The fluid dynamical model is used to study the reactions 20Ne+238U and 40Ar+40Ca at Elab=390 MeV/nucleon. The calculated double differential cross sections d²ð​/dΩdE exhibit sidewards maxima in agreement with recent experimental data. The azimuthal dependence of the triple differential distributions, to be obtained from an event-by-event analysis of 4π; exclusive experiments, can yield deeper insight into the collision process: Jets of nuclear matter are predicted with a strongly impact-parameter-dependent thrust angle θ​jet(b). NUCLEAR REACTIONS Ar+Ca, Ne+U, Elab=393 MeV/nucleon, fluid dynamics with thermal breakup, double differential cross sections, azimuthal dependence of triple differential cross sections, event-by-event thrust analysis of 4&#960; exclusive experiments

Buchwald, Gerd

Csernai, László Pal

Cusson, R. Y.

Graebner, Gerhard

Greiner, Walter

Kruse, Hans

Maruhn, Joachim

Stöcker, Horst

English

Hochschulschriftenserver - Universität Frankfurt am Main

PHYSICAL REVIEW C  VOLUME 25, NUMBER 4  APRIL 1982 Jets of nuclear matter from high energy heavy ion collisions H. Stöcker Gesellschaft  für Schwerionenforschung, D6100 Darmstadt,  Germany and Nuclear Science Division, Lawrence Berkeley Laboratory, Ciniuersity of Colifornia, Berkeley, California 94720 L. P. Csernai,* G. Graebner, G. Buchwald, H. ~ruse,"f. Y. Gusson,fJ. A. Maruhn, and W. Greiner Institut für  Theoretische Physik, D6000 Frankfurt arn Main, Germany (Received 2 March 198  1 i The fluid dynamical model is used to study the reactions 2"Ne+23XU  and 40Ar+40Ca  at EI„  =  390 MeV/nucleon.  The calculated double differential cross sections d 2u/d12  dE ex- hibit sidewards maxima in  agreement with recent experimental data.  The azimuthal depen- dence of  the triple differential distributions, to be  obtained frorn an  event-by-event analysis of  477  exclusive experiments, can yield deeper insight into the collision process:  Jets of  nu- clear matter are predicted with a strongly impact-parameter-dependent thnist angle B„,(b). NUCLEAR  REACTIONS  Ar +  Ca, Ne+ U,  Elab  =  393 MeV/nucleon, fluid dynamics with thermal breakup, double differential cross sections, azimuthal dependence of  triple differential cross sections, event-by-event thrust analysis of  4~ exclusive experiments. Recent  measurements  of  proton  cross  sections with  high  associated m~lti~licities'  provide further evidence  for  predominant  sidewards  emission  of fragments2 from  high-energy  heavy  ion  collisions. This might indicate the presence of strong compres- sion effects, which are predicted in the nuclear fluid dynamical  (NFD) m0de1.~-~  Here we  present  the first quantitative  comparison  of  an NFD calcula- tion  with  the  multiplicity  triggered  experimental data.'  The NFD mode13 includes a realistic treat- ment of the nuclear binding6 and the final thermal break~~.'-~  Nuclear viscosity and thermal conduc- tivity8-"  have  been  neglected  as  in  all  previous three-dimensional calculations because of numerical expenditure;  the  thermal  energy  is  produced  by shock heatir~~.~-~  Azimuthally (4)  averaged double differential  particle cross sections d 2a/dfl  dE and 4-dependent  triple  differential  distributions d35/d  cosOd4 dE  are calculated, boosting the inter- nal  (Maxwell Boltzmann) momentum  distribution f (k)=  f (p,T) in  each  fluid  element  by  the corresponding collective flow velocity into the labo- rat~ry.~  The proton distributions are calculated by allowing  only  the  emission  of  unbound  particles with  e2rnpc2,  ~(k)  being the total energy per pro- ton  in the rest  frame of  each  fluid  element.  The freezeout is done in a late stage in the reaction, so that  the final  distributions depend  only negligibly on  the  exact  value  of  the  breakup  density psl,-0.5~0  !-9 Figure l(a)  shows the measured angular distribu- tions  of  protons  emitted  from  high  multiplicity selected  (i.e.,  central)  collisions  of  20~e  (393 MeV/n~cleon)+~~~~.'  The data exhibit sidewards maxima;  fonvard emission is  strongly  suppressed. The angular  distributions  of  protons  and  summed charges  as  calculated  in  the  present  work  are  in agreement with the data [see Fig. l(a)]. It is impor- tant  to point  out  that  the sidewards  maxima  are predicted  to  be  even  more  pronounced  for  the summed charges than for protons.  In fact, such a behavior  has  been  found  in  experiments  with  a- particle  detectors.'  Also,  the  high  multiplicity selected  angular distributions of  2~  and  3~  (Ref. 15) show sharper sidewards peaking than the pro- tons.  On  the  other  hand,  cascade  calculations, which treat reactions of  heavy nuclei as a sequence of independent free nucleon-nucleon co~lisions,~' l3 predict, in general, strongly forward peaked proton distributions  even  when  small  impact  Parameters are  ~elected,~,'~  in  contrast  to  the  data.',15  The qualitative disagreement of the data and the cascade ~alculations~"~~'~  points  out  that it is necessary to incorporate  realistic  many-body  interactions14 of nucleons in dense nuclear matter into a microscopic approach to high energy heavy ion collisioris. 2.2  1873  63 1982 The Arnerican Physical Society FIG. 1.  (a)  The angular distributions of  protons emit- ted from central (high multiplicity selected) collisions of ''Ne  (393 Me~/nucleon)+~~~~  are shown.  The experi- mental  data (left) exhibit sidewards maxima  and  are in agreement with the results of the fluid dynamical calcula- tion  (right) with  an  impact  parameter cut at  b„,  =  1.5 fm.  The dashed  line  indicates the  results for summed charges (multiplied by  0.2 to fit in the figure). The num- bers  indicate the kinetic energy (laboratory)  of  the emit- ted protons, respectively.  (b) Azimuthally dependent  tri- ple  differential  invariant  particle  cross  sections l/p d3a/d~d  cos8dg (nMeV-2 sr-'C-')  in  the scatter- ing  plane  #=0"/180°  at  vanous  impact  parameters. Shown are contour diagrams in  the plane of  transverse 1 momentum PT in units of pr/(mNc)  and rapidity yll= In  [(E+pII  1  /Pd )/(E  -pll)] for the reaction  20Ne+238U at Elab  =  393 MeV/nucleon.  Shaded areas indicate flat 10- cal maxima.  The lower nght frame shows the proton dis- tnbution at b =4 fm to be compared with the distnbution of all particles in the lower left frame. The qualitative features of the 4-averaged distri- butions calculated in the present work, however, do not  change  dramatically  with  impact  parameter, once violent collisions with  b 54  fm  are selected. This means, unfortunately,  that 4-averaged double differential  cross  sections are of  limited  value for obtaining  information  on  details  of  the  reaction dynamics  and  on  the nuclear  equation  of  ~tate.~'~ Therefore, we next consider whether the azimuthal dependence of  the differential  cross sections, to be obtained from 4~ exclusive experiments with single event analysis,15  can provide more specific dynami- cal information. Figure l(b)  shows the triple differential cross sec- tions d3cr/d cosOd4dE in the scattering plane, i.e., the  y11  /pT  plane  at  4=O0/180",  for  the  reaction 20~e  (393 ~e~/nucleon)  +238~  at various  impact parameters b.  For head-on collisions, b =O  fm, the two  maxima  at pT  /m z  0.1 -0.2  indicate the  az- imuthally symmetric large angle sidewards emission of  cold (T  < 10 MeV) matter.6  At intermediate im- pact  parameters,  a  considerable  azimuthal  asym- metry appears.  A strong maximum at small trans- Verse  and longitudinal  velocities indicates the pres- ence  of  a  large  chunk  of  cold,  slowly  moving matter,  namely,  the target  residue  at 4 =  180".  A flat  local  maximum  in  the  projectile  hemisphere (4=0") at larger pT and  reflects some sidewards deflected  fragments  of  the  beam  particles.  The spread of  the maxima  in 4 depends strongly on b; for intermediate b it  is  on  the order  of  A$-40". The apparent large collective transverse and longi- tudinal  momentum  transfer  (the bounce  off  pro- ces~~~'~)  results from the high pressure in the "parti- cipant"  head shock Zone, pushing the nuclear resi- dues apart to opposite directions (Ac$ =  180"). This process is of great importance, as it intimately con- nects  the  momentum  transfer  to be  observed  in bounce off events with  the quantity  of  central in- terest,  namely,  the  nuclear  equation  of  state P(~,T).'~  At large  impact  parameters  (b  >6  fm) the invariant cross sections peak more closely to the initial projectile and  target  momenta.  Maxima at finite pT  are found even in the azimuthally averaged particle cross sections. The  symmetric  system  @~r  (388 MeV/nucleon)+@~a  shows  a  similarly  forward- backward  peaked  distribution  at  large  impact parameters.  At  smaller  b,  the 4-averaged  double differential invariant proton cross sections exhibit a structureless "fireball"  distribution, i.e., the contour lines in the y  11 /pT plane are circles centered around Y,,,,  . However, we observe in the triple differential cross sections again a symmetric two jet structure at finite pT being superimposed on the broad thermal "fireball"  background.  The connection between the two jet  maxima-the  jet  axis-immediately  yields 25  -  JETS OF NUCLEAR MATTER FROM HIGH ENERGY HEAVY ION. . .  1875 the direction  of  the main momentum flow relative to the beam axis.  It thus defines the angle Bjet in the c.m. frame at which the thrust T=m_axC I pi.R I /C  I pi  /  (1) "i  i occurs, which has been introduced to analyze jetting phenomena  in e+-e-  ~ollisions.'~  Here  Pi is the momentum of each fragment and R is a unit vector pointing  in any direction.  The thrust angle, Oj„,  is strongly impact parameter dependent (see Table I): For both Ar+Ca and Ne+U it is 0" at large b and increases to 90" for central collisions. The measurement  of  the triple differential  cross section can yield, however, considerably more infor- mation about the collision dynamics than the thrust analysis alone:  The distance between the jet  maxi- ma,  i.e.,  the mean  momentum  along  the jet  axis, may serve as a measure of  the transport properties of  the matter:  For example, a large viscosity slows down the collective fluid motion in the jet direction. There  are  many  other  features  of  the  reaction dynamics which are only accessible by  detailed in- spection of the triple differential cross sections:  For head-on collisions of  equal nuclei, the compression in  the shock  Zone  is maximized,  and most  of  the matter participates in the strong compression.  The two-jet  Patterns  give way  to an  azimuthally sym- metnc disk  of  nuclear  matter,  expanding  towards 90" in  the  c.m.  system.18  It  eventually  results  in doughnut-shaped (toroidal) triple differential  cross sections  symmetric  around  the  beam  axis.  The strong collective transverse matter flow18 with large mean  velocity, pT/m m0.4  is  caused  by  the  high pressure in the shock region, in analogy to the inter- mediate  impact  parameters.  Remnants  from  the squeezeout  can  still  be  seen  at  small,  but  finite impact  parameters,  b-2  fm,  thus  giving  rise  to additional  out-of-plane  jet  structures- four -jet -events-at  O,,,,  =  90",  4 =  90°, as the out- flow of the compressed matter perpendicular to the scattering  plane  is  not  hindered  by  "spectator" matter.  These  predictions,  however,  do not  take TABLE I.  The center-of-mass jet angle, O„„  relative to the  beam  axis  as  a  function  of  impact  parameter  at Elab  =  390 MeVhucleon. b  (fm)  0  1  23468 into account the limitations (e.g., considerable fluc- tuations) of  Eulerian  fluid dynamics  when  applied to light systems:  microscopic cal~ulations'~-'~  for C +  C and Ne +  Ne  indicate  large  nonequilibrium contributions.  However,  while  the  cascade cal~ulations'~~'~-based  on  free n-n  collisions-do not  show  a  considerable  transverse  momentum transfer even for heavy nuclei, many body calcula- tions with realistic n-n interactionsI4 predict hydro- dynamic features such as the 90" sideways peaking for  systems  with  Ar,Ap  240.  Unfortunately,  the heaviest  presently available projectiles have a mass Ap m40.  Heavier  symmetric  systems  should  be more suitable for a quantitative comparison to the present predictions. Beyond the jet  analysis, the "chemical"  composi- tion19 in various regions of  phase space is another observable of great importance, which may yield in- formation on the nuclear  equation of  state.  Since the temperature in the shock Zone  is much higher than  the temperatures  in  the projectile and  target remnants, we predict the emission of predominantly unbound  nucleons from the "fireball."  Hence, the actual jet  structure is much  more  pronounced  for bound  nuclei  (e.g., a,12c). The reason  for that is twofold:  Clusters  are  heavier  and  thus  have  a smaller thermal velocity than nucleons at the same temperature,  so  that  their  distributions  are  not broadened as much by  thermal effects.  In addition, they are produced preferentially in the "cold"  parts of the matter distribution, which for the bounce off is just  the central  part of  the projectile and target residues.  This is illustrated by comparing the distri- bution  of  all particles to the Proton distribution in Fig. l(b). The latter is less structured and resembles a large fraction of  the thermal background  in  the particle distribution.  One is thus led to the conclu- sion that the collective effects should be observable most  clearly  in, e.g.,  the a particle distrib~tions.~ Therefore, a detailed calculation of the cluster for- mation,  e.g.,  in a chemical equilibrium  model,I9 is required for a quantitative comparison  with future 4n exclusive experiments. In conclusion, we have shown that triple differen- tial particle cross sections offer a unique tool for the investigation of  the complicated reaction  dynamics in high energy heavy ion collisions.  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Jets of nuclear matter from high energy heavy ion collisions

Jets of nuclear matter from high energy heavy ion collisions

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