverage NTDs have marked advantages over other detector systems. A single CR-39 NTD can be used to detect a wide range of charges down to Z"5e even in ultra-relativistic energy region [1]. A number of authors [2}10] have studied fragmentation properties of relativistic heavy ions using di!erent NTDs. One of the essential re-
* Corresponding author. Tel.: 92-51-207269; fax: 92-51429533. E-mail address: [email protected] (I.E. Qureshi).
quirements of these studies is the unambiguous identi"cation of ionic charge states. This requires a carefully designed calibration procedure based on the high-energy heavy-ion characteristics and the properties of the detection medium. Previously, for the present reaction a single calibration curve has been developed by two di!erent measurement procedures (base area and cone height of etched tracks) [11]. For the charge region 5)Z)74, base area procedure was applied whereas for higher charges Z*75, cone height technique was used. It is well known that the charge resolution based on base area measurements becomes worse as the charge of the fragment increases because in the high-charge region the
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 0 0 4 7 0 - 8
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S. Manzoor et al. / Nuclear Instruments and Methods in Physics Research A 453 (2000) 525}529
change in the diameter of the base cone is very small for adjoining charge states [12,13]. Here, we have made a new charge calibration curve for CR-39 based on measurements of etched cone heights (41)¸)248 lm) of fragments (63)Z)83) produced by the interaction of Pb ions with the thick copper target. The CR-39 of thickness 600 lm used in this work was made by the Intercast Europe Co. of Parma, Italy [14]. This CR-39 has been used in the MACRO experiment as one of the detectors for the detection of cosmic ray particles at the underground Gran Sasso Laboratory [15].
2. Experimental procedure For the study of the fragmentation of the ultrarelativistic CERN Pb beam we have exposed three stacks of CR-39 NTD with Al, Cu and Pb as targets. The beam was "rst allowed to pass through some foils of CR-39 detectors, for the determination of the total number of incoming Pb ions incident on the stack. The beam then passed through a target of thickness typically half of the mean free path of the Pb ions in the given target. CR-39 foils placed after the target material recorded both the surviving Pb ions and their fragments produced in the interaction of the Pb ions with the thick target material. The areal density of lead beam was about 1500 ion/cm. After exposure, the CR-39 nuclear track detectors were etched for 72 h in 4 N KOH water solution at a temperature of 453C. The KOH etchant has been selected due to its very small swelling e!ect on CR-39 plates. For this etching time period, an average thickness of 8 lm was removed from both sides of the detector material with an average speed of < "(0.112$0.017) lm/h. < is the bulk etch velocity of the detector measured by the change in the thickness of the detector before and after etching of the detector [16]. Fig. 1 shows the geometry of an etched cone produced by a relativistic charged particle with normal incidence on the surface of the detector. The refractive index (R ) of the CR-39 has been experimentally determined by measuring the actual thickness of the detector by depth-measuring instrument and observed thickness with the help of optical microscope. Its value comes out to be 1.561, which was
Fig. 1. Geometry of an etched track normal to the detector surface.
used for the determination of the total height of an etched cone. Two CR-39 foils located before and after the copper target were measured with the optical microscope manually (approximately 6300 etched cones were measured). The etched cone lengths were measured using a Zeiss microscope with a magni"cation of 40;. The measurements yield a resolution of p K3.64 lm * at Z"82 (see Table 1). In Fig. 2 at Z"83 is a peak which corresponds to charge pick-up reaction whereas peaks with Z"63}81 represent the fragments formed in the interaction of Pb with copper.
3. Results Fig. 2 shows the etched cone distribution for the lead ions and their fragments produced in the interaction of Pb with Cu target observed on a single sheet of the CR-39 track detector. As all the peaks are well separated, we may assign a charge to each peak. Assigned charges with their resolution are presented in Table 1. Under these etching conditions we have a good charge resolution up to a charge value Z"63 for 600 lm thick CR-39. The resolution of CR-39 is equally good in the charge region 63)Z)83 and its value is &0.2e.
S. Manzoor et al. / Nuclear Instruments and Methods in Physics Research A 453 (2000) 525}529 Table 1 The average cone heights and the assigned charges with charge resolution measured by the interaction of high energy Pb ions in the Cu target Cone height (lm)
Charge (e)
Resolution (e)
41.05$3.18 49.99$3.87 59.94$4.28 70.43$4.09 82.63$4.62 92.58$4.22 103.49$4.14 115.77$3.61 125.51$4.95 136.96$3.42 148.46$3.56 157.86$3.61 170.33$3.56 182.12$4.65 191.12$3.48 203.11$3.33 214.34$4.43 225.53$3.73 237.16$3.73 247.57$3.64 259.64$2.15
63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
0.185 0.225 0.249 0.238 0.269 0.245 0.241 0.210 0.288 0.199 0.207 0.210 0.207 0.271 0.203 0.194 0.258 0.217 0.217 0.212 0.125
527
4. Discussion Fig. 3 shows a correlation plot between the assigned charges of nuclear fragments and the mean values of etched cone lengths taken from Fig. 2. The cone length is an increasing function of the charge, as shown in Fig. 3, because the Restricted Energy Loss (REL) value is a function of charge only at relativistic energy. The charge resolution p of the 8 CR-39 detector has been calculated as p p " * 8 d¸/dZ
(1)
where p is the standard deviation of the individual * peaks and is obtained from the data presented in Table 1 and d¸/dZ is the slope (11.010$0.035) of the plot in Fig. 2. The calibration curve for charge identi"cation is obtained by correlating two functions, one of which depends on etch cone length and the other containing the charge of incident ion Z. The "rst of these functions is the reduced track etch rate p ("< /< ) while the most appro2 priate function involving ion charge is the so-called &REL' de"ned as REL"(dE/dx) ## 4 Z Z C b d 2 ln ! ! "C b A I 2 2 2
(2)
Fig. 2. Cone heights distribution of Pb ions and the heavy fragments produced in the interaction of lead with thick copper target material, detected in the CR-39 nuclear track detector.
The lower charges can also be measured by this cone height measurement procedure if we increase the etching time. In our case we cannot increase the processing time beyond 72 h due to the limitation of the detector thickness (600 lm).
Fig. 3. Correlation plot of the charges to their mean etch cone heights measured in the CR-39 NTD for the Pb#Cu reaction.
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S. Manzoor et al. / Nuclear Instruments and Methods in Physics Research A 453 (2000) 525}529
where C "4nN rm c and C " (2m cbcE . At these energies the nuclear
component of the energy loss is negligible. In Eq. (2), the value of C "0.307 MeV cm/g; z/b refers to the ion fragment, Z and A are the average 2 2 charge and mass values of the target (CR-39: Z /A "0.533), the mean ionization potential of 2 2 CR-39 is I"70 eV, and E "200 eV; the density
correction d was calculated according to Ref. [17]. The track etch rate used in calculation of reduced etch rate p (< /< ) for fragments produced in the 2 interaction of 158A GeV with Cu target in CR-39 is calculated from the formula ¸ < "< # 2 t
(3)
Fig. 4 shows the reduced etch rate p vs REL value. The error bars include statistical and systematic uncertainties; the main contribution to the errors comes from the uncertainty in the determination of the bulk etch velocity < . The points are the experimental data and the solid line is the best "t to the data points. The value of s/d.o.f. is found to be 0.05. The "tted equation is valid only in the REL range 3700}7100 MeV cm/g. In our measurement procedure the p value is associated with the etch cone height and we are not able to measure p value for charges having REL lower than
3700 MeV cm/g under these etching conditions. The etching interval is limited to 72 h because of small thickness (600 lm) of the detector. The other important factor responsible for the REL range is d¸/dZ [18]. The etch cone height is not measurable for fragments with Z(63 under these processing conditions (see Fig. 3).
5. Conclusions We have studied the response of CR-39 nuclear track detector to relativistic lead ions and the fragments produced in the thick target material using measurements of the etch pit cone heights in the wide charge region 63)Z)83. By measuring the cone heights we obtain a charge resolution p K0.18 e (Z"63) and p K0.21 e (Z"82) for 8 8 measurements of tracks in one sheet of CR-39. By this method we can thus separate the nuclear fragments with high Z (*63) from the lead ions of the beam which is rather very di$cult by the base area measurement procedure due to very small change in the base diameter. For the future research work it is suggested that a long etch processing time should be used to enhance the charge range by using a thick CR-39 (*1.4 mm).
Acknowledgements We acknowledge the collaboration of the sta! of the CERN SPS. We thank E. Bottazzi, M. Folesani, F. Nicoli and the technical sta! of the INFN Section of Bologna for their contributions. Thanks are also for the technical help by Mr. Bashir and Mr. Rizwan. S.M. thanks ICTP } Trieste for a fellowship in the framework of the Italian Lab. Programme. V.P. thanks INFN for providing an FAI grant. V.T. acknowledges a fellowship from Intercast Europe Co., Parma.
References Fig. 4. Restricted energy loss (REL) vs the reduced etch rate (p) of the relativistic fragments measured by the etch cone heights.
[1] S.E. Hirzebruch et al., Phys. Rev. C 51 (1995) 2085. [2] C. Brechtmann, W. Heinrich, Z. Phys. A 330 (1988) 407. [3] C. Brechtmann, W. Heinrich, Z. Phys. A 331 (1988) 463.
S. Manzoor et al. / Nuclear Instruments and Methods in Physics Research A 453 (2000) 525}529 [4] C. Brechtmann, W. Heinrich, Phys. Rev. C 39 (1989) 2222. [5] S.E. Hirzebruch, W. Heinrich, K.D. Tolstov, A.D. Kovalenko, E.V. Benton, Phys. Rev. C 46 (1992) 1487. [6] J. Westphal et al., Phys. Rev. C 44 (1991) 1687. [7] D.P. Bhattacharyya et al., Nucl. Instr. and Meth. B 61 (1991) 197. [8] S.E. Hirzebruch et al., Nucl. Instr. and Meth. B 74 (1993) 519. [9] D.P. Bhattacharyya et al., Nuovo Cimento C 16 (1993) 249. [10] S.P. Ahlen et al., Nucl. Instr. and Meth. A 324 (1993) 337. [11] G. Giacomelli et al., Nucl. Instr. and Meth. A 411 (1998) 41.
529
[12] G. Giacomelli et al., DFUB 29/96, 1996. [13] G. Giacomelli et al., Proceedings of the 18th International Conference on Nuclear Tracks in Solids, Cairo, Egypt; 1996, Nucl. Tracks and Rad. Meas. 28 (1997) 217. [14] S. Cecchini et al., Nuovo Cimento A 109 (1996) 1119. [15] M. Ambrosio et al., MACRO coll., Phys. Lett. B 406 (1997) 249. [16] R. Fleischer, P.B. Price, R.M. Walker, Nuclear Tracks in Solids, University of California Press, Berkeley, CA, 1975. [17] W.R. Leo, Techniques for Nuclear and Particles Physics Experiments, Springer, Berlin, 1987, p. 26. [18] M. Giorgini, M.Sc. Thesis, Bologna University, Italy, 1996.
Charge identi"cation in CR-39 nuclear track detector using relativistic lead ion fragmentation S. Manzoor , I.E. Qureshi *, M.A. Rana , M.I. Shahzad , G. Sher , M. Sajid , H.A. Khan , G. Giacomelli, M. Giorgini, G. Mandrioli, L. Patrizii, V. Popa, P. Serra, V. Togo Radiation Physics Division, PINSTECH, P.O. Nilore, Islamabad, Pakistan University of Bologna and INFN, V. Berti Pichat 6/2, Bologna I-40127, Italy Received 19 January 2000; accepted 4 March 2000
Abstract Three stacks of plastic CR-39 Nuclear Track Detectors (NTD) were exposed to 158 A GeV Pb ions at the CERN-SPS beam facility. The main purpose of this experiment was the calibration of the CR-39 for the search of atmospheric magnetic monopoles. Di!erent targets (Al, Cu and Pb) were used to produce a large spectrum of charge ions for the purpose of calibration as well as the study of ultrarelativistic lead ion fragmentation. The exposure of each stack was performed at normal incidence with a #uence of about 1500 ion/cm. The total number of lead ions in each spill was about 7.8;10 and there were eight spills incident on each stack. For the stack with the Cu target, the lengths of etched cones on one face of the CR-39 were measured. From this measurement procedure, a new calibration curve has been generated for the extended charge region 63)Z)83. The charge resolution (p ) achieved by this technique is 8 &0.18e}0.21e. 2000 Elsevier Science B.V. All rights reserved.
1. Introduction For the registration of heavy ions with wide angular coverage NTDs have marked advantages over other detector systems. A single CR-39 NTD can be used to detect a wide range of charges down to Z"5e even in ultra-relativistic energy region [1]. A number of authors [2}10] have studied fragmentation properties of relativistic heavy ions using di!erent NTDs. One of the essential re-
* Corresponding author. Tel.: 92-51-207269; fax: 92-51429533. E-mail address: [email protected] (I.E. Qureshi).
quirements of these studies is the unambiguous identi"cation of ionic charge states. This requires a carefully designed calibration procedure based on the high-energy heavy-ion characteristics and the properties of the detection medium. Previously, for the present reaction a single calibration curve has been developed by two di!erent measurement procedures (base area and cone height of etched tracks) [11]. For the charge region 5)Z)74, base area procedure was applied whereas for higher charges Z*75, cone height technique was used. It is well known that the charge resolution based on base area measurements becomes worse as the charge of the fragment increases because in the high-charge region the
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 0 0 4 7 0 - 8
526
S. Manzoor et al. / Nuclear Instruments and Methods in Physics Research A 453 (2000) 525}529
change in the diameter of the base cone is very small for adjoining charge states [12,13]. Here, we have made a new charge calibration curve for CR-39 based on measurements of etched cone heights (41)¸)248 lm) of fragments (63)Z)83) produced by the interaction of Pb ions with the thick copper target. The CR-39 of thickness 600 lm used in this work was made by the Intercast Europe Co. of Parma, Italy [14]. This CR-39 has been used in the MACRO experiment as one of the detectors for the detection of cosmic ray particles at the underground Gran Sasso Laboratory [15].
2. Experimental procedure For the study of the fragmentation of the ultrarelativistic CERN Pb beam we have exposed three stacks of CR-39 NTD with Al, Cu and Pb as targets. The beam was "rst allowed to pass through some foils of CR-39 detectors, for the determination of the total number of incoming Pb ions incident on the stack. The beam then passed through a target of thickness typically half of the mean free path of the Pb ions in the given target. CR-39 foils placed after the target material recorded both the surviving Pb ions and their fragments produced in the interaction of the Pb ions with the thick target material. The areal density of lead beam was about 1500 ion/cm. After exposure, the CR-39 nuclear track detectors were etched for 72 h in 4 N KOH water solution at a temperature of 453C. The KOH etchant has been selected due to its very small swelling e!ect on CR-39 plates. For this etching time period, an average thickness of 8 lm was removed from both sides of the detector material with an average speed of < "(0.112$0.017) lm/h. < is the bulk etch velocity of the detector measured by the change in the thickness of the detector before and after etching of the detector [16]. Fig. 1 shows the geometry of an etched cone produced by a relativistic charged particle with normal incidence on the surface of the detector. The refractive index (R ) of the CR-39 has been experimentally determined by measuring the actual thickness of the detector by depth-measuring instrument and observed thickness with the help of optical microscope. Its value comes out to be 1.561, which was
Fig. 1. Geometry of an etched track normal to the detector surface.
used for the determination of the total height of an etched cone. Two CR-39 foils located before and after the copper target were measured with the optical microscope manually (approximately 6300 etched cones were measured). The etched cone lengths were measured using a Zeiss microscope with a magni"cation of 40;. The measurements yield a resolution of p K3.64 lm * at Z"82 (see Table 1). In Fig. 2 at Z"83 is a peak which corresponds to charge pick-up reaction whereas peaks with Z"63}81 represent the fragments formed in the interaction of Pb with copper.
3. Results Fig. 2 shows the etched cone distribution for the lead ions and their fragments produced in the interaction of Pb with Cu target observed on a single sheet of the CR-39 track detector. As all the peaks are well separated, we may assign a charge to each peak. Assigned charges with their resolution are presented in Table 1. Under these etching conditions we have a good charge resolution up to a charge value Z"63 for 600 lm thick CR-39. The resolution of CR-39 is equally good in the charge region 63)Z)83 and its value is &0.2e.
S. Manzoor et al. / Nuclear Instruments and Methods in Physics Research A 453 (2000) 525}529 Table 1 The average cone heights and the assigned charges with charge resolution measured by the interaction of high energy Pb ions in the Cu target Cone height (lm)
Charge (e)
Resolution (e)
41.05$3.18 49.99$3.87 59.94$4.28 70.43$4.09 82.63$4.62 92.58$4.22 103.49$4.14 115.77$3.61 125.51$4.95 136.96$3.42 148.46$3.56 157.86$3.61 170.33$3.56 182.12$4.65 191.12$3.48 203.11$3.33 214.34$4.43 225.53$3.73 237.16$3.73 247.57$3.64 259.64$2.15
63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
0.185 0.225 0.249 0.238 0.269 0.245 0.241 0.210 0.288 0.199 0.207 0.210 0.207 0.271 0.203 0.194 0.258 0.217 0.217 0.212 0.125
527
4. Discussion Fig. 3 shows a correlation plot between the assigned charges of nuclear fragments and the mean values of etched cone lengths taken from Fig. 2. The cone length is an increasing function of the charge, as shown in Fig. 3, because the Restricted Energy Loss (REL) value is a function of charge only at relativistic energy. The charge resolution p of the 8 CR-39 detector has been calculated as p p " * 8 d¸/dZ
(1)
where p is the standard deviation of the individual * peaks and is obtained from the data presented in Table 1 and d¸/dZ is the slope (11.010$0.035) of the plot in Fig. 2. The calibration curve for charge identi"cation is obtained by correlating two functions, one of which depends on etch cone length and the other containing the charge of incident ion Z. The "rst of these functions is the reduced track etch rate p ("< /< ) while the most appro2 priate function involving ion charge is the so-called &REL' de"ned as REL"(dE/dx) ## 4 Z Z C b d 2 ln ! ! "C b A I 2 2 2
(2)
Fig. 2. Cone heights distribution of Pb ions and the heavy fragments produced in the interaction of lead with thick copper target material, detected in the CR-39 nuclear track detector.
The lower charges can also be measured by this cone height measurement procedure if we increase the etching time. In our case we cannot increase the processing time beyond 72 h due to the limitation of the detector thickness (600 lm).
Fig. 3. Correlation plot of the charges to their mean etch cone heights measured in the CR-39 NTD for the Pb#Cu reaction.
528
S. Manzoor et al. / Nuclear Instruments and Methods in Physics Research A 453 (2000) 525}529
where C "4nN rm c and C " (2m cbcE . At these energies the nuclear
component of the energy loss is negligible. In Eq. (2), the value of C "0.307 MeV cm/g; z/b refers to the ion fragment, Z and A are the average 2 2 charge and mass values of the target (CR-39: Z /A "0.533), the mean ionization potential of 2 2 CR-39 is I"70 eV, and E "200 eV; the density
correction d was calculated according to Ref. [17]. The track etch rate used in calculation of reduced etch rate p (< /< ) for fragments produced in the 2 interaction of 158A GeV with Cu target in CR-39 is calculated from the formula ¸ < "< # 2 t
(3)
Fig. 4 shows the reduced etch rate p vs REL value. The error bars include statistical and systematic uncertainties; the main contribution to the errors comes from the uncertainty in the determination of the bulk etch velocity < . The points are the experimental data and the solid line is the best "t to the data points. The value of s/d.o.f. is found to be 0.05. The "tted equation is valid only in the REL range 3700}7100 MeV cm/g. In our measurement procedure the p value is associated with the etch cone height and we are not able to measure p value for charges having REL lower than
3700 MeV cm/g under these etching conditions. The etching interval is limited to 72 h because of small thickness (600 lm) of the detector. The other important factor responsible for the REL range is d¸/dZ [18]. The etch cone height is not measurable for fragments with Z(63 under these processing conditions (see Fig. 3).
5. Conclusions We have studied the response of CR-39 nuclear track detector to relativistic lead ions and the fragments produced in the thick target material using measurements of the etch pit cone heights in the wide charge region 63)Z)83. By measuring the cone heights we obtain a charge resolution p K0.18 e (Z"63) and p K0.21 e (Z"82) for 8 8 measurements of tracks in one sheet of CR-39. By this method we can thus separate the nuclear fragments with high Z (*63) from the lead ions of the beam which is rather very di$cult by the base area measurement procedure due to very small change in the base diameter. For the future research work it is suggested that a long etch processing time should be used to enhance the charge range by using a thick CR-39 (*1.4 mm).
Acknowledgements We acknowledge the collaboration of the sta! of the CERN SPS. We thank E. Bottazzi, M. Folesani, F. Nicoli and the technical sta! of the INFN Section of Bologna for their contributions. Thanks are also for the technical help by Mr. Bashir and Mr. Rizwan. S.M. thanks ICTP } Trieste for a fellowship in the framework of the Italian Lab. Programme. V.P. thanks INFN for providing an FAI grant. V.T. acknowledges a fellowship from Intercast Europe Co., Parma.
References Fig. 4. Restricted energy loss (REL) vs the reduced etch rate (p) of the relativistic fragments measured by the etch cone heights.
[1] S.E. Hirzebruch et al., Phys. Rev. C 51 (1995) 2085. [2] C. Brechtmann, W. Heinrich, Z. Phys. A 330 (1988) 407. [3] C. Brechtmann, W. Heinrich, Z. Phys. A 331 (1988) 463.
S. Manzoor et al. / Nuclear Instruments and Methods in Physics Research A 453 (2000) 525}529 [4] C. Brechtmann, W. Heinrich, Phys. Rev. C 39 (1989) 2222. [5] S.E. Hirzebruch, W. Heinrich, K.D. Tolstov, A.D. Kovalenko, E.V. Benton, Phys. Rev. C 46 (1992) 1487. [6] J. Westphal et al., Phys. Rev. C 44 (1991) 1687. [7] D.P. Bhattacharyya et al., Nucl. Instr. and Meth. B 61 (1991) 197. [8] S.E. Hirzebruch et al., Nucl. Instr. and Meth. B 74 (1993) 519. [9] D.P. Bhattacharyya et al., Nuovo Cimento C 16 (1993) 249. [10] S.P. Ahlen et al., Nucl. Instr. and Meth. A 324 (1993) 337. [11] G. Giacomelli et al., Nucl. Instr. and Meth. A 411 (1998) 41.
529
[12] G. Giacomelli et al., DFUB 29/96, 1996. [13] G. Giacomelli et al., Proceedings of the 18th International Conference on Nuclear Tracks in Solids, Cairo, Egypt; 1996, Nucl. Tracks and Rad. Meas. 28 (1997) 217. [14] S. Cecchini et al., Nuovo Cimento A 109 (1996) 1119. [15] M. Ambrosio et al., MACRO coll., Phys. Lett. B 406 (1997) 249. [16] R. Fleischer, P.B. Price, R.M. Walker, Nuclear Tracks in Solids, University of California Press, Berkeley, CA, 1975. [17] W.R. Leo, Techniques for Nuclear and Particles Physics Experiments, Springer, Berlin, 1987, p. 26. [18] M. Giorgini, M.Sc. Thesis, Bologna University, Italy, 1996.