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Do Energetic Heavy Nuclei Penetrate Deeply Into Earth's Atmosphere? (Cosmic Rays/High-Energy Interactions/Hypothetical Particles) P

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Do Energetic Heavy Nuclei Penetrate Deeply Into Earth's Atmosphere? (Cosmic Rays/High-Energy Interactions/Hypothetical Particles) P Proc. Natl. Acad. Sci. USA Vol. 77, No. 1, pp. 44-48, January 1980 Physics Do energetic heavy nuclei penetrate deeply into Earth's atmosphere? (cosmic rays/high-energy interactions/hypothetical particles) 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 mass-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 nature 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 quarks 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 particle 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 <i. f-1 C1 =Nt(0) - C k=i Thus, C11 = N1(0), C21 = C11M21/(M22- M1), C22 = N2(0) -C21, etc. This form of the solution, rather than N(x) = N(0) exp(Mx), was chosen because of the computational simplicity that this method offers. Once we find the coefficient matrix, C, for different values of x, we only have to compute a column vector of exponentials, rather than exp(Mx). In doing the calculations, the ajis were generated from the semiempirical values of Silberberg and Tsao (20, 21), and for E the ajis the results of Westfall et al. (19) were used: (A 10 oUj = 7rro2(AT'/3 + AB1/3 -b)2 [2] ._ where AT is the mass number of the target, AB is the mass cox number of the beam, r.
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