The sensitivity of probes to DDSP - uni

Report
The sensitivity of probes to
DDSP at high densities
Qingfeng Li
* DDSP: Density dependent symmetry potential
Outline





Brief introduction to the DDSP.
Predicted sensitive probes to DDSP at high
densities.
However, too many (huge) uncertainties from
other potentials, from collision term, from
models and from experiments, etc are awaiting
us to solve.
Several examples.
No conclusions, only remarks.
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SP is relatively small
Binding energy from Liquid-drop mass formula:
=
Isospin-dependent EoS (energy density as a function of  and ):
E(,  )  E(,0)  Esym ( ) 2  O( 4 ),   (n   p ) / 
Initial 2: Au: 0.0392; Pb:0.0447
Zr96:0.0278;Ru96:0.0069
Sn132:0.0587;Sn124:0.0375
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It would not be a big deal
if the uncertainty in Esym was not big
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The origin of the DDSP ---From the
RBUU point of view.
L  LF  LI

i
1
1
LF    x        x   M N  x   x       F  F 
2
2
4

1   1

        L  L  U    U    U    U   
2
4
 
1 

Lint  g   g     g        g   
2



p
 


p

X






X
,
p
,
t



Re
X
,
p
,
t

 X HF
F

p

*
M
Re

 
X

 X   Re F  X , p, t  p   p Re F  X , p, t  

H

X


M*
 *
f X, p
E  p




 
 
1
dp2 dp3 dp4
4


 
2


p

p

p
2
3  p4  E  p   E  p2   E  p3   E  p4 
2 2 3 2 3 2 3


 Wel ,in  p, p2 , p3 , p4  Fel2,in  Fel1,in
~  d 3 p2  v
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d el ,in s, t 
d


d
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The isospin effects in RBUU
ESym
2
2
g2
1 K f 1 g

 { 2 2(
6 E f 2 4m m
M
*2
)} B
g
EF2 [1  2 A( K f , M * )]
m
2
Hartree Term
A( K f , M ) 
*
 pp ,nn ,np   d
d pp ,nn ,np
d
1
 2  d cos
1
d pp ,nn ,np
d
4
(2 )3
 d k (k
k2
3
2
2
 M * )3 / 2
2i
Fi t   2
i  t

Interaction
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Direct Term
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Exchange Term
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Density dependence of symmetry
potential at low and high densities

Phenomenological
Skyrme parameter
sets
18 sets
From B.
Alex Brown,
PRL 85,
5296 (2000)
Uncertainty comes mainly
from high density region
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Is the DDSP at high densities mainly
important to neutron star?
It might impact on nuclear physics when
one investigates the HICs induced by
radioactive beam at intermediate
energies.
 Now, the community tries to find the
effect of DDSP on observables from
HICs at intermediate energies (~0.252.0A GeV)

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Predicted probes of DDSP at high
densities from the HICs
 The
(double) ratio of multiplicities of
charged nucleons, s, s, pions, kaons
and hard photons as functions of Eb, b,
N/Z; pt, y, Ekin, etc.
 The (double) flow, flow difference,
differential flow of nucleons, pions as
functions of Eb,b,N/Z,pt, y, Ekin, etc.
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Difficulties and Uncertainties

With the increase of beam energy (to ~A GeV):
①
the compression stage is shorter
The effect of nucelar MF on dynamics is weaker
The isospin asymmetry during dynamic evolution is reduced
②
③





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The dynamics is dominated by CT rather than the
nuclear MF.
In addition to  and , other resonances and
mesons produce which makes the situation much
more complicated
Large medium modification on the collision term
The relativistic effects in kinetic or dynamic
transports
……(from experimental sides?)
Not easy to achieve our goal
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Meson multiplicity ratio and double ratio
New “puzzles”
Eb=1.528A GeV
INM
Au+Au
(N/Z=1.494)
HIC
132Sn+124Sn
From W. Reisdorf etal, NPA781,459(2007)
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From X. Lopez etal PRC75,
011901(R) (2007)
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The update of UrQMD for heavy ion
reactions at Eb~0.1-2A GeV

SP for all baryons. (for some non-nucleonic particles,
C-G coefficients of isospin coupling are employed.
 MD for all baryons. (isospin independent)
 Coulomb interaction between two mesons or MesonBaryon.
 More EoS parameter sets. (H, S, HM, SM), which
describe the ground state properties of finite nuclei
equally well (KNM ranges from 200 to 400 MeV).
 The medium modified N-N elastic cross section
(optional).
 Relativistic effect on relative distances in phase space
of two particles (Lorentz transformation).
See, e.g., JPG32,151(2006) and PLB659,525(2008)
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Example I
uncertainty from Afterburner program


1.
2.

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To construct clusters of nucleons, one Afterburner
analyzing program is usually used to couple to the
transport model.
But, usually, it is paid less attention. There exist
two types:
In QMD-like models, the phase-space coalescence
model is employed.
In BUU-like models, a density cut (in coordinate
space) is often used to find out free nucleons.
Due to the smallness of DDSP effect, one should
check the effect from the difference of the two
types.
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Cluster freeze-out
“Coalescence Model”
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“Density-cut”
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pt dependence of the N/Z ratio
c=0/10
Sensitive to SP at both low and high densities
n/p (double) ratios at small pt are influenced by the freeze-out criteria
The ratios at large pt are not influenced by the freeze-out criteria.
Argument: one needs to investigate the isospin dependent momentum dependent term
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Example II:
contamination in  reconstruction
 at freeze-out
“contaminated reconstruction” mode
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“clean reconstruction” mode
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pt dependence of 0/++ ratio
“contamination” effect is
huge at small Ekin due to
the rescattering of nucleons.
Two modes give two
different ratios (L) and scaled
ratios (R) vs Ekin in both
low and high regions.
The reconstruction should be analyzed with care.
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Example III:
Mesonic Coulomb Potential and reduction of N channel on
Pion flows (v1 and v2)
0.05
1.5A GeV
FOPI data, from W.Reisdorf etal, NPA781,459(2007)
-
v1
-
+
0
=<px/pt>
+
0.04
-v2
=<(px2-py2)/pt2>
0
b0:0.25-0.45
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Several remarks

The isospin-independent terms are also needed to
check carefully when investigating the symmetry
potential at high densities.
 Nucleon-related quantities should be paid much more
attention.
 Higher beam energy HIC is not always better. HICs at
beam energies ~100-800A MeV are recommended at
this time.

Better Afterburner program is needed

Detailed comparison between transport models is
urgently needed. I call for closer cooperation
between theoretical and experimental physicists.
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As were done before
We will be the next, yes?
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Thanks
Contact me?
[email protected]
[email protected]
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