Probing the Equation of State of NeutronRich Matter with HeavyIon Reactions

1
Probing the Equation of State of Neutron-Rich
Matter with Heavy-Ion Reactions

• Gao-Chan Yong
• Institute of Modern Physics, Chinese Academy of
  Science
• Bao-An Li
• Arkansas State University, USA
• Wei Zuo
• Institute of Modern Physics, Chinese
  Academy of Science

• Equation of State and Symmetry Energy of
  Neutron-Rich Matter
• A Transport Model for Nuclear Reactions Induced
  by Radioactive Beams
• 3. Determining the Equation of State of
  Neutron-Rich Matter
• 4. Summary

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?. A great deal of information
about the EOS of symmetric matter E(?,0) has been
obtained from studying heavy-ion reactions for
almost 30 years. ?. Further progress on
determining the E(?,0) requires a better
determination of the Esym(?). ?. The symmetry
energy itself is very important for many
interesting questions in both nuclear physics and
astrophysics?. Nuclear reactions induced by
neutron-rich nuclei provide a unique opportunity
to constrain the symmetry energy Esym(?) in
neutron-rich matter in a broad density range.
Equation of State of neutron-rich matter at T0,
density ? and isospin asymmetry
is
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Esym (?) predicted by microscopic many-body
theories
Symmetry energy (MeV)
DBHF
RMF
BHF
Effective field theory
Greens function
Variational
Density
A.E. L. Dieperink et al., Phys. Rev. C68 (2003)
064307
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with
3-body force
without
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The EOS of symmetric and pure neutron matter for
2?0lt ? lt 5?0 using flow data
P. Danielewicz, R. Lacey and W.G. Lynch Science
298, 1592 (2002)

• Corresponding EOS for neutron matter
• Two regions correspond to two different
  Esym(?), the width is completely due to the
  uncertainty in Esym(?).

• Zero-temperature EOS for symmetric nuclear
  matter. The shaded region corresponds to the
  region of pressure consistent with the
  experimental flow data. The various curves and
  lines show predictions for different symmetric
  matter.

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Comparing momentum-dependent IBUU04 calculations
with data on isospin transport /neutron-skin in
208Pb
Most acceptable result from experiments Esym(?)
31.6 (?/?0 )0.69 for ?lt1.2?0 Kasy(?0)-500_50
MeV
B.A. Li and L.W. Chen, nucl-th/0508024 Andre
W.Steiner and Bao-An Li, nucl-th/0505051
Isobaric incompressibility of asymmetric nuclear
matter
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Initialization procedures
(1) r-space distribute n and p according to
predictions by structure models, e.g., RMF (2)
p-space using local Thomas-Fermi (3) check
stability
RMF (TM1)
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Symmetry energy and single nucleon potential used
in the IBUU04 transport code for reactions with
radioactive beams
stiff
soft
HF using a modified Gogny force


B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC
69, 034614 NPA 735, 563 (2004).
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Neutron-proton effective mass splitting in
neutron-rich matter
With the modified Gogny effective
interaction B.A. Li, C.B. Das, S. Das Gupta and
C. Gale, PRC 69, 034614 (2004) NPA 735, 563
(2004).
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Momentum and density dependence of the symmetry
potential
Lane potential extracted from n/p-nucleus
scatterings and (p,n) charge exchange reactions
provides only a constraint at ?0
for Ekin lt 100 MeV P.E. Hodgson, The Nucleon
Optical Model, World Scientific, 1994 G.W.
Hoffmann et al., PRL, 29, 227 (1972). G.R.
Satchler, Isospin Dependence of Optical Model
Potentials, 1968
The used Lane potential is well consistent with
the existed experiment data
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Nucleon-nucleon elastic cross sections in
neutron-rich matter for intermediate energy
collisions
in neutron-rich matter
is the reduced mass of the colliding pair NN in
medium
NN cross section in free-space

• In-medium xsections are reduced
• nn and pp xsections are splitted
• due to the neutron-proton effective mass
  slitting in neutron-rich matter

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Nucleon-nucleon in-elastic cross sections in
neutron-rich matterfor intermediate energy
collisions
B.J. VerWest. et al PRC25,(1982)1979
Detailed balance principle
Only elastic cross sections Breit-Wigner formula
Few publications cover in-medium inelastic NN
cross sections, especially for asymmetric nuclear
matter, So still free inelastic NN cross sections
are used
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Predictions for reactions with neutron-rich
beamsat FAIR/GSI, NSCL/MSU, RIA/USA, CSR/Lanzhou

• Isospin distillation/fractionation
• p - yields and p -/p ratio
• Neutron-proton differential transverse flow
• Double n/p ratio
• Double p -/p ratio ?

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Formation of dense, asymmetric nuclear matter
Soft Esym
n/p ratio of the high density region
Soft Esym
Stiff Esym
Stiff Esym
B.A. Li, G.C. Yong and W. Zuo, PRC 71, 014608
(2005)
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Isospin fractionation (distillation) at isospin
equilibrium low density region is more
neutron-rich with stiff symmetry energy
Isospin asymmetry of free nucleons
soft
stiff
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Near-threshold pion production with radioactive
beams at RIA and GSI
soft
stiff
yields are more sensitive to the symmetry energy
Esym(?) since they are mostly produced in the
neutron-rich region formed preferentially with
the soft symmetry energy
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Pion ratio probe of symmetry energy
Connection with the symmetry energy
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Time evolution of p-/p ratio in central
reactions
From the overlapping n-skins of the colliding
nuclei
soft
stiff
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Differential p-/p ratios
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Transverse flow as a probe of the nuclear EOS
px
y
Neutron-proton differential flow as a probe of
the symmetry energy
for n and p
symmetry potential is generally repulsive for
neutrons and attractive for protons
Bao-An Li, PRL 85, 4221 (2000).
G.C. Yong, B.A. Li, W. Zuo, Chin. Physics Letter
(2005).
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Comparing momentum-dependent IBUU04 calculations
with data on isospin transport /neutron-skin in
208Pb
Most acceptable result from experiments Esym(?)
31.6 (?/?0 )0.69 for ?lt1.2?0 Kasy(?0)-500_50
MeV
B.A. Li and L.W. Chen, nucl-th/0508024 Andre
W.Steiner and Bao-An Li, nucl-th/0505051
Isobaric incompressibility of asymmetric nuclear
matter
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Double n/p ratio
to calculate for NSCL/MSU
The single n/p ratio in the two systems
The large difference of n/p ratio for Sn124Sn124
is due to large isospin asymmetry of the
reaction system
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• the main advantage of the double n/p ratio is to
  reduce
• effects of the Coulomb force and
  inefficiencies of detecting low energyneutrons

2. the symmetry energy effects are much stronger
for peripheral collisions
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Coulomb effects on p-/p ratio
Double p-/p ratio is also needed to reduce
Coulomb effects
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Double p-/p ratio
Unfortunately, we can not disentangle the
symmetry energy between X 0 and X -1 by using
the double pion-/pion ratio. Big impact
parameter is ok?
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Summary

• ? Transport models are invaluable tools for
  studying the EOS of neutron-rich matter
• ? Experiments indicate that the symmetry energy
  at about Esym(?) 31.6(?/?0 )0.69
• ? Radioactive beams at MSU, RIA and GSI
• will allow us to study the EOS of n-rich
  matter using several sensitive probes of the
  symmetry energy Esym(?).

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thank you