Differences between the Nantes-Ganil-Grenoble (NGG) LV-model and the original VUU approach are analysed. It is found that the LV code tends to simulate - for small timesteps - a non-viscous testparticle fluid

Greiner, Walter

Hartnack, Christoph

Stöcker, Horst

English

Hochschulschriftenserver - Universität Frankfurt am Main

%~&rnrnBiTs UFTP  preprint 216/1988 Institut  fürTheoretiwhe Physik Johann Wolfgang Goethe Universität Frankfurt arn  Main Landau-Vlasov model versus Vlasov-Uehling-Uhlenibeck- approach Different flow effects frorn the sarne theory?" C. Hartnack, H.  Stöcker and W.  Greiner Institut für Theoretische Physik, Universität F'rankfurt, Germany I * -- This work has been funded in part by  the German Federal Minister for Research and Technology  (BMFT) under the contract numbers  06 OF  772, 06 HD 776 and by  the  Gesellschaft für Schwerionenforschung (GSI)  . Institut für Theoretische Physik  der Universität Frankfurt Robert-Mayer-Str.  8-10.  D-6000  Frankfurt am  kin Landau-Vlasov model versus Vlasov-Uehling-Uhlenbeck- approach Different flow effects from the Same theory? C. Hartnack, H. Stöcker and W. Greiner Institut für Theoretische Physik, Universität Frankfurt, Germany Abstract: Diflerences between the Nantes-Ganil-Grenoble (NGG)  LV-model und the original VUU  approach are analysed. It is found  that the LV  code tends to  simulate - for small timesteps -  a  non uiscous testpartiele fluid. ,.  -.  . The Nantes-Ganil-Grenoble (NGG) collaboration has recently applied '  the Landau- Vlasov (LV) transport code  to study collective flow effects in heavy ion collisions. It was found '  that "the LV  model provides large flow even with i  soft nuclear equation of  state (eos), in strong contrast to the earlier work  based on the microscopic VUU calculations which shows evidence for a stiff  OS.'' It was concluded that "these discrepancies between models based on similar approaches have certainly to be traced back to the treatment of  two body collisions, which requires a closer study of  the Uehling Uhlenbeck collision term.'" In the present note we take up this task - the origin of the large differences between the L\'  and VUU predictions are explored. In the LV  code nucleons are represented by a large collection (typically -  30) gaussian te~t~articles.'-~  Collisions between the testparticles occur if  the centroids of  two gaussians approach each other with a distance of  closest approach d~„,  < (u~„~/?r)'/~.  The NGG  collaboration chooses  UT„,  = UNN.  This lias drastic consequences:  the resulting classical * mean free path of  such testparticles would be very short, XTett  = (uTerf  .  -  1/20fm for  @T,.,  = 30eo and thm the testparticles would behave like a perfect, i.e. nonviscous, fluid. In order to re-introduce n longer mean free path into the model, the NGG collaboration decided to introduce the constraint that a given testparticle cannot undergo more than one collision per timestep. Consequently, the mean free path of  the testparticle increases to XTEIt -  vion  .  At  which yields  XTest  -  0.5fm  for the timesteps At -  lfmlc employed in the LV  calculation. (These values of  XtWt  are, however, still too short as compared to the N-N  mean free path XN,v -  2  f m at P,.  A timestep of  At -  4  fmlc  would be needed to simulate roughly the nonequlibrium effects -  AIR but such a At  is too long to ensure a reasonable accuracy in the numerical integration of  the classical equations of  motion.) for the sake of  sirnplicity let us  negloct  the Pauli blocking in the qualitative discussion Thus, the prescription chosen in ref.  1-3 introduces an explicit timestep dependence of  the collision frequency and, therefore,  of  other physical  observables.  To  obtain a quantitative feeling for this effect, we implemented these conditions  into our VUU code 4,5, i.e. the following results are obtained with Pauli blocking included.  (Note that we employ  nonreduced  cr~~  values and point-like testparticles in VUU, which  is not relevant in the argument here.) The number of  testparticle collisions versus the timestep At is shown for Ca (400 MeV/n, b=2fm) + Ca in fig.  la. Note the  l/At dependence of  Ncoli  for the sirnulated LV  case (triangles) as compared to the negligible depeiideiice of  Ncoil on At in the original VUU  code (squares).  Also note the factor of  3  -  G  tirnes larger absolute value of  NcOlr  in the LV  case. This means that the LV  code approximates a nearly ideal testparticle "fluid"  with a quite short mean free path XT„~/R < 1 and therefore with a very small effective viscosity 11  -+  0.  However, we know that the actual nuclear  viscosity is subst,antial, 7) x  50MeV/fm2c.  677  In fact, viscous fluid dynamical calculations6 have exhibited the strong dependence of the transverse flow on the viscosity: The ideal fluid (11  = 0) predictions for the transverse momentum transfer px(Y) exceed the viscous fluid results (with 1)  = 6OMeVl  fm2c)  by about afactor of two.  It is therefore not surprising that this factor of  two difference is indeed also observed in fig. lb, which compares the vahies of  the simu!ated  LV  code with our original VUU calculati~n.~'~  Note that the LV  values approach the VUU  result for At % 4fmlc i.e.  X  % 2fm.  For the LV  case with At _<  2fmlc we indeed find - as it should be for a perfect, i.e. nonviscous, fluid - that the p,y  values are nearly independent (within about 20 percent) of  the rapidly changing value of  Nc,li(At)  (The VUU approach gives per construction At independent results.) We have also studied the dependence of  the observables on the nurnber of  testparticles used  in the LV  code.  Since XT~~~  -  (NTOt/A)-'  we expect  again that e.g.  px  should nppruach the aqymptotic "ideal fluid" value for  large enough to ensure AT„,  <  R. Fig.  2 shows that this is indeed the case:  The p,y  value at 50 MeV  even changes sign when  XTe.t  is decreased. Wre  woiild  like to conclude by  noting that we  have found similar effects of  At and -hTc0ir  also at lower energies where the LV  code has been employed extensively before (see fig.  2).  The effects are also observed for a cascade version (i.e.  no potential, no Pau!i  blocking) of  the simulated LV  code.  G. Peilert has observed analogous results in a niudified QMD program. Stimuiatiiig discussion with C. Gregoire, P. Schuck and A. Bonasera on the LV  code a11d ivith B. SchBrma~ui  on the "testparticle fluid" are gratefully acknowledged. ,.  -..  Figures Fig.1: Comparison of  the dependence of  the number of  unblocked coilisions (divided by  NTWt/A)  from the timestep At  for VUU  and LV  (with NTmt/A  = 25) Fig.2: Comparison of  the dependence of  the flow p,y  at projectile rapidity from the timestep At  for VUU and LV  (with NT„,/A  = 25) Fig.3: Dependence of  the flow p,y  at projectile rapidity from the number of  Testpar- ticles NT„t/A  for LV  at low energies (with At = 2.5) References [l]  F.Sebille,  G.Royer,  C.Gregoire,  B.Remaud,  P.Schuck,  Nuclear  dynamics with the (finite range) Gogny force: flow effects, GANIL preprint  1988 [2] C. Gregoire, B.Remaud, F.Sebille and L.Vinet, Phys. Lett. B 186 (1987) 14 C. Gregoire, B.Remaud, F.Sebille and L.Vinet, Nucl.Phys A465 (1987) 317 B. Remaud, C. Gregoire, F.Sebille and L.Vinet, Phys. Lett. B 180 (1986) 198 .  B. Remaud, C. Gregoire, F.Sebille L.Vinet and Y.Raffray, Nucl.Phys  A447  (1985) 555C A.  Bonasera, C. Gregoire, Ambinguities in the estimate of  hard photon production in intermediate energy nucleus-nucleus collisions, GANIL preprint 1988 C. Gregoire, D.  Jaquet, M. Pi, B.  Remaud,  F. Sebille, E.  Surrand, P. Schuck, L. Vinet, GANIL preprint P 87-15 L. Vinet, C. Gregoire, P. Sdiuck, GANIL preprint P 86-28 [3] C. Gregoire, private communications 141  H. Kruse, B.V.Jacak, H. Stöcker, Phys.Rev.Lett. 54 (1985) 289  i J.J. Molitoris and H. Stöcker, Phys.Rev. C32 (1985) 47 J.J. Molitoris, D. Hahn and H. Stöcker, Nucl.Phys. A447  (1985) 13C H. Stöcker and W.Greiner, Phys.Rep. 137 (1986) 277 (51  G. Peilert, A.  Rosenhauer, H. Stöcker, W. Greiner, J. Aichelin, Mod.Phys.Lett. A3 (1988) 459 [G] T.Rentzsch, W.Schmidt, J.A.Maruhn, H.Stöcker, W.Greiner, Hirschegg Proc. Jan. 1988 and to be published H.Stöcker, Proc. High Energy Heavy Ion Study LBL Nov.1987 Berkely G.Buchwaid, L.P.Csernai, J.A.Maruhn, W.Greiner, H.Stöcker, Phys.Rev. C24  (1981) 2848 [7] A.R. ßodmer, Microscopic and hydrodynamic descriptions of  high energy heavy ion collisions, Argonne prepnnt 1979, unpublished B.Schürmann, W.Zwermann, Phys.Rev.Lett.  59 (1987) B.Schürmann, Mod.Phys.Lett in print a  LV VUU A  LV VUU 0  1  2  3 timestep  At Ca(SOMeV)+Ca  LV Hard 

G.Royer, C.Gregoire, B.Remaud, P.Schuck, Nuclear dynamics with the (finite range) Gogny force: flow effects, GANIL preprint 1988 [2] C. Gregoire, B.Remaud, F.Sebille and L.Vinet,

Landau-Vlasov model versus Vlasov-Uehling-Uhlenbeck-approach : different flow effects from the same theory?

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