Nucleon-nucleon cross sections in symmetry and asymmetry nuclear matter

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Nucleon-nucleon cross sections in symmetry and
asymmetry nuclear matter
Hong-fei ZHANG (???)

• School of Nuclear Science and Technology,
• Lanzhou University, 730000, China

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Collaborators

• U. Lombardo
• Z.H. Li
• F. Sammarruca
• W. Zuo
• J. M. Dong

Papers on the work
1. H.F. Zhang, Z.H. Li, U. Lombardo, P.Y. Luo,
and W.Zuo, Phys. Rev. C, Vol. 76, 054001
(2007). 2. H.F. Zhang, U. Lombardo, J.M. Dong,
Z.H. Li, W. Zuo, Nucleon-nucleon cross
sections and nucleon mean free paths in
asymmetricnuclear matter In preparation.
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Outline

• Introduction
• BHF with microscopic three-body forces
• Nucleon-nucleon cross sections in symmetry
• and asymmetry nuclear matter
• Summary

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?. Introduction

• Heavy-ion collisions are theoretically described
  by transport-model simulations whose input data
  are the in-medium cross sections and the nuclear
  mean field. Being intimately related to each
  other through the nuclear matter equation of
  state (EOS), they must be consistently
  determined.
• In-medium cross sections are necessary to study
  the mean free path of nucleons in nuclear matter
  and thus nuclear transparency.
• Size of exotic nuclei

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?. BHF with Microscopic three-body forces
In asymmetry nuclear matter, one can define the
isospin asymmetry parameter
For a given total density?and asymmetryß.a bare
two-body forcev as input, solve the Equs
self-consistently
Pauli operator
where
BBG equation
BHF
In-medium effective Interaction G matrix
s.p. energy
Defect function
s.p. auxiliary potentials
vv3eff
v
V3eff is reduced to a density-dependent two-body
force
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?. Nucleon-nucleon cross sections
In Brueckner theory, the G matrix plays the role
of the in-medium scattering amplitude, with
medium effects being introduced through the mean
field and Pauli blocking. In the zero density
limit, the G matrix reduces to the T martix, and
the Brueckner-Beth-Goldstone (BBG) equation to
the Lippmann-Schwinger equation.
Beyond the scattering amplitude, nucleon-nucleon
collisions in nuclear matter are also driven by
kinematic degree of freedom, i.e.,entrance flow
and density of states in the exit channel.
Both are related to the nucleon effective mass,
which, in turn, is related to the self-energy.
The latter is modified by a 3BF, which
also generates quite large rearrangement terms,
leading to a large reduction of the effective
mass. Thus one can expect that 3BFs might have a
strong influence on the in-medium cross
section, as they depend quadratically on the
effective mass.
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Real and imaginary parts of the 1S0 components
of the G matrix
While 3BFs are negligible at low density, they
start to be noticable at saturation density and
become more and more effective as density
increase.
The real part of the G matrix is reduced due to
Pauli blocking and dispersive effects.
The imaginary part of the G matrix, which is
related to the particle-hole excitations, become
larger because of the 3BF enhancement of the
ground correlations.
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2. Effective mass
In the medium, the additional contribution from
the self-energy can be reasonablely approximated
by replacing the bare mass with the effective
mass
The effective mass becomes substantially smaller
with the inclusion of the 3BF, an effective which
will impact the in-medium cross sections through
the level density in the entrance and exit
channels, along with the 3BF enhancement of the
repulsive components in the effective interaction.

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3 Free-space cross sections
Argonne V14 is used
The total cross sections converge rapidly to the
corresponding experimental values with increasing
number of partial waves
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4. Total cross sections for identical nucleons
Up to the saturation density, the effect of the
3BF is small, and the medium suppression is
mainly controled by the reduction of density of
state due to Pauli blocking.
At the higher density, the 3BF produces a larger
reduction of the cross section, which persists up
to high energy. The latter is mainly due to the
strong 3BF renormalization of the effective mass.
The scattering amplitude is also affected by the
3BF
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5. Differential cross section for identical
nucleons
The reduction of the cross sections is more
sizable in the forward and backward
directions, since low momentum transfers are
strongly suppressed by the Pauli principle. This
effect leads to distributions that are almost
flat at high density. This feature justifies the
frequency practice of adopting isotropic cross
sections in HIC simulations.
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6. Total cross sections for nonidentical nucleons
In scattering of distinguishable nucleons, the
T0 component of the interaction is also
included. As a consequence, the free cross
sections for unlike particle is larger than the
one for like particles, a property which remains
true in the medium.
The 3Bf effect on the cross section is evident,
especially in high density.
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7. Differential cross section for nonidentical
nucleons
The differential cross section is strongly
asymmetric. The in-medium values exhibit similar
asymmetry although less pronounced.
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8. Comparison with DBHF predictions
Energy and density dependent appear
quite consistent among the two cases,
although the cross sectios from 2BF3BF is
somewhat larger than the values from DBHF across
the broad.
The cross sectios from 2BF3BF are in
good agreement with thevalues from DBHF, with
the exception of the highest density.
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Examination of the last column in the left table
clearly suggests that 3BF other than Z diagrams
are the main cause of the discrepancies between
the DBHF and BHF3BF predictions of the EOF
and, consequently, of the respective
cross sections.
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9. nucleon-nucleon cross section in
asymmetry nuclear
Bonn B potential and a new version of three-body
Force are used, Dr. Z.H. li will give a talk
on the improvement for the previous BHF with 3BF
!
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Isospin dependent of total nucleon-nucleon
cross sections
The lowering (rising) proton (neutron) Fermi
mementum and the reduced (increased) proton
(neutron) effective mass tend to move the cross
section in opposite direction. With pauli
blocking applied to intermediate and final
states, the final balance is that The
neutron-neutron effective cross section is more
strongly suppressed.
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?. Summary

• The TBF provides a repulsive contribution to
• the EOS and improves remarkably the predicted
  
• saturation properties, which suppress the
• magnitude of cross sections.
• The TBF from the Z-diagram provides the
• saturation mechanism and gives the main
• relativistic effect in DBHF approach.

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• Thank you !
• ??!