In the framework of relativistic quantum molecular dynamics the authors find that the pion system produced in central heavy-ion collisions at Elab/A approximately 1 GeV/nucl. is out of chemical equilibrium. Pion chemical potential is large and decreases during the expansion stage

Bandyopadhyay, Debades

Gorenstein, Mark I.

Greiner, Walter

Sorge, Heinz

Stöcker, Horst

English

Hochschulschriftenserver - Universität Frankfurt am Main

I. Phys. G: Nucl.  Part. Phys. 18 (1992) L187-Ll90.  Printed in the UK LElTER TO THE EDITOR Pion chemical equilibration in heavy-ion collisions: relativistic quantum molecular dynamic analysis Debades BandyopadhyaytP, Mark Gorensteintll, Horst Stocker?, Walter Greinert and Heinz Sorget t lnstitut fur Theoretische Physik  der J W  Goethe Univenitl, Postfach 111932, D-6000 Frankfurt am Main 11, Federal Republic of Germany $Theory, T-2, MS 8243, Los Alamos National Laboratory, PO Box 1663. Los Alamas, NM 87545, USA Received 6 July 1992 Abstract.  In the framework of  relativistic quantum molecular dynamics we find that the pion  system produced  in central  heavy-ion collisions at E,,,/A -  1  GeVInucl is out of chemical  equilibrium.  Pion  chemical  potential  is  large  and  decreases  during  the expansion stage. Data of  pion production in heavy-ion collisions show the enhancement of  n-  spectra at low transverse momenta. This widely debated phenomenon looks quite universal: low-p,  excess of pions  is  seen  in  CERN experiments  at the bombarding energy El,,/A =  200GeV/nucl [I], in  AGS  at E,.,/A = 15 GeV/nucl [2] and in Bevalac at Ela,/A =  0.5 t  1.8 GeV/nucl [3]. Resonance  decays  and  collective  (transverse)  flow  were  suggested  to  fit  ex- perimental data. One can find in the literature different combinations of  these two mechanisms  and  also  different  conclusions  (see  reference  [4]  and  references therein). An interesting idea to explain n-  spectra in CERN experiments by positive pion chemical potential pn  has been proposed  in [5-71.  Fitting n-  spectra in 0 +  Au at 200 GeV/nucl,  the freeze-out temperature  T  and pion  chemical  potential  pn are found to be: T = 167 MeV, px =  126 MeV [6] (without transverse collective flow), or T = 100 MeV, pn  = 120 MeV [7] (with transverse collective flow). In  [8] the  possibility  of  pn  >  0  was  discussed  for  small  bombarding  energies -1 GeV/nucl.  It was stressed that for the collisions of  heavy  nuclei  the chemical potential  of  n+  is  always smaller than that of n- and this difference can lead to some observable consequences. A  positive  value  of  pz means  that  at  some  stage  of the  particle  production process the number of  pions,  generated  by  hadron dynamics,  is  larger  than  that corresponding  to chemical  equilibrium.  Then  the  pion  system  can  be  thermally equilibrated due to elastic collisions, but it will be out of chemical equilibrium if the rate of  inelastic reactions is not high enough. Bose-statistic effects  then become very 5 Alexander van Humboldt Fellow. 11 Permanent address: Institute for Theoretical Physics. 252130 Kiev-130, Ukraine. 0954-3899/92/110187+04 $07.50 0  1992 IOP Publishing Ltd  L187 L188  Letter to the Editor important and should be included in pion kinetics.  One has, however, to postulate some initial conditions for the pion distribution function. It was argued in [5,7]  that the source of  the ‘extra’  pions  is decay of  resonances, so  that  there is complete thermal and chemical equilibrium in hot, dense matter and fix increases from zero during the expansion  stage reaching its maximum value  at the thermal freeze-out. This picture  was  also assumed in  hydrochemical  calculations of  reference  [9].  In [lo], on the other hand, it was suggested that primary  nucleon-nucleon  collisions can  produce  ‘too many’  pions  so that from the very  beginning of the expansion process the pion system is out of  chemical equilibrium. In this letter we present the results of  our analysis of  pion chemical equilibration in  the framework of  relativistic quantum  molecular dynamics (ROMD).  This micro- scopic model  combines the relativistic  invariant  (classical) propagation  of hadrons (including  produced  particles)  with  certain  quantum  features, such  as  stochastic scattering and resonance decays (see the review of  ROMD  in  [ll]). We  study  central  La +  La  collisions  at E,,,/A  = 1.35 GeV/nucl. To avoid  the problem of  the collective  flow we chose the cubic cell with volume  V = 125 fm3 in the geometrical centre of  our system (which is at rest in the centre-of-mass system of La + La). Generating the ensemble of central collision events, we have ‘measured’ pion (n-)  spectra in the cell Vat different  stages of the expansion from dense matter with baryonic density n =  2no (no- 0.16  fm-’  is the normal nuclear matter density) down to n =  0.5n0 when  particle  momentum  freeze-out is expected.  We have not observed  any  angular  dependence of  pion  spectra  in  the  cell  chosen  and  have represented pion energy spectra in the form dN,  V =-f  (1)  (E2  -  m:)ln/E  dE  2n2 where E is the pion energy and m, is the pion mass. Assuming thermal (but not chemical) equilibrium one can expect Bose distribu- f.- 1 0.1 n.ni 0  50  100  150  200  250  300  350  LOO (E  -  m.1  (MeV) Figure 1. RQMD results far f,  in  central La +  La  collisions a1 E,,,/A = 1.35 GeV/nucl. Upper histogram  corresponds  to n =  2n,  and  lower histogram to  n =  O.Sn,,. Lines  are Boltzmann  distributions  (3)  with  T -60MeV,  px -230MeV  (dotted line)  and  T E 30 MeV, p,, = 160 MeV (solid line). Letter to the Editor  L189 tion for the f,  function There  are no  Bose-statistic  effects,  however,  in  the  present  formulation of  RQMD. Therefore,  instead  of  (2),  thermal  equilibration  corresponds  to  the  Boltzmann distribution In  figure  1 we  present  our  results  of  RQMD  fn  calculations  at  n =  2n,  and n =  0.5n0.  RQMD  pion spectra can be fitted perfectly by the Boltzmann  distribution (3)  with  parameters  Tg-OMeV,  pn=230MeV  at  n=2n,  and  T-30MeV, p,, =  160 MeV at n =  0.511~. on the baryonic density. In figure 2 we show the RQMD results for the dependence of The main conclusions of  our analysis are the following: (i)  the  pion  system  reaches  local  thermal  (Boltzmann  distribution)  but  not chemical equilibrium; (ii)  the pion chemical potential is large and decreases (opposite to the previous expectations [5,7,11])  during the expansion process; (iii)  the very large value of p,,  (p,, >  m,,)  means that the classical (Boltzmann) approximation,  used  in  our analysis, is  not adequate and quantum (Bose)  effects (which guarantee p, s  m,)  should be implemented in RQMD. In the energy range EI,,/A -  1  GeV/nucl considered in this letter the number of produced  pions  per nucleon  is  small:  n,/n  ~0.2.  Nevertheless,  we  find  at zero 240  ,  ,  ,  ,  ,  ,  ,  ,  I  ,  ,  ,  ,  ,  I lZ00  100  0.L  0.6  0.8  1.0  1.2  1.4  1.6  1.8  2.0 dns Figure  2.  The  dependence  of  px on  the  baryonic  density  (px is  obtained from  the Bollzmann approximation (3) far f, calculated in RQMD). L190  Letter to the Editor momentum limit for pion fn  and nucleon fN  distribution functions SO that Bose effects  for pions are more important than Fermi effects for nucleons. The large values of  pz during the expansion stage can he checked experimentally by  measuring the lepton pair production due to z+z-  annihilation reactions, as was suggested recently in [12]. We  are  indebted  to R  Mattiello,  I  Mishustin,  L  Satarov,  T  Schonfeld  and  L Winkelmann  for  fruitful  discussions.  One  of  the  authors  (MG)  expresses  his gratitude  for  the  warm  hospitality  at  the  Institute  for  Theoretical  Physics  of Frankfurt University while holding a visiting professorship supported by  Deutsche Forschungsgemeinschaft. References [l] Stroebele H el 01  1988 Z.  Phys. C38 89 (21  Love W A el 01 1991 Proc. Quork Moller  '90  (Nucl. Phys. A525  601~) [3] Brackmann R ef  al 1984 Phys. Rev. Leu 53 463 Harris J W ef  a1  1987 Proc. Inr. Workrhop on the Gross Properties of Nuclei ond Nuclear Excila~iom [4] Sollfrank J, Schnedermann E, Koch P and Heniz U 1991 Proc. Hadron Srrucrure  '91 (Slam Lema, [SI Goity J L and Leutwyler H 1989 Phys. Len. 2288  425 (61  Kataja M and Ruuskanen P V 1990 Phys. Leu 243B 181 171  Gerber P, Leutwyler H and Goity I L 1990 Phys. Len. 2468 513 [XI  Gorenstein M I and Yang S  N  1991 Phys. Reu. C44  2875 [9] Garenstein M I, Yang S N and KO C M 1992 Phys. Len. ZSlB 197 XV (Hirscheg, Awlria, 1987) p 67 Czechoslovnkia  , 1991) [lo] Mishustin I N, Satarov L M, Maruhn J, Stocker H and Greiner W 1992 Phys. Len. 276B  403 1111  Sorge H, Stkker H  and Greiner W 1989 Ann. Phys. 192 266 [12] Koch  P  1992  Large  positive  pion  chemical  potential  and  lepton  pair  production  in  heavy  ion ' collisions Preprinf TPR-92-10 (Regensburg) 

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Large positive pion chemical potential and lepton pair production in heavy ion ' collisions Preprinf TPR-92-10

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Pion chemical equilibration in heavy ion collisions : relativistic quantum molecular dynamic analysis

Pion chemical equilibration in heavy ion collisions : relativistic quantum molecular dynamic analysis

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