In the multiparticle productions at cosmic ray energies the experimental data have been analysed by the small fireballs (Hquanta) and the large ones (SH-quanta) .u The masses 1'v1u=2~3 GeV and 1'.1sH=20 "-'30 Ge V; the average charged pion multiplicities (k"')H~4 and (k"')sH=20~30. On the other hand FNAL and ISR data on small Pr and large Pr have been analysed by the productions of H's and SH's respectively. 'l • 3 l "\Ve present here a simple one-dimensional multiperipheral model with Regge

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... exchange for SH production as well as for H production. 2 l The inclusive one pion cross section, momentum transfers between fireballs and the production cross section of SH are evaluated. Let us consider a one-dimensional (longitudial) multiperipheral production of n fireballs (Pi) and two leading nucleons (Po, Pn+1) in the proton-proton CPa, h) collision. In terms of rapidities the energy and momentum conservations are written where m and 1'.1 are masses of nucleon and fireball, respectively and 7Jh 7J2·"1Jn are rapidities of fireballs, 7Jo and 7Jn+ 1 (Ya and Yb) are those of leading (incident) protons; 7Jo <;;, 7J1 <;;, .. • S 7J n + b Yb-Ya :::= Y =In s, transverse momennta being ignored. For massive fireballs 1\ilym a simple relation holds at large Ins for the average multiplicity (n) =bIns+ canst, where /C is the average inelastisity, ~C~1/2, since in average events, equal spacing is expected, (7jj)= Ya+LI+JA, J..= (lns-2LI)/ ((n)+1), e-•=1-/C and then e-1 c-:'.m~C/ M(1-~C)~1/20~1 forM=MsH· The average four momentum transfer squared can also be evaluated using e-1.~1. (CPa -2.j~~oPi) 2 ) c-:' . -mMsH for sebsequent SH's and ((Po-Pa) 2 ) = ( (Pn+1-Po) 2 > c-:' . -m 2 /2 for a leading nucleon and next SH. The cross section for n fireball production may be given as 2 l g's are coupling constants at vertices. 'lJa and 7J 0 are the kinematical boundary of 'l) 1 "?:.7Ja and 7Jn<;;,·r;b. In c.m. system ·r;u= -rJa = Y/2 and Y :::= 7Jb-'f/a =2 cosh -1 [ {s+ (111 +m) 2 -m 2 }/2(M-i-m)vs], c-:'.ln{s/(M+m) 2 } for ln s/ lvf2y 1. This comes from the extreme case that a leading nucleon and a fireball are emitted with the same rapidity and another nucleon is emitted in the opposite direction, other fireballs being ignored. Taking K ( 7J) = 7JC 2 "" as discussed in Ref. 2) we have the fireball cross section, where 2a -1g-2 = 0 is used for the constant limit of up(=) =ga 2 gb 2 e-2 Y+ ( 2 a+olYj2g. The average multiplicity and inclusive one fireball cross section are given as (n)=~ gY(1+e-ol') (1-e-oF) -1/2, (4) drJp/d7J=r1p(=H g{1-e-o(2'i+Yl} Comparing each leading term m (1) and