Transcript PowerPoint 프레젠테이션

Nucleon-nucleon cross sections in symmetry
and asymmetry nuclear matter
Hong-fei ZHANG (张鸿飞）
School of Nuclear Science and Technology,
Lanzhou University, 730000, China
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 asymmetric
nuclear matter
In preparation.
Outline
• Introduction
• BHF with microscopic three-body forces
• Nucleon-nucleon cross sections in symmetry
and asymmetry nuclear matter
• Summary
Ⅰ. Introduction
•
Heavy-ion collisions are theoretically described by transport-
model simulations whose input data are the in-medium cross se
ctions and the nuclear mean field. Being intimately related to ea
ch other through the nuclear matter equation of state (EOS), th
ey must be consistently determined.
•
In-medium cross sections are necessary to study the mean fre
e path of nucleons in nuclear matter and thus nuclear transpare
ncy.
•
Size of exotic nuclei
Ⅱ. BHF with Microscopic three-body forces
In asymmetry nuclear matter, one can define the isospin asymmetry parameter
For a given total densityρand asymmetryβ.a bare two-body forcev as input, solve the Equs self-consistently：
Pauli operator
where
BBG equation
s.p. energy
BHF
In-medium effective
Interaction G matrix
Defect function
s.p. auxiliary potentials
v
v+v3eff
V3eff is reduced to a de
nsity-dependent twobody force
12 (r , r )   r , r  |
Q
G 12
e
Ⅲ. 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.
1.
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.
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.
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
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
5. Differential cross section for identical nuc
leons
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.
6. Total cross sections for nonidentical nucleons
In scattering of distinguishable nucleons, the T=0 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.
7. Differential cross section for nonidentical nuc
leons
The differential cross section is strongly asymmetric. The in-medium values
exhibit similar asymmetry although less pronounced.
8. Comparison with DBHF predictions
The cross sectios from 2BF+3BF are in good
agreement with thevalues from DBHF, with the
exception of the highest density.
Energy and density dependent appear quite
consistent among the two cases, although
the cross sectios from 2BF+3BF is somewhat
larger than the values from DBHF across the
broad.
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
BHF+3BF predictions of the EOF and,
consequently, of the respective cross
sections.
9. nucleon-nucleon cross section
in asymmetry nuclear
50
-3
 = 0.17 [ fm ]
 = 0.80
pn
pp
nn
NN [ mb ]
40
30
20
10
100
150
200
250
300
350
400
E [ MeV ]
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 !
Isospin dependent of total nucleon-nucleon
cross sections
25
 = 0.17 [ fm
pn
pp
nn
-3
]
E = 300 [ MeV ]
25
pn
pp
nn
-3
]
E = 212 [ MeV ]
20
NN [ mb ]
NN [ mb ]
20
 = 0.34 [ fm
15
15
10
10
5
0.0
0.1
0.2
0.3
0.4

0.5
0.6
0.7
0.8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8

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.
Ⅳ. 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.