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The study of dynamical effects of isospin on reactions of p + 112-132 Sn

The study of dynamical effects of isospin on reactions of p + 112-132 Sn Li Ou and Zhuxia Li (China Institute of Atomic Energy, Beijing 102413). Outline. Introduction The ImQMD model The mechanism of intermediate energy proton induced reactions

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The study of dynamical effects of isospin on reactions of p + 112-132 Sn

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  1. 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)

  2. Outline • Introduction • The ImQMD model • The mechanism of intermediate energy proton • induced reactions • 4) The dynamical effects of isospin on p + 110-132Sn • 5) Summary

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

  4. Density dependence of symmetry energy at low densities by comparison between data and the transport model calculations Esym=31.6( )0.69 D.V. Shetty, et.al. PRC75,34602 Isoscaling parameters(data with AMD) Esym=31.6( )1.05 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

  5. 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.

  6. 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

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

  8. 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.

  9. The relations between the parameters in ImQMD and Skyrme interaction

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

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

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

  13. III. The mechanism of proton induced reactions 300 dynamical process+statistical decay

  14. 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 also the DDCS of neutrons at backward angles

  15. 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

  16. p + 16O

  17. P+27Al

  18. P+56Fe

  19. P+208Pb

  20. IV. Dynamical effects of isospin on p + 112-132Sn excitation functions of reaction cross sections Usym=Ulin is the probability for inelastic scattering process 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

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

  22. as function of A1/3 for p+A reactions Sn empiric formula(Carlson) for nuclei along -stability line Carlson -SL 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 The lines for empiric formula are moved upwards 0.38, 0.38, 0.2, 0.14fm for E=100,200,250,300MeV,respectively Obvious departure of the line for Sn isotopes from the empiric formula

  23. Origin of isospin effects: Symmetry energy Isospin dependence of nucleon-nucleon cross sections is about 2-3 time larger than at low energies How do the effects from theses factors interplay dynamically ?

  24. 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.

  25. 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 changes?

  26. 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 0.0 0.5 1.0 1.5 Vsym depends on , ,

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

  28. 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 Ncoll(with sym.pot) R= 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

  29. Effect of symmetry energy II 100MeV p + 132Sn b=7.5fm angular distribution of emitted protons with no two-body collision experienced angular distribution of emitted protons with two-body collisions experienced distributed in 00-1800 distributed at front angle angular distribution of emitted protons depends on the symmetry energy obviously

  30. 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!

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

  32. Density distributions of 132Sn for normal and enlarged neutron skin <r2>1/2 is enlarged 0.1 fm for large thickness case b/bmax 0.38 0.69

  33. 100MeV p + 112-132Sn Enlarged thickness of neutron skin In general, theeffect is reduced but no feature change in the slope of as function of A1/3 for different symmetry energies

  34. thin thick ~ A1/3 is sensitive to the symmetry energy but not very sensitive to the thickness of neutron skin

  35. 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 • 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

  36. 100MeV n + A reactions Sn 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 0.1 Shifted 0.2 Angular distribution of emitted neutrons sensitive to the symmetry energy

  37. 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

  38. 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.

  39. Thanks! Thanks!

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