VOLUME 48. NUMBER 22 PHYSICAL REVIEW LETTERS 31MAY1982 S. Kawaji and J. Wakabayashi, Solid State Cor 550(1981) 22,87(1977 D. C. Tsui, Solid State Commun. 21, 675(1977) 15D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys Rev.B25,1405(1982) T. Ando and Y Uemura, J. Phys. Soc. Jpn 36,959 6D. C. Tsui, H. L Stormer, A.C. Gossard, and (1974) w. Wiegmann, Phys. Rev. 21, 1589(1980); Th. engle ST. A Kennedy, R.J. Wagner, B.D. McCombe, and D. C. Tsui, and A. C. Gossard, Surface Sci. 113, 295 D. C. Tsui, Solid State Commun. 22, 459(1977) ' B. A. Wilson, S.J. Allen, and D. C. Tsui, Phys. Rev 1M. A. Paalanen, D. C. Tsui, and A C. Gossard 44,479(1980) Phys.Rev,B25,5566(19 Fukuyama and P A, Lee, Phys. Rev. B 18, 6245 (1978) 1H. Aoki and H. Kamimura, Solid State Commun. 21 A, Y Cho and J. R. Arthur, Prog. Solid State Cher D.J. Bishop, D. C. Tsui, and R. C Dynes, Phys Rev. Lett. 44, 1153 H, L. Stormer, A. Pinczuk, A C. Gossard, and R. B. Laughlin, Rev,B23,5632(1981) W. Wiegm Appl. Phys. Lett. 38, 691(1981), T.J. 2w. P Su and J. R Schrieffer, Phys. Rev. Lett. 46, Morkoc, and A. Y. Cho, J. Appl. Phy 738(1981) 。-130091 2D. Yoshioka and H. Fukuyama, J. Phys. Soc.Jpn K. von Klitzing, G. Dorda, and M. Pepper, Phys 47,394(1979),and50,1560(1981) Rev.Lett.45,494(980) 2G. A Baraff and D. C. Tsui, Phys. Rev. B 24, 2274 AD. C. Tsui and A. C. Gossard, Appl. Phys. Lett.37 (1981) Test of High-Pr Scaling from Cosmic-Ray Interactions up to 400 TeV W. E. Hazen and A, Z. Hendel Randall Laboratory of Physics, University of Michigan, Ann Arbor Michigan 48109 A. G. Ash, J. M. Foster. A. L. Hodson. and M.R. porter Department of Physics, University of Leeds, Leeds, United Kingdom M. Bull Department of Physics, University of Nottingham, Nottingham, United Kingdom (Received 19 April 1982) he rate of subcores in cosmic-ray air showers has been measured near sea level wit a close-packed 35-m" array of spark chambers at Leeds, Auxiliary experiments demon strate that our transition effects are negligible. The rate of subcores versus shower size is translated into the rate of high-pr events versus energy of the interacting hadron. Com- parison with calculations of Halzen favors Pr over Pr scaling. The highest energy bin is centered on 350 Tev PAcS numbers: 94. 40.Rc Cosmic rays provide a hadron beam with inten In view of the conflict in results among previous sity sufficient for exploratory study of interac experiments, we first review the case in favor tions up to energies of a few 100 Tev, that is, of our results. We then describe the analysis of ten times higher than the energy from the super our data and compare to Halzen's scaling from proton synchrotron collider at CERN. There accelerator data. The results strongly favor the fore, the results can still be of interest in spite parton model with Pr scaling. of the limit to accuracy inherent in the cosmic In order to interpret any subcore data, a con nection must be made between high-energy sec This is a report of an experiment to test mod- ondary hadrons produced in the atmosphere and els for deep-inelastic interactions by measuring the subcore as observed in a detector The in the energy dependence of the cross section fo formation used to link the two comes either from high-Pr production. The results btained computer simulations, or from analytical solu from the observed rate of subcores in cosmic tions of cascade shower equations, or from a ray air showers combination. These have been carried out for 1562