IMPORTANCE OF MOMENTUM DEPENDENT INTERACTIONS FOR ...

JOURNAL DE PHYSIQUE Colloque C2, suppl6ment au no 6, Tome 48, juin 1987

IMPORTANCE OF MOMENTUM DEPENDENT INTERACTIONS FOR THE EXTRACTION OF THE NUCLEAR EQUATION OF STATE FROM HIGH ENERGY HEAVY ION COLLISIONS

J. AICHELIN, A. ROSENHAUER*, G. PEILERT*, H. STOECKER* and W. GREINER* Institut fiir Theoretische Physik der Universitat Heidelberg and Max-Planck-Institut fur Kernphysik, 0-6900 Heidelberg, F.R.G. * ~ n s t i t u tfur Theoretische Physik, Johann Wolfgang Goethe Universitat Frankfurt, 0-6000 Frankfurt, F.R.G.

Abstract: interactions

We

demonstrate

that

momentum

dependent

nuclear

(MDI) have a large effect on the dynamics and on the

observables of high energy heavy ion collisions: Pion are strongly su~~ressed by

W I . This effect is

and

kaon yields

stronger than the

supression due to a hard local potential, which introduces an ambiguity into the recent extraction of the nuclear equation of state from pion (and kaon) yields. Also the transverse momentum distributions exhibit a strong dependence on the

MDI. The collective flow angles and the

deuteron to proton ratios, on the other hand, are rather insensitive to the

MDI. They m y therefore be related directly to the nuclear equation

of

state

at

high

density.

Simultaneous

measurements

of

these

observables in heavy ion collisions can give clues on the nuclear equation of state at densities of interest for supernova collapse and neutron star stability. The current studies of high energy heavy ion collisions are of broad scientific interest. This is for two reasons: first, they offer a unique

testing ground

for newly developped methods

to study

the

behaviour of strongly interacting quantum systems with finite particle number far from the groundetate. Secondly one hopes that information on the equation of state of dense nuclear matter can be extracted from the experimental data. This knowledge is essential for an understanding of the collapse of supernovae, for neutron star stability and for the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987224

JOURNAL DE PHYSIQUE

C2-166

onset of a possible transition from hadron matter to the quark gluon plasma. It has been proposed for m y years to use pion production and the collective flow in central high energy Collisions to investigate the nuclear EOS at high density and temperature1-4. The microscopic Vlasov Uehling Uhlenbeck (VUU) t h e ~ r y ~has - ~ exhibited the sensitivity of the

yield^"^,

pion

subthreshold kaon yields5 and the collective flow1'3'4

to the nuclear EOs. It has recently been suggested6 to test whether this sensitivity to the equation of state might be di$torted

by

introdacing momentum dependent interactions (MDI) into the theory. Such interactions had dynamicsw7 and

been the

implemented

time dependent

into

the classical

meson

"molecular

field approach8 ,

which

a collective sidewards flow in qualitative agreement with the data

10

-

Here we demonstrate the importance of the momentum dependent interactions using an extension of the VUU approach, dubbed molecular d-ics"

(@ID) l , which combines

"quantum

the important quantum

features of the WU theory, namely the Pauli principle, stochastic ~ , the long range N- body scattering and particle p r o d ~ c t i o n ~ ' ~ -with correlations found in the classical molecular dynamics method7-':

N

gaussian wavepackets with a finite width in configuration and momentum space move on trajectories given by the N-body interaction, following Hami l ton's equations, dp/dt =

-

W d q , dq/dt = p/m + dU/dp. Two wave

packets can also scatter stochastically at short distances. The width of the wave packets allows for a computation of

the phase space

occupancy (l-f ) which determines the Pauli blocking probabili tyl1 of attempted collisions in the same m y as in the WU a p p r ~ a c h ~ -Deltas. ~. pions and kaons are produced using the elementary scattering cross sections in the same way as in the YUU approach3-5.11 The potential U is given by U

P

X t16(rf-r;) i

+ t2(

a

H 6(r1-rill + Ucoul + U(Ap)6(r1-r;). i

The momentum dependent term U(Ap) energy dependence of the proton range of 10 MeV