Isospin Dynamics in Heavy Ion Collisions: EoS-sensitive Observables

Article (PDF Available)inNuclear Physics A 787(1):585-594 · October 2006with19 Reads
DOI: 10.1016/j.nuclphysa.2006.12.088 · Source: arXiv
Abstract
Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation and at high nucleon momenta. In this report we present a selection of reaction observables particularly sensitive to the isovector part of the interaction, i.e. to the symmetry term of the nuclear Equation of State (EoS) At low energies the behavior of the symmetry energy around saturation influences dissipation and fragment production mechanisms. Predictions are shown for deep-inelastic and fragmentation collisions induced by neutron rich projectiles. Differential flow measurements will also shed lights on the controversial neutron/proton effective mass splitting in asymmetric matter. The high density symmetry term can be derived from isospin effects on heavy ion reactions at relativistic energies (few AGeV range), that can even allow a “direct” study of the covariant structure of the isovector interaction in the hadron medium. Rather sensitive observables are proposed from collective flows and from pion/kaon production. The possibility of the transition to a mixed hadron-quark phase, at high baryon and isospin density, is finally suggested. Some signatures could come from an expected “neutron trapping” effect.
arXiv:nucl-th/0609081v1 29 Sep 2006
Isospin Dynamics in Heavy Ion Collisions: EoS-sensitive Observables
M.Di Toro
a
, V.Baran
b
, M.Colonna
a
, G.Ferini
a
, T.Gaitanos
c
, V.Greco
a
, J.Rizzo
a
,
H.H.Wolter
c
.
a
Laboratori Nazionali del Sud INFN, I-95123 Catania, Italy,
and Physics-Astronomy Dept., University of Catania
b
Dept.of Theoretical Physics, Bucharest Univ., Magurele, Bucharest, Romania
c
Dept. f¨ur Physik, Universit¨at M¨unchen, D-8574 8 Garching, G ermany
Heavy Ion Collisions (HIC) r epresent a unique tool to probe the in-medium nuclear
interaction in regions away from saturation and at high nucleon momenta. In this report
we present a selection of reaction observables particularly sensitive to the isovector part
of the interaction, i.e. to the symmetry term of the nuclear Equation of State (EoS) At
low energies the behavior of the symmetry energy around saturation influences dissipation
and fragment production mechanisms. Predictions are shown for deep-inelastic and frag-
mentation collisions induced by neutron rich projectiles. Differential flow measurements
will also shed lights on the controversial neutron/proton effective mass splitting in asym-
metric matter. The high density symmetry term can be derived from isospin effects on
heavy ion reactions at relativistic energies (few AGeV range), that can even allow a “di-
rect” study of the covariant structure of the isovector interaction in the hadron medium.
Rather sensitive observables are proposed from collective flows and fr om pion/kaon pro-
duction. The possibility of the transition to a mixed hadron-quark phase, at high baryon
and isospin density, is finally suggested. Some signatures could come from an expected
“neutron trapping” effect.
1. Introduction
The symmetry energy E
sym
appears in t he energy density ǫ(ρ, ρ
3
) ǫ(ρ)+ρE
sym
(ρ
3
)
2
+
O(ρ
3
)
4
+.., expressed in terms of total (ρ = ρ
p
+ρ
n
) and isospin (ρ
3
= ρ
p
ρ
n
) densities.
The symmetry term gets a kinetic contribution directly from basic Pauli correlations and
a potential par t from the highly controversial isospin dependence of the effective interac-
tions [ 1]. Both at sub-saturation and supra-saturation densities, predictions based of the
existing many-body techniques diverge rather widely, see [ 2]. We take advantage of new
opportunities in theory (development of rather reliable microscopic transport codes for
HIC) and in experiments (availability of very asymmetric radioactive beams, improved
possibility of measuring event-by-event correlations) t o present results that are severely
constraining the existing effective interaction models. We will discuss dissipative colli-
ditoro@lns.infn.it
2 M.Di Toro
-200
-150
-100
-50
0
oct(a.u.)
0
10
20
30
40
50
60
N
-200
-150
-100
-50
0
50
oct(a.u)
0
10
20
30
40
50
60
70
-90
-60
-30 0 30
60
90
oct(a.u)
0
50
100
150
200
(a)
(b)
(c)
Figure 1. Distribution of the octupole moment of primary fragments for the
132
Sn +
64
Ni
reaction at 10 AMeV (impact parameters (a):b = 6fm, (b):7fm, (c):8fm). Solid lines:
asysoft. Dashed lines: asystiff
sions in a wide range of energies, from just above the Coulomb barrier up to a few AGeV .
The transport codes are based on mean field theories, with correlations included via hard
nucleon-nucleon elastic and inelastic collisions and via stochastic forces, selfconsistently
evaluated from the mean phase-space trajectory, see [ 1, 3, 4, 5]. Stochasticity is essential
in order to get distributions as well as to allow the growth of dynamical instabilities.
2. Isospin effects on Deep-Inelastic Collisions
Dissipative semi-peripheral collisions at low energies, including binary and three-body
breakings, o ff er a good opportunity to study phenomena occurring in nuclear matter under
extreme conditions with respect to shape, excitation energy, spin and N/Z ratio (isospin).
In some cases, due to a combined Coulomb and a ngular momentum (deformation) effect,
some instabilities can show up [ 6]. This can lead to 3-body breakings, where a light cluster
is emitted from the neck region. Three body processes in collisions with exotic beams
will allow to investigate how the development of surface (neck-like) instabilities, that
would help ternary breakings, is sensitive to the structure of the symmetry term around
(below) saturation. In order to suggest proposals f or the new RIB facility Spiral 2, [
7] we have studied the reaction
132
Sn +
64
Ni at 10AMeV in semicentral events, impact
parameters b = 6, 7, 8fm, where one observes mostly binary exit channels, but still in
presence of large dissipation. Two different behaviors of the symmetry energy below
saturation have been tested: one (asysoft) where it is a smoo t h decreasing function
towards low densities, and a nother one (asystiff) where we have a rapid decrease, [
1]. The Wilczynski plots, kinetic energy loss vs. deflection angle, show slightly more
dissipative events in the asystiff case, consistent with the point that in the interaction
at lower densities in very neutron-rich matter (the neck region) we have a less repulsive
symmetry term. In fact the neck dynamics is rather different in the two cases, as it can be
well evidenced looking at the deformation of the P LF/T LF residues. The distribution
of the octupole moment over the considered ensemble of events is shown in Fig.1 for
the three considered impact parameters. Except for the most peripheral events, larg er
deformations, strongly suggesting a final 3- body outcome, are seen in the asystiff case.
Now, due to the lower value of the symmetry enrgy, the neutron-rich neck connecting
Isospin Dynamics 3
the two systems survives a longer time leading to very deformed primary fragments,
from which eventually small clusters will be dynamically emitted. Finally we expect
to see effects o f the different interaction times on the charge equilibration mechanism,
probed starting from entrance channels with large N/Z asymmetries, like
132
Sn(N/Z =
1.64) +
58
Ni(N/Z = 1.07). Moreover the equilibration mechanism is also directly driven
by the strenght of the symmetry term.
3. Isospin Dynamics in N eck Fragmentation at Fermi Energies
It is now quite well established that the la r gest part of the reaction cross section for
dissipative collisions at Fermi energies goes through the Neck Fragmentation channel, with
IMF s directly produced in t he interacting zone in semiperipheral collisions o n very short
time scales [ 8]. We can predict interesting isospin transport effects for this new frag-
mentation mechanism since clusters are formed still in a dilute asymmetric matter but
always in contact with the regions of the projectile-like and target-like remnants almost at
normal densities. Since the difference between local neutron-proton chemical potentia ls
is given by µ
n
µ
p
= 4E
sym
(ρ
3
), we expect a larger neutron flow to the neck clusters
for a stiffer symmetry energy around saturation, [ 1, 9]. The isospin dynamics can be
directly extracted from correlations between N/Z, alignement and emission times of the
IMF s. The alignment between P LF IMF and P LF T LF directions represents a
very convincing evidence of t he dynamical o r ig in of the mid-rapidity fragments produced
on short time scales [ 10]. The form of the Φ
plane
distributions (centroid and width)
can give a direct informatio n on the fragmentation mechanism [ 11]. Recent calculations
confirm that the light fra gments are emitted first, a general feature expected for that
rupture mechanism [ 12]. The same conclusion can be derived from direct emission time
measurements based on deviations fr om Viola systematics observed in event-by-event ve-
locity correlations between IMF s and the P LF/T LF residues [ 10, 11, 13]. We can figure
out a continuous transition f r om fast produced fragments via neck instabilities to clusters
formed in a dynamical fission of the projectile(target) residues up to the evaporated ones
(statistical fission). Along this line it would be even possible to disentangle the effects of
volume and shape instabilities. A neutron enrichment of the overlap (”neck”) region is
expected, due to the neutron migration from higher (spectator) to lower (neck) density
regions, directly related to the slope of the symmetry energy [ 12]. A very nice new ana l-
ysis has been presented on the Sn + Ni data at 35 AMeV by the Chimera Collab., Fig.2
of ref.[ 14]. A strong correlation between neutron enrichemnt and alignement (when the
short emission time selection is enforced) is seen, that can be reproduced only with a stiff
behavior of the symmetry energy. This is the first clear evid ence in favor of a rel atively
larg e slope (symmetry pressure) around saturation.
4. Effective Mass Splitting and Collective Flows
The problem of Momentum Dependence in the Isovector channel (Iso MD) is still
very controversial and it would be extremely important to get more definite experimen-
tal information, see the recent refs. [ 15, 16, 17, 18, 19, 20]. Intermediate energies are
important in order to have high momentum particles and to test regions of high baryon
(isoscalar) and isospin (isovector) density during the reactions dynamics. Collective flows
4 M.Di Toro
[ 21] are very g oo d candidates since they are expected to be very sensitive to the mo-
mentum dependence of the mean field, see [ 22, 1]. The transverse flow, V
1
(y, p
t
) = h
p
x
p
t
i,
provides information on the anisotropy of nucleon emission on the reaction plane. Very
important for the reaction dynamics is the elliptic flow, V
2
(y, p
t
) = h
p
2
x
p
2
y
p
2
t
i. The sign
of V
2
indicates the azimuthal anisotropy of emission: on the reaction plane (V
2
> 0) or
out-of-plane (squeeze out, V
2
< 0) [ 21, 22]. We have then tested the Iso MD of
the fields just evaluating the Difference of neutron/proton transverse and elliptic flows
V
(np)
1,2
(y, p
t
) V
n
1,2
(y, p
t
) V
p
1,2
(y, p
t
) at various rapidities and transverse momenta in
semicentral (b/b
max
= 0.5)
197
Au +
197
Au collisons at 250AMeV , where some proton data
are existing from the F OP I collaboration at GSI [ 23, 24]. The transport code has been
implemented with a BGBD like [ 25, 26] mean field with a different (n, p ) momentum
dependence, see [ 16, 17, 18], that allow to follow the dynamical effect of opposite n/p ef-
fective mass splitting while keeping the same density dependence of the symmetry energy.
Figure 2. Difference between proton and neutron V
1
flows in a semi-cent ral reaction
Au+Au at 250 AMeV for three rapidity ranges. Upper Left Panel: |y
(0)
| 0.3; Upper
Right: 0.3 | y
(0)
| 0.7; Lower Left: 0.6 |y
(0)
| 0.9. Lower Right Panel: Comparison
of the V
1
proton flow with FOPI data [ 23] for three rapidity ranges. Top: 0.5 |y
(0)
|
0.7; center: 0.7 |y
(0)
| 0.9; bottom: 0.9 |y
(0)
| 1.1.
For the difference of nucleon transverse flows, see F ig. 2, the mass splitting effect is
evident at all rapidities, and nicely increasing at larger rapidities and transverse mo-
menta, with more neutron flow when m
n
< m
p
. Just to show that our simulations give
realistic results we compare in lower right panel of Fig. 2 with the pro t on data of the
F OP I collabora tion for similar selections of impact parameters rapidities and transverse
Isospin Dynamics 5
momenta. The same analysis has been performed for the difference of elliptic flows, [
17]. Again the mass splitting effects are more evident for higher rapidity and tranverse
momentum selections. In particular the differential elliptic flow becomes negative when
m
n
< m
p
, revealing a faster neutron emission and so more neutron squeeze out (more
spectator shadowing). The measurement o f n/p flow differences appears essential. Due to
the difficulties in measuring neutrons, our suggestion is to measure the difference between
light isobar flows, like
3
H vs.
3
He and so on. We expect to clearly see the effective mass
splitting effects, maybe even enhanced due to larger overall flows shown by clusters, see [
1, 27].
5. Relativistic Collisions
Finally we focus our attention on relativistic heavy ion collisions, that provide a unique
terrestrial oppo rt unity to probe the in-medium nuclear interaction at high densities. An
effective Lagrangian a pproa ch to the hadron interacting system is extended to the isospin
degree of freedom: within the same frame equilibrium properties ( EoS, [ 28]) and trans-
port dynamics [ 29, 30] can be consistently derived. Within a covariant picture of the
nuclear mean field, for the description of the symmetry energy at saturation (a
4
param-
eter of the Weizs¨aecker mass formula) (a) only the Lorentz vector ρ mesonic field, and
(b) both, the vector ρ (repulsive) and scalar δ