BNU The study of dynamical effects of isospin on reactions of p Sn Li Ou and Zhuxia Li (China Institute of Atomic Energy, Beijing )

BNU Outline 1)Introduction 2)The ImQMD model 3)The mechanism of intermediate energy proton induced reactions 4) The dynamical effects of isospin on p Sn 5) Summary

BNU 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/ 3 He,, K + /K -, / Isoscaling, R 12 (N,Z)=Y 2 (N,Z)/Y 1 (N,Z)=Cexp( N+ Z) Flow effects: elliptic flow, neutron-proton differential flow Isospin diffusion, Review article: L.W.Chen, et.al.Nucl-th/

BNU Esym=31.6( ) 0.69 Esym=31.6( ) 1.05 Isoscaling parameters(data with AMD) Density dependence of symmetry energy at low densities by 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

BNU 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.

BNU 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, （ 2003 ）, Phys.Rev C69,034608(2004) Each nucleon is represented by a wave packet H

BNU 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, (2002) Zhang, Li, Phys.Rev.C71, (2005), 74,014602(2006)

BNU 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

BNU The relations between the parameters in ImQMD and Skyrme interaction

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

BNU Charge distribution of products in HIC Zhang, Li, PRC71(2005)24604

BNU Charge distribution of products Exp.data W. Trautmann and W.Reidorf Zhang,Li PRC74,014602(2006)

BNU III. The mechanism of proton induced reactions dynamical process+statistical decay 30 0

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

BNU The contributions from reactions with different impact parameters Large impact parameters forward angles near E p Small impact parameters low energy part backward angles The contribution from b/b max = 0.38, 0.69 are the most important

BNU p + 16 O

BNU P+ 27 Al

BNU P+ 56 Fe

BNU P+ 208 Pb

BNU excitation functions of reaction cross sections U sym =U lin 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 IV. Dynamical effects of isospin on p Sn is the probability for inelastic scattering process

BNU Sn 132 Ba 112 Sn 112 Cd The spectrum of emitted protons in 100MeV p+A with different impact parameters 132 Sn el.sc. More neutron-rich nuclei have smaller elastic cross sections i.e. larger reaction cross sections

BNU empiric formula(Carlson) for nuclei along -stability line R 0 =1.45fm for E p =25-100MeV R 0 =1.35 fm for E p >180MeV R 0 =1.40fm for whole range of energy as function of A 1/3 for p+A reactions R p and r 0 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 - SL Carlson Obvious departure of the line for Sn isotopes from the empiric formula

BNU 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 ?

BNU Dynamical effects of symmetry energy on p 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.

BNU

The dependence of the thickness of the neutron skin of 112,132 Sn and 132 Ba, 112 Cd 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

BNU MeV p Sn Peripheral collisions Symmetry potential of target provides an attractive force on incident proton, which directly influences the motion of incident proton proton 132 Sn V sym depends on,,

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

BNU 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 Sn Soft symmetry energy leads to larger reaction cross sections R= N coll (with sym.pot) N coll (no sym.pot.) Effect of symmetry energy I

BNU MeV p Sn 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 angular distribution of emitted protons depends on the symmetry energy obviously Effect of symmetry energy II

BNU MeV p Sn 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

BNU The influence of the different symmetry energies on the reaction cross sections as function of A 1/3 The slopes ofas function of A 1/3 measurement of for Sn isotopes can give a very stringent constraint to the density dep. of symmetry energy

BNU /2 is enlarged 0.1 fm for large thickness case Density distributions of 132 Sn for normal and enlarged neutron skin b/b max

BNU Enlarged thickness of neutron skin In general, the effect is reduced but no feature change in the slope of as function of A 1/3 for different symmetry energies 100MeV p Sn

BNU thin thick ~ A 1/3 is sensitive to the symmetry energy but not very sensitive to the thickness of neutron skin

BNU 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 A 1/3 The slope of 100MeV p Sn 132 Sn no S.E.,only cross sections

BNU MeV n + A reactions Sn Angular distribution of emitted neutrons sensitive to the symmetry energy 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 Shifted 0.2 Shifted 0.1

BNU 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

BNU 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.

BNU Thanks!