Proc. Natl. Acad. Sci. USA Vol. 77, No. 1, pp. 44-48, January 1980 Do energetic heavy nuclei penetrate deeply into Earth's atmosphere? (cosmic rays/high-energy interactions/hypothetical ) P. B. PRICE, F. ASKARY, AND G. TARLt Space Sciences Laboratory and Department of Physics, University of California, Berkeley, California 94720 Contributed by P. Buford Price, October 25, 1979

ABSTRACT We calculate the expected fluxes of cosmic ray (11), monopoles (11, 12), tachyons (11, 12), and other massive nuclei with charge 5 < Z < 28 at various depths in the earth's hypothetical particles (11, 12) by using the earth's atmosphere atmosphere, taking into account the initial charge distribution, to screen out primary cosmic rays or as a target within which ionization loss, and various modes of fragmentation. The flux of surviving heavy nuclei is too low by a factor t10-10 to ac- the hypothetical particles might be generated in high-energy count for the ultra-high-energy Centauro events. We describe cosmic ray interactions. Only two of these groups designed their an experiment to search for highly ionizing particles that may detector to look exclusively for very highly ionizing particles or may not be nuclei. (13, 14). Both groups obtained negative results. A third reason is the possibility that the spectacularly ener- Because of the rapid, exponential absorption of energetic getic cosmic ray interactions discovered at Mt. Chacaltaya by complex nuclei in the earth's atmosphere, essentially all of our a Brazil-Japan collaboration (15) and dubbed Centauro events knowledge of the primary cosmic ray charge composition might be caused by a very heavy nucleus or a more exotic object comes from experiments on stratospheric balloons and space- (16). The peculiar features of the Centauro events-the essential craft. The interaction mean free path of nuclei in air decreases absence of neutral pions and electronic cascade despite the high from ;t75 g/cm2 for protons to ;14 g/cm2 for iron and is even multiplicity, n102, of hadrons in the interaction, and the high shorter for the very rare nuclei heavier than iron. By contrast average transverse momentum of the hadrons, ;1.7 GeV/ the thickness of the atmosphere is 103 g/cm2. Thus, the flux c-have not been explained by conventional physics of high- of primary cosmic rays-those that survive without a: single energy interactions. The flux of very heavy nuclei energetic collision-is vanishingly small for nuclei as heavy as helium at enough to account for the Centauro events needs to be calcu- sea level. The energy spectrum of secondary protons at sea level lated and the plausibility of such an explanation, assessed. If a is fairly well known (1), the energy spectrum of secondary nucleus can be ruled out, the door is open to a more exotic ex- deuterons at 750 g/cm2 has begun to be investigated (2), and planation such as a dense, highly charged object. a few secondary 4He nuclei at mountain altitudes have been reported (2, 3). Even at the highest cosmic ray observatory, on Integral flux of heavy cosmic ray nuclei calculated at Mt. Chacaltaya (540 g/cm2 depth), the survival probability of various depths a nucleus heavier than He is extraordinarily small: for survival As the starting point of our calculation, we adopted the isotopic of primary 12C it is exp(-540/27) t3 X 109. When the various composition of cosmic rays arriving at the top of the atmo- modes of fragmentation of heavy nuclei are taken into account, sphere, calculated by Tsao et al. (17) from data obtained at an the net flux of a particular nuclide produced through all possible energy of 2 GeV/nucleon. We then constructed a table (18) of fragmentation chains of progenitors is still extraordinarily small 220 isotopes with 5 S Z S 28 and lifetimes greater than 0.1 at both sea level and mountain altitudes. msec. (A nucleus with E t 2 GeV/nucleon takes ;t. 1 msec to There are several reasons why the weak flux of energetic penetrate the t30-km atmospheric height to sea level.) heavy particles of natural origin deep in the atmosphere is of If N1(x) represents the flux of particles of type i that traverse interest. First and of greatest practical concern is the question x g/cm2 of atmosphere, then the differential equation gov- of radiation hazard to passengers on supersonic transport planes, erning the behavior of Ni (19) is which fly at an atmospheric depth of t40 or 50 g/cm2. Several groups (4, 5) have measured the fluxes of the heavy nuclei of dNa (NA- N1Ni+ E ai ANj, [1] greatest biological hazard at depths to ;100 g/cm2 and have discussed the risks to crew and passengers. At the depths of where ass is the -changing cross section for the ith type, aY 250-300 g/cm2 frequented by subsonic commercial airlines the is the total production cross section for the ith type from the jth flux is far too low to pose a hazard. type, NA is Avogadro's number, and AT is the mass number of A second reason, of particular interest to us, is the desire to the target nucleus, taken as 14.4 for air. The validity of this establish the baseline flux levels of highly ionizing particles of one-dimensional equation depends on the assumptions that the known origin so that hypothetical new particles of high ion- interactions are velocity-preserving and that there is no net ization rate can be sought by detectors of very great collecting scattering. power deployed at various depths in the atmosphere. The his- Viewing Eq. 1 as a system of linear differential equations, tory of study of new particles in with detectors at sea we can write it in the matrix form level and at mountain altitude includes the cloud chamber observations of positrons (6), of muons (7, 8), and of V-particles -N = MN, (9, 10) (later recognized as charged and neutral kaons). Re- dx cently, various groups have unsuccessfully looked for where The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "ad- vertisement" in accordance with 18 U. S. C. §1734 solely to indicate this fact. N N220 44 Downloaded by guest on October 2, 2021 Physics: Price et al. Proc. Natl. Acad. Sct. USA 77 (1980) 45 is the column vector representing the number of isotopes at x, where K(Z,A) is a constant depending on Z,A, with a value and x(g/cm2) is the depth in the atmosphere. determined by setting E = 2 GeV/nucleon and equating our The entries of the matrix M are defined by: flux to that of Tsao et al. (17). ( NA The ionization energy loss was estimated as NA If..i w-it El,. (0) = (2 MeV per g/cm2)(Z2/A)fijr (x/cos 0), tij NAUq- if i 6 jandj producesi where x/cos 0 is the distance in g/cm2 traversed by a 0 AT otherwise. traveling at an angle ( to the local vertical and (Z2/A)fjnA is the value appropriate to the final particle after previous nuclear interactions. This simple expression ignores the increase in Arranging the equations such that the species of larger Z dE/dx as a particle slows down and avoids the complexity of appear first (heavier isotopes of the same Z appear first also), following the succession of decreases in the value of Z2/A the matrix M is lower triangular. during the various nuclear interactions. The errors introduced by these simplifications are smaller than errors in the cross (N 1 I d (Mil sections; for example, a 50% error in El. would correspond to a total error of only -40% in the final answer. The flux was numerically integrated over all zenith angles N220MJ2o01 ... M220,220 N220 and from final energies from 0 to infinity at depth x. The contributions of various isotopes of the same element were Assuming that the diagonal entries of M are different, we can added. Fig. 1 shows the fluxes of nuclei with charges from 5 solve it by to 28 reaching detectors at depths of 0, 300, 540, 600, 650, and 1034 g/cm2. The flux at the top of the atmosphere does not NI C1 eMljX decrease much with Z in the interval from 5 < Z < 28. With (N1)(C~l....0 (¢ .I1 increasing depth in the atmosphere, the decline in flux with N220 C220,1 ... C220,220 M22O,2oX increasing Z rapidly steepens. One can see qualitatively that this results from the appearance in the exponentials exp(Mijx) where C is the coefficient matrix and its entries are constants. of cross sections that increase with nuclear size (see Eq. 2). C is also lower triangular and the recursion formulas for are Cqj

Jct} = M -t M1) for j

where AT is the mass number of the target, AB is the mass cox number of the beam, r. = 1.47 ± (SD) 0.04 fm, and b = 1.12 CL + 0.16. The last two numbers, obtained by Westfall et al. (19), are best fits to experimental results. Different nuclei with the same mass number A would have the same cross section, according to Eq. 2, but the solution scheme is applicable only if no two of the diagonal entries of matrix M are equal. A more exact equation in place of Eq. 2 would have included the effects of Coulomb scattering, which would make the cross sections and thus the diagonal entries of M different. Because no data were available to allow Coulomb effects to be incorporated, we decided systematically but ar- bitrarily to change the mass numbers of nuclei of the same Z by steps of 0.1 (for the purpose of this calculation only) such that the nucleus with highest Z had the highest A. This resulted in 1 z differences in cross sections of only part in 104. FIG. 1. Calculated flux of energetic nuclei of various charges at The integral flux of nuclei with energy per nucleon greater top of atmosphere, at 300 g/cm2 (typical jet plane altitude), 540 g/cm2 than E is taken as a power law (experiment at Mt. Chacaltaya), 600 g/cm2 (experiment at summit of White Mountain), 650 g/cm2 (experiment at Barcroft Lab, White Flux (Z,A,E) = K(ZA)E-1.7 Mountain), and 1034 g/cm2 (sea level). Downloaded by guest on October 2, 2021 46 Physics: Price et al. Proc. Natl. Acad. Sci. USA 77 (1980)

The total mass-changing cross sections, u", are known to -4 X 10-11 cm-2 sr-' sec-1. Tonwar et al. (25), with equip- !10%. An error of 10% in aii leads, at a depth of -600 g/cm2, ment at 2200 m, saw two events with At > 20 nsec and E, > to an error of about a factor of seven in flux, the same as would 40 GeV, implying a mass >10 GeV and a flux 410-1O cm-2 sr-1 result from a 10% change in depth. sec-1. In neither of these experiments could charge be deter- mined. No mundane explanation of the delayed massive par- Previous experiments ticles has been found. Having calculated the background level of energetic nuclei as Could high-energy heavy nuclei cause the Centauro a function of Z at various depths, we briefly consider various events? experiments with detectors of very large collecting power. The Lexan array of Fleischer et al. (13) had too high a threshold for With a two-story high emulsion chamber 44 m2 in area exposed particle detectability (Z/,B > 65) and too low a collecting power for several years atop Mt. Chacaltaya, a Brazil-Japan collabo- (t1013 cm2 sr sec) to detect any heavy nuclei at sea level. Yock's ration (15) has found one definite and several possible examples detector (14), beneath 600 g/cm2 of concrete at sea level, also of a bizarre high-energy interaction named by them Centauro fell many orders of magnitude short of recording a single heavy events. A primary particle of energy z1015 eV interacts in the nucleus with Z > 7. air above the chamber, producing t50-100 very energetic All of the following experiments had far too small a collecting hadrons unaccompanied by gamma rays (from neutral pions). power, by orders of magnitude, to detect energetic heavy The event has been described (15) in terms of the production nuclei, but they provide interesting examples of searches for of a leading "fireball" of mass ;200 GeV that isotropically exotic particles in the cosmic rays. They fall into three catego- decays into t102 hadrons other than pions. Another surprising ries: feature of the interaction is the very large average transverse (i) Search for single, unaccompanied particles ofunusual momentum of the secondaries, (PT) = 1.7 ± (SD) 0.7 GeV/c. charge or mass. Searches (11) for quarks have together set The absence of -r° mesons in the event suggests the breakup overall upper limits of g10-11 cm-2 sr- sec-1 on the flux of of a 1015-eV nucleus of mass A > 50 into nucleons. To account quarks with 1/3 e and t2 X 10-11 cm2 srI sec-1 on the flux for the high (PT) and for the survival of the initiating object of quarks with 2/3 e. In a recent sea level search Bakich et al. through more than 500 g/cm2 of air, Bjorken and McLerran (3) set an upper limit of -2 X 10-10 cm-2 sr1 sec-1 on the flux (16) hypothesized that the object was a metastable glob of highly of singly charged particles with M > 5 GeV/c2 and ,B < 0.7. compressed nuclear or quark matter present in the primary Beauchamp et al. (22) set an upper limit of ;4 X 1010 cm-2 cosmic rays. Abnormally dense nuclear matter has been the sr-1 sec-1 on the flux of diquarks of charge . 4/3 e at a depth subject of much theoretical discussion in recent years (26-28), of 750 g/cm2. In a recent experiment at 690 g/cm2, Bashind- particularly as the opportunity to bombard a uranium target zhagyan et al. (23) looked for particles of fractional charge and with a GeV/nucleon uranium beam at the Lawrence Berkeley large mass (>10 GeV). Their report of a group of particles of Laboratory Bevalac accelerator nears reality. charge -1.2 to t1.5 e (interpreted as evidence for diquarks of McCusker (postdeadline talk at 16th International Cosmic charge 4/3 e) at a flux of ;10-9 cm2 srI1 sec-4 was viewed Ray Conference) has estimated that enough heavy (A > 40) skeptically at the 16th International Cosmic Ray Conference fragments of interactions of primary Fe nuclei with E > 10'5 because the group appeared to be part of the tail of a distribu- eV would survive to a depth of t500 g/cm2 to account for the tion of singly charged particles. Centauro events. This explanation, if correct, would remove (ii) Search for peculiar particles accompanying air showers. the necessity to invoke new physical objects or processes. Assuming that quarks are produced with an average transverse However, the calculated survival probability is extremely momentum of t0.5 GeV/c in very high energy collisions, a sensitive to the value chosen for XFe, the total interaction mean of relatively small rest mass would hit a sea-level detector free path of Fe in air. For example, use of the incorrect value rather far from the core of an air shower and should be detected XFe = 25.7 g/cm2, which is the measured value for Fe in nu- in the first class of searches. If its rest mass were quite large, it clear emulsion, instead of the relevant value for Fe in air, which would usually lie within the shower core and escape detection is only about half as large, would make the explanation appear unless the apparatus were designed to trigger on showers. Re- marginally acceptable. cent experiments with cloud chambers (11) provide convincing To demonstrate that a heavy nucleus, even with extreme evidence against the existence of fractionally charged cos- fluctuations, cannot account for the Centauro events, we go mic-ray quarks in air showers at flux levels above _10-11 cm-2 through the calculation here. First we need an accurate value sric sec-1. In all such experiments the charge was inferred from for XFe. Israel et al. (29) have measured a value XFe = 13.2 i droplet density. (SD) 1.1 g/cm2 for loss of at least one proton in air. By inter- (i) Time delay searches for massive hadrons. If a particle polation of the measurements of Westfall et al. (19), we find = of rest mass Mx and Lorentz factor yx = EX/Mx is produced AFe = 14.2 g/cm2 for loss of at least one proton and XFe 13.2 in a high-energy interaction at a height y above a detector, it g/cm2 for loss of at least one nucleon. Independently, Orth et will arrive at the detector delayed by a time At behind the al. (30) derived the value XFe = 13.7 g/cm2, and we use XFe = shower front consisting of particles with v t c, with 13.5 g/cm2 below. Next we need the probabilities that in such an interaction the projectile loses various amounts of charge. At y/2'yX2c, Yx >> 1. Following McCusker, we assume that after more than six units Thus, a particle of mass 5 GeV with an energy of 100 GeV of charge have been lost, too few nucleons remain to provide produced 10 km above a detector would arrive 40 nsec behind the hadrons for a Centauro event. Table 1 gives two sets of the shower front. A simultaneous measurement of time delay probabilities, the first from measurements by McCusker of and total energy of the delayed particle then sets limits on interactions of Fe in emulsion and the second from the cross possible and production heights. sections calculated by Silberberg and Tsao (20, 21). The most = Two groups have reported the observation of long-lived (r important entry, that for AZ 0, is much higher as determined > 10-7 sec) hadrons with mass >5 or 10 GeV. Goodman et al. by emulsion observations than by calculation. Despite the (24), with equipment at 2900 m, saw three events with At > well-known fact that it is very difficult to detect all mini- 30 nsec and E, > 45 GeV, implying a mass >5 GeV and a flux mum-ionizing protons in an interaction with 100% efficiency Downloaded by guest on October 2, 2021 Physics: Price et al. Proc. Natl. Acad. Sci. USA 77 (1980) 47 Table 1. Fragmentation probabilities for Fe in air AZ 0 1 2 3 4 5 6 P(AZ), McCusker 0.26 0.056 0.031 0.031 0.046 0.051 0.051 P(AZ), Silberberg-Tsao 0.15 0.072 0.073 0.045 0.055 0.029 0.039 (and thus the entry in the column AZ = 0 may be overesti- and the Silberberg and Tsao fragmentation probabilities in mated), we treat both rows of Table 1 on an equal basis and do Table 1. the calculation separately for each set of probabilities. A detector Finally, we need to know the integral flux of nuclei with Z for rare, highly ionizing particles 26 at energies greater than ;1015 eV or 2 X i0'3 eV/nucleon. Single, highly ionizing particles cannot be detected in the huge Orth et al. (30) recently measured an integral flux for Z > 25 emulsion chambers located at Mt. Chacaltaya, at Mt. Pamir (in of N(>E) = 1.08 E-1-26 m 2 sr-1 sec-1 (GeV/N)l. Goodman the Hindu Kush), and at Mt. Fuji. Centauro and other very et al. (31) made an indirect measurement of Fe at an energy high-energy interactions are detected by visual or photometric closer to that of interest, leading to a very similar integral flux: scanning for macroscopic gray regions in x-ray film caused by N(>E) = 0.93 E-1'36. The flux at energies above 2 X 1013 an electromagnetic cascade of sufficiently high multiplicity. eV/nucleon is thus 1.3 x 10-6 m2 sr-1 sec-1. Assuming con- To examine whether a highly ionizing particle could account servatively only one genuine Centauro event in 5 yr over an for the Centauro events, it is desirable to have a detector that area of 44 M2, the number of starting Fe nuclei at the top of the is completely insensitive to the electromagnetic cascade and atmosphere is 8000. to individual hadrons, but that records minimum-ionizing The probability of survival to a depth of 540 g/cm2 with final particles of charge 26e with high efficiency, even at a flux as charge Z > 20 is low as one per 100 m2 per year. Lexan satisfies the former but not the latter criterion, having a minimum value of Z/,B of -65 ______m 6. (6-AZI for track production. e-m + E1 m p(S ) |6-E P(AZ2)| n=1 n! Azl=o The CR-39 plastic track detector developed in our laboratory AZ2=0 (32-34) is ideally suited for a low-level search for such particles. P(AZn)j... JJJ, [3] Fig. 2 shows the high contrast and visibility achieved when CR-39 was exposed at normal incidence to particles with Z/3 where m is the = 11.8 and etched in hot sodium hydroxide solution. After mean number of collisions expected to 540 g/ etching for a long time, pits such as these reach a size that cm2, given by m = 540/13.5 = 40; and P(AZ1) is the probability one of a loss AZ pit can be detected easily in a typical 1Q3-cm2 sheet by scanning getting in the ith collision. with a hand lens. For a given etch time the diameter and depth By using m = 40 and McCusker's fragmentation probabilities of an etch increases from Table 1, we get a survival probability P(AZtOt < 6) = 1 X pit monotonically as Z/(3 exceeds a critical 10-11 and an expected number of Centauro events of value of tO. The rate of change of etch pit size from top to bottom of a sheet, together with the initial size, enable # and 8000 X P(AZ7tot < 6) = 8 X 10-8. Z to be determined (35). We plan a 1-yr exposure of lO0 m2 of CR-39 at the summit Use of the fragmentation probabilities from Silberberg and Tsao of White Mountain, CA (608 g/cm2) and 44 m2 of CR-39 at Mt. in Table 1 gives a survival probability of 3 X 10-13 and an ex- Chacaltaya, Bolivia. From Fig. 1 one sees that the probability pected number of Centauro events of t2.4 X 10-9. of detecting a single cosmic ray nucleus with Z/3 as low as 10 As an independent check, the summed flux of particles with is only t10-3 per 100 m2 per yr at White Mountain and :0.03 Z > 20 at E > 2 X 1013 eV/nucleon at 540 g/cm2, using the at Chacaltaya. With a threshold at Z/,B = 10 it is, of course, matrix calculation, is 6 X 10-21 particle/M2 sec. In an area of possible to detect a slow particle with lower Z over a limited 44 m2 during 5 yr, the number of particles is ;4 X 10-11, about velocity interval. From Fig. 1 and the constraint that / < Z/10, 1/60th of the number obtained in the cruder way using Eq. 3 we find that for no nucleus with Z as low as 3 does the expected number of events become as high as one per 100 m2 per yr. Therefore, any possible signal would herald an event of po- II E1*: tentially great importance. 9 This work was supported by the National Aeronautics and Space Administration (Grant NGR 05-003-376) and by the National Science Foundation (Grant PHY 78-24357). .I...',, }^ 1. Brooke, G. & Wolfendale, A. W. (1964) Proc. Phys. Soc. London 83,843-851. 2. Barber, H. B. (1976) Dissertation (University of Arizona, Tucson, AZ). 3. Bakich, A. M., Peak, L. S., Riley, P. A. & Winn, M. M. (1979) Proceedings of the 16th International Cosmic Ray Conference, Kyoto 6,53-56. 4. Fukui, K., Lim, Y. K. & Young, P. S. (1969) Nuovo Cimento B 61,210-218. 5. Allkofer, 0. C. & Heinrich, W. (1974) Health Phys. 27,593- 599. 6. Anderson, C. D. (1933) Phys. Rev. 43, 491-494. 7. Neddermeyer, S. H. & Anderson, C. D. (1937) Phys. Rev. 51, FIG. 2. Photomicrograph of etch pits of 15-MeV/nucleon 3He ions 884-886. in CR-39 after chemical etching in 6 M sodium hydroxide for 5 hr at 8. Street, J. C. & Stevenson, E. C. (1937) Phys. Rev. 51, 1005 90'C. The average pit diameter is 6 j~m. (abstr.). Downloaded by guest on October 2, 2021 48 Physics: Price et al. Proc. Natl. Acad. Sci. USA 77 (1980) 9. Rochester, G. D. & Butler, C. C. (1947) Nature (London) 160, 23. Bashindzhagyan, G. L., Sarycheva, L. I. & Sinev, N. B. (1979) 855-857. Proceedings of the 16th International Cosmic Ray Conference, 10. Seriff, A. J., Leighton, R. B., Hsiao, C., Cowan, E. W. & Anderson, Kyoto 6, 143-147. C. D. (1950) Phys. Rev. 78,290-291. 24. Goodman, J. A., Ellsworth, R. W., Ito, A. S., MacFall, J. R., Siohan, 11. Jones, L. W. (1977) Rev. Mod. Phys. 49, 717-752. F., Streitmatter, R. E., Tonwar, S. C., Vishwanath, P. R. & Yodh, 12. Goldhaber, A. S. & Smith, J. (1975) Rep. Prog. Phys. 38, 731- G. B. (1979) Proceedings of the 16th International Cosmic Ray 770. Conference, Kyoto 6,64-67. 13. Fleischer, R. L., Hart, H. R., Nichols, G. E. & Price, P. B. (1971) 25. Tonwar, S. C., Sreekantan, B. V. & Vatcha, R. H. (1977) Pramana Phys. Rev. D 4,24-27. 8,50-55. 14. Yock, P. C. M. (1975) Nucl. Phys. B 86,216-220. 26. Bodmer, A. R. (1971) Phys. Rev. D 4,1601-1606. 15. Brazil-Japan Emulsion Chamber Collaboration (1973) Pro- 27. Lee, T. D. & Wick, G. C. (1974) Phys. Rev. D 9,2291-2316. ceedings of the 13th International Cosmic Ray Conference, Denver 4, 2671-2675. 28. Migdal, A. B., Sorokin, G. A., Markin, 0. A. & Mishustin, I. N. 16. Bjorken, J. D. & McLerran, L. D. (1979) Phys. Rev. D 1, in (1977) Phys. Lett. B 65,423-426. press. 29. Israel, M. H., Klarmann, J., Love, P. L. & Tueller, J. (1979) Pro- 17. Tsao, C. H., Shapiro, M. M. & Silberberg, R. (1973) Proceedings ceedings of the 16th International Cosmic Ray Conference, of the 13th International Cosmic Ray Conference, Denver 1, Kyoto 1, 323-328. 107-110. 30. Orth, C. D., Buffington, A., Smoot, G. F. & Mast, T. S. (1978) 18. Lederer, C. M., Hollander, J. M. & Perlman, I. (1967) Table of Astrophys. J. 226, 1147-1161. Isotopes (Wiley, New York), 6th Ed., pp. 5-21. 31. Goodman, J. A., Ellsworth, R. W., Ito, Al S., MacFall, J. R., Sio- 19. Westfall, G. D., Wilson, L. W., Lindstrom, P. J., Crawford, H. ham, F., Streitmatter, R. E., Tonwar, S. C., Vishwanath, P. R. & J., Greiner, D. E. & Heckman, H. H. (1979) Phys. Rev. C 19, Yodh, G. B. (1979) Phys. Rev. Lett. 42, 854-857. 1309-1323. 32. Cartwright, B. G., Shirk, E. K. & Price, P. B. (1978) Nucl. Instr. 20. Silberberg, R. & Tsao, C. H. (1973) Astrophys. J. Suppl. 25, Meth. 153, 457-460. 315-368. 33. Price, P. B., Shirk, E. K., Kinoshita, K. & Tarle, G. (1979) Pro- 21. Silberberg, R. & Tsao, C. H. (1977) Proceedings of the 15th In- ceedings of the 16th International Cosmic Ray Conference, ternational Cosmic Ray Conference, Plovdiv, Bulgaria 2, Kyoto 11, 80-85. 84-88. 34. Kinoshita, K. & Price, P. B. (1980) Rev. Sci. Instrum. 51, 63. 22. Beauchamp, W. T., Bowen, T., Cox, A. J. & Kalbach, R. M. (1972) 35. Fleischer, R. L., Price, P. B. & Walker, R. M. (1975) Nuclear Phys. Rev. D 6, 1211-1217. Tracks in Solids (Univ. of California Press, Berkeley, CA). Downloaded by guest on October 2, 2021