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The study of dynamical effects of isospin
on reactions of p + 112-132Sn
Li Ou and Zhuxia Li
(China Institute of Atomic Energy, Beijing 102413)
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Outline
1) Introduction
2) The ImQMD model
3) The mechanism of intermediate energy proton
induced reactions
4) The dynamical effects of isospin on p + 110-132Sn
5) Summary
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I. Introduction
The present status for the study of the density dependence of
symmetry energy:
Quite a few observables in heavy ion collisions have been
proposed as candidates of probes of symmetry energy
Particles emitted : n/p ratio, double n/p ratio, t/3He,
, K+/K-,   /  
Isoscaling , R12(N,Z)=Y2(N,Z)/Y1(N,Z)=Cexp(  N+ Z)
Flow effects: elliptic flow, neutron-proton differential flow
Isospin diffusion,
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Review article: L.W.Chen, et.al.Nucl-th/07042340
Density dependence of symmetry energy at low densities
by comparison between data and the transport model
calculations
u   / 0 )0.69
Esym=31.6(
D.V. Shetty, et.al. PRC75,34602
Isoscaling parameters(data with AMD)
u   / 0 )1.05
Esym=31.6(
L.W.Chen, et.el., PRL94,032701
Isospin diffusion (data with IBUU)
It is still needs further conformation for the density
dependence of the symmetry energy at low densities
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motivations for studying intermediate energy
p + A reactions
1) Wide applications in many fields such as material and biology
science, medical therapy, accelerator-driven subcritical reactors
for nuclear waste transmutation.
There have been accumulated a lot of experimental data which
can be used to test the theoretical model.
2) There is a great demand for a good theoretical model in the usage
of the calculations of spallation reactions for various applications
3) The mechanism is relatively simple compared with A+A reactions.
The reaction process is more intuitive.
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II. ImQMD05 model
The motion of particles is described in
6-A dimensional phase space
Each nucleon is represented by a wave packet
Wang, Li, Wu, Phys.Rev.C65,064608(2002),
Phys.Rev C69,024604（2003）,
Phys.Rev C69,034608(2004)
H
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ImQMD: Improvements
more realistic energy density functional is used
the Pauli blocking in the collision term is treated
more rigorously
phase space occupation number constraint is introduced
system size dependent wave packet width
the improvement in initial conditions
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Wang, Li, Wu, Phys.Rev.C65, 064608(2002)
Zhang, Li, Phys.Rev.C71, 024604(2005),
74,014602(2006)
ImQMD05
Version II
The potential energy density functional is taken
from the Skyrme interaction directly
Surface energy
Surface symm.energy
Bulk symmetry energy
Correction to mass, Thomas-Fermi appox.
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The relations between the parameters in ImQMD and
Skyrme interaction
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The time evolution of binding energies and rms radii
of 56Fe and 208Pb
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Charge distribution of products in HIC
Zhang, Li, PRC71(2005)24604
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Charge distribution of products
Zhang,Li PRC74,014602(2006)
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Exp.data W. Trautmann and W.Reidorf
III. The mechanism of proton induced reactions
300
dynamical process+statistical decay
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The influence of effective interactions(SkP,SIII)
7.50
300
600
1500
SkP is better
in describing
DDCS of
neutrons
Different interactions influence the low energy part and
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The contributions from reactions with different impact parameters
Large impact parameters
forward angles
near Ep
Small impact parameters
low energy part
backward angles
The contribution from
b/bmax= 0.38, 0.69
are the most important
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p + 16O
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P+27Al
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P+56Fe
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P+208Pb
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IV. Dynamical effects of isospin on
p + 112-132Sn
excitation functions of reaction cross sections
Usym=Ulin
is the probability
for inelastic scattering
process
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The behavior of energy dependence of  r is the same
for Sn isotopes and is in agreement with exp. data
The magnitudes of  r increases with A
The spectrum of emitted protons in 100MeV p+A
with different impact parameters
112Cd
112Sn
132Ba
132Sn
132Sn
el.sc.
el.sc.
More neutron-rich nuclei have smaller elastic cross sections
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i.e. larger reaction cross sections
as function of A1/3 for p+A reactions
Sn
Carlson
empiric formula(Carlson)
 -SL for nuclei along  -stability line
Rp and r0 are fitting parameters:
R0=1.45fm for Ep=25-100MeV
R0=1.35 fm for Ep>180MeV
R0=1.40fm
for whole range of energy
Obvious departure of the line for
Sn isotopes from the empiric formula
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The lines for empiric formula are moved
upwards 0.38, 0.38, 0.2, 0.14fm for
E=100,200,250,300MeV,respectively
Origin of isospin effects:
Symmetry energy
Isospin dependence of nucleon-nucleon cross sections
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is about 2-3 time larger than
at low energies
How do the effects from theses factors interplay
dynamically ?
Dynamical effects of symmetry energy on p + 112-132 Sn
1) The thickness of neutron skin of target is strongly correlated
with the density dependence of the symmetry energy
2) The symmetry potential of target gives an attraction to incident
proton, directly influences on the motion of the incident proton.
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The dependence of the thickness of the neutron skin
of 112,132Sn and 132Ba,112Cd on the symmetry energy
Sampling with
the constraint
of neutron skin
The stiffer the symmetry energy is ,
the larger the thickness of neutron skin is
Neutron density distribution is different
How
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changes?
>
,
100MeV p + 132 Sn
proton
Peripheral collisions
132Sn
Symmetry potential of target
provides an attractive force
on incident proton, which
directly influences the motion
of incident proton
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0.0
0.5
 / 0
1.0
1.5
Vsym depends on  ,  , 
The dependence of number of collisions for emitted
protons on the asymmetry of target
SkP
The ratios between the
colls. numbers of emitted
protons for 132Sn/132Ba
and 112Sn /112Cd
>
  0.24
132Sn
  0.15
132Ba
Neutron skin effect
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Effect of symmetry energy I
100MeV p + 132 Sn
The number of collisions
experienced by the emitted
protons as function of impact
parameters for different
symmetry energies
R=
Ncoll(with sym.pot)
Ncoll(no sym.pot.)
the collisions experienced by emitted protons are
enhanced for the softer symmetry energy case
Soft symmetry energy leads to larger reaction cross sections
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Effect of symmetry energy II
100MeV p + 132Sn b=7.5fm
angular distribution of emitted protons
with no two-body collision experienced
distributed at front angle
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angular distribution of emitted protons
with two-body collisions experienced
distributed in 00-1800
angular distribution of emitted protons depends
on the symmetry energy obviously
Effect of symmetry energy II
100MeV p + 132Sn b=8.5fm
Angular distribution for emitted protons
experienced no two-body collisions
(elastic scattering)
Angular distribution for emitted protons
experienced with two-body collisions
(reactions)
Angular distribution of emitted protons is very sensitive to
the density dependence of the symmetry energy!
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The influence of the different symmetry energies
on the reaction cross sections as function of A1/3
measurement
of  r for Sn
isotopes can give
a very stringent
constraint to the
density dep. of
symmetry energy
The slopes of
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as function of A1/3
Density distributions of 132Sn
for normal and enlarged neutron skin
<r2>1/2 is enlarged 0.1 fm
for large thickness case
b/bmax
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0.38
0.69
100MeV p + 112-132Sn
Enlarged thickness of neutron skin
In general, the effect is reduced but no feature
change in the slope of
as function of A1/3
for different symmetry energies
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thin
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thick
~ A1/3 is sensitive to the symmetry energy
but not very sensitive to the thickness of neutron skin
100MeV p + 112-132Sn
The slope of
as function of A1/3
132Sn
Normal N.S.
Enlarged N.S.
no S.E.,only cross sections
1) The general feature is the same :
is sensitive to
symmetry energy and the slope is enhanced for soft symmetry
energy for Sn isotopes
2) The difference in the slope between Sn isotopes and nuclei on
 -stability line depends on the thickness of neutron neck
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100MeV n + A reactions
Sn
Shifted 0.1
Shifted 0.2
Angular distribution of
emitted neutrons
sensitive to the symmetry
energy
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reaction cross section as function
of system size
is less sensitive to the
density dep. of S.E.
The reaction cross sections are
suppressed for neutron-rich targets
100MeV n + A reactions
Enlarged the thickness
of neutron skin
the comparison
The influence of different density dep. of symmetry energy
is weeker than p+Sn reactions
The effect of the thickness of neutron skin is enhanced
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Summary
1) The ImQMD(SkP inter.)+SDM can describe
intermediate energy proton induced reactions well.
2) The reaction cross sections for p + Sn isotopes is
departure from the systematic behavior of p + nuclei
along  - stability line, which show strong isospin effects
3) The measurement of  r and the angular distribution of
emitted protons for p + Sn isotopes can give a stringent
constraint for the density dependence of symmetry energy.
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Thanks!
Thanks!
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