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)

OutlineIntroductionThe ImQMD model The mechanism of intermediate energy proton induced reactions4) The dynamical effects of isospin on p + 110-132Sn5) Summary

I. IntroductionThe 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

Esym=31.6( )0.69Esym=31.6( )1.05Isoscaling 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 densitiesD.V. Shetty, et.al. PRC75,34602L.W.Chen, et.el., PRL94,032701

motivations for studying intermediate energy p + A reactions1) 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.

II. ImQMD05 modelThe motion of particles is described in 6-A dimensional phase spaceWang, Li, Wu, Phys.Rev.C65,064608(2002),Phys.Rev C69,0246042003,Phys.Rev C69,034608(2004)Each nucleon is represented by a wave packetH

phase space occupation number constraint is introduced system size dependent wave packet widthImQMD: 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)

Version IIThe potential energy density functional is taken from the Skyrme interaction directlyImQMD05Correction to mass, Thomas-Fermi appox.Surface symm.energyBulk symmetry energySurface energy

The relations between the parameters in ImQMD and Skyrme interaction

The time evolution of binding energies and rms radii of 56Fe and 208Pb

Charge distribution of products in HICZhang, Li, PRC71(2005)24604

Charge distribution of productsExp.data W. Trautmann and W.ReidorfZhang,Li PRC74,014602(2006)

III. The mechanism of proton induced reactionsdynamical process+statistical decay300

The influence of effective interactions(SkP,SIII) Different interactions influence the low energy part and also the DDCS of neutrons at backward angles 7.503006001500SkP is betterin describing DDCS of neutrons

The contributions from reactions with different impact parametersLarge impact parameters

forward anglesnear Ep Small impact parameterslow energy partbackward angles The contribution from b/bmax= 0.38, 0.69are the most important

p + 16O

P+27Al

P+56Fe

P+208Pb

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 AIV. Dynamical effects of isospin on p + 112-132Sn is the probability for inelastic scattering process

132Sn132Ba112Sn112CdThe spectrum of emitted protons in 100MeV p+A with different impact parameters132Snel.sc.el.sc.More neutron-rich nuclei have smaller elastic cross sections i.e. larger reaction cross sections

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 energyas 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

Symmetry energy Isospin dependence of nucleon-nucleon cross sectionsOrigin of isospin effects: is about 2-3 time larger than at low energiesHow do the effects from theses factors interplay dynamically ?

Dynamical effects of symmetry energy on p + 112-132 Sn The thickness of neutron skin of target is strongly correlated with the density dependence of the symmetry energy

The symmetry potential of target gives an attraction to incident proton, directly influences on the motion of the incident proton.

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

100MeV p + 132 Sn Peripheral collisions Symmetry potential of target provides an attractive force on incident proton, which directly influences the motion of incident protonproton132SnVsym depends on , , 0.00.51.01.5

The ratios between the colls. numbers of emitted protons for 132Sn/132Ba and 112Sn /112CdThe dependence of number of collisions for emitted protons on the asymmetry of target >132Sn132BaSkPNeutron skin effect

The number of collisions experienced by the emitted protons as function of impact parameters for different symmetry energiesthe collisions experienced by emitted protons are enhanced for the softer symmetry energy case 100MeV p + 132 SnSoft symmetry energy leads to larger reaction cross sectionsR=Ncoll(with sym.pot)Ncoll(no sym.pot.)Effect of symmetry energy I

100MeV p + 132Snangular 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 angledistributed in 00-1800 angular distribution of emitted protons depends on the symmetry energy obviously Effect of symmetry energy II

100MeV p + 132SnAngular distribution for emitted protons experienced no two-body collisions(elastic scattering)Angular distribution for emitted protons experienced with two-body collisions(reactions)b=8.5fmAngular distribution of emitted protons is very sensitive to the density dependence of the symmetry energy! Effect of symmetry energy II

The influence of the different symmetry energies on the reaction cross sections as function of A1/3 The slopes ofas function of A1/3measurementof for Snisotopes can give a very stringent constraint to the density dep. of symmetry energy

1/2 is enlarged 0.1 fm for large thickness caseDensity distributions of 132Snfor normal and enlarged neutron skinb/bmax 0.38 0.69

Enlarged thickness of neutron skin In general, the effect is reduced but no feature change in the slope of as function of A1/3for different symmetry energies 100MeV p + 112-132Sn

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

Normal N.S. Enlarged N.S.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 132Snno S.E.,only cross sections

100MeV n + A reactionsSnAngular distribution of emitted neutronssensitive to the symmetry energyreaction 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

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 enhanced100MeV n + A reactionsthe comparison

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.

Thanks!Thanks!