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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) Introduction2) The ImQMD model 3) The mechanism of intermediate energy proton induced reactions4) The dynamical effects of isospin on p + 110-132Sn5) 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 flowIsospin diffusion,

Review article: L.W.Chen, et.al.Nucl-th/07042340

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Esym=31.6( )0.69

Esym=31.6( )1.05

Isoscaling parameters(data with AMD)

Density dependence of symmetry energy at low densitiesby comparison between data and the transport model calculations

Isospin diffusion (data with IBUU)

It is still needs further conformation for the density dependence of the symmetry energy at low densities

D.V. Shetty, et.al. PRC75,34602

L.W.Chen, et.el., PRL94,032701

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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

Wang, Li, Wu, Phys.Rev.C65,064608(2002),Phys.Rev C69,024604（ 2003） ,Phys.Rev C69,034608(2004)

Each nucleon is represented by a wave packet

H

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phase space occupation number constraint is introduced

system size dependent wave packet width

ImQMD: Improvements

the Pauli blocking in the collision term is treated more rigorously

more realistic energy density functional is used

the improvement in initial conditions

Wang, Li, Wu, Phys.Rev.C65, 064608(2002)Zhang, Li, Phys.Rev.C71, 024604(2005), 74,014602(2006)

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Version II

The potential energy density functional is taken from the Skyrme interaction directly

ImQMD05

Correction to mass, Thomas-Fermi appox.

Surface symm.energy

Bulk symmetry energy

Surface energy

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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

Exp.data W. Trautmann and W.Reidorf

Zhang,Li PRC74,014602(2006)

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III. The mechanism of proton induced reactions

dynamical process+statistical decay

300

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The influence of effective interactions(SkP,SIII)

Different interactions influence the low energy part and also the DDCS of neutrons at backward angles

7.50

300

600

1500

SkP is betterin describing DDCS of neutrons

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The contributions from reactions with different impact parameters

Large impact parameters

forward anglesnear Ep

Small impact parameters

low energy partbackward angles

The contribution from b/bmax= 0.38, 0.69are 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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excitation functions of reaction cross sections

Usym=Ulin

The behavior of energy dependence of is the same for Sn isotopes and is in agreement with exp. data The magnitudes of increases with A

r

IV. Dynamical effects of isospin on p + 112-132Sn

r

is the probability for inelastic scattering process

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132Sn

132Ba112Sn112Cd

The spectrum of emitted protons in 100MeV p+A with different impact parameters

132Sn

el.sc.el.sc.

More neutron-rich nuclei have smaller elastic cross sections i.e. larger reaction cross sections

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empiric formula(Carlson) for nuclei along -stability line

R0=1.45fm for Ep=25-100MeVR0=1.35 fm for Ep>180MeVR0=1.40fm for whole range of energy

as function of A1/3 for p+A reactions

Rp and r0 are fitting parameters:

The lines for empiric formula are moved upwards 0.38, 0.38, 0.2, 0.14fm for

E=100,200,250,300MeV,respectively

Sn

-SLCarlson

Obvious departure of the line forSn isotopes from the empiric formula

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Symmetry energy

Isospin dependence of nucleon-nucleon cross sections

Origin of isospin effects:

is about 2-3 time larger than at low energies

How do the effects from theses factors interplay dynamically ?

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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

The stiffer the symmetry energy is ,the larger the thickness of neutron skin is Neutron density distribution is different > ,

How changes?

Sampling with the constraint of neutron skin

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100MeV p + 132 Sn

Peripheral collisions

Symmetry potential of target provides an attractive force on incident proton, which directly influences the motion of incident proton

proton

132Sn

Vsym depends on , ,

0.0 0.5 1.0 1.5

0/

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The ratios between the colls. numbers of emitted protons for 132Sn/132Ba and 112Sn /112Cd

The dependence of number of collisions for emitted protons on the asymmetry of target

>

24.0 132Sn

15.0 132Ba

SkP

Neutron skin effect

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The number of collisions experienced by the emitted protons as function of impact parameters for different symmetry energies

the collisions experienced by emitted protons are enhanced for the softer symmetry energy case

100MeV p + 132 Sn

Soft symmetry energy leads to larger reaction cross sections

R=Ncoll(with sym.pot)

Ncoll(no sym.pot.)

Effect of symmetry energy I

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100MeV p + 132Sn

angular distribution of emitted protons

with no two-body collision experienced

b=7.5fm

angular distribution of emitted protons

with two-body collisions experienced

distributed at front angle distributed in 00-1800

angular distribution of emitted protons depends on the symmetry energy obviously

Effect of symmetry energy II

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100MeV p + 132Sn

Angular distribution for emitted protons experienced no two-body collisions(elastic scattering)

Angular distribution for emitted protons experienced with two-body collisions(reactions)

b=8.5fm

Angular distribution of emitted protons is very sensitive to the density dependence of the symmetry energy!

Effect of symmetry energy II

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The influence of the different symmetry energies on the reaction cross sections as function of A1/3

The slopes of as function of A1/3

measurementof for Snisotopes can give a very stringent constraint to the density dep. of symmetry energy

r

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<r2>1/2 is enlarged 0.1 fm

for large thickness case

Density distributions of 132Snfor normal and enlarged neutron skin

b/bmax 0.38 0.69

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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

100MeV p + 112-132Sn

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thin thick

~ A1/3 is sensitive to the symmetry energybut not very sensitive to the thickness of neutron skin

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Normal N.S.

Enlarged N.S.

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

as function of A1/3The slope of

100MeV p + 112-132Sn

132Sn

no S.E.,only cross sections

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100MeV n + A reactions

Sn

Angular distribution of emitted neutronssensitive to the symmetry energy

reaction cross section as functionof system size is less sensitive to the density dep. of S.E.The reaction cross sections are suppressed for neutron-rich targets

Shifted 0.2Shifted 0.1

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Enlarged the thickness of neutron skin

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

100MeV n + A reactions

the comparison

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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 and the angular distribution of emitted protons for p + Sn isotopes can give a stringent constraint for the density dependence of symmetry energy.

r

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Thanks!

Thanks!