Nucleon-nucleon cross sections in symmetry and asymmetry nuclear matter School of Nuclear Science and Technology, Lanzhou University, , China Hong-fei ZHANG ( 张鸿飞 ）

Collaborators: U. Lombardo Z.H. Li F. Sammarruca W. Zuo J. M. Dong Papers on the work: 1. H.F. Zhang, Z.H. Li, U. Lombardo, P.Y. Luo, and W.Zuo, Phys. Rev. C, Vol. 76, (2007). 2. H.F. Zhang, U. Lombardo, J.M. Dong, Z.H. Li, W. Zuo, Nucleon-nucleon cross sections and nucleon mean free paths in asymmetric nuclear matter In preparation.

Outline Introduction BHF with microscopic three-body forces Nucleon-nucleon cross sections in symmetry and asymmetry nuclear matter Summary

Ⅰ. Introduction Heavy-ion collisions are theoretically described by transport- model simulations whose input data are the in-medium cross se ctions and the nuclear mean field. Being intimately related to ea ch other through the nuclear matter equation of state (EOS), th ey must be consistently determined. In-medium cross sections are necessary to study the mean fre e path of nucleons in nuclear matter and thus nuclear transpare ncy. Size of exotic nuclei

In asymmetry nuclear matter, one can define the isospin asymmetry parameter where In-medium effective Interaction G matrix V 3 eff is reduced to a de nsity-dependent two- body force v+v 3 eff v Defect function Ⅱ. BHF with Microscopic three-body forces For a given total densityρand asymmetryβ.a bare two-body forcev as input, solve the Equs self-consistently ： BBG equation s.p. energy s.p. auxiliary potentials BHF Pauli operator

Ⅲ. Nucleon-nucleon cross sections In Brueckner theory, the G matrix plays the role of the in-medium scattering amplitude, with medium effects being introduced through the mean field and Pauli blocking. In the zero density limit, the G matrix reduces to the T martix, and the Brueckner-Beth-Goldstone (BBG) equation to the Lippmann-Schwinger equation. Beyond the scattering amplitude, nucleon-nucleon collisions in nuclear matter are also driven by kinematic degree of freedom, i.e.,entrance flow and density of states in the exit channel. Both are related to the nucleon effective mass, which, in turn, is related to the self-energy. The latter is modified by a 3BF, which also generates quite large rearrangement terms, leading to a large reduction of the effective mass. Thus one can expect that 3BFs might have a strong influence on the in-medium cross section, as they depend quadratically on the effective mass.

1. Real and imaginary parts of the 1 S 0 components of the G matrix While 3BFs are negligible at low density, they start to be noticable at saturation density and become more and more effective as density increase. The real part of the G matrix is reduced due to Pauli blocking and dispersive effects. The imaginary part of the G matrix, which is related to the particle-hole excitations, become larger because of the 3BF enhancement of the ground correlations.

2. Effective mass In the medium, the additional contribution from the self-energy can be reasonablely approximated by replacing the bare mass with the effective mass: The effective mass becomes substantially smaller with the inclusion of the 3BF, an effective which will impact the in-medium cross sections through the level density in the entrance and exit channels, along with the 3BF enhancement of the repulsive components in the effective interaction.

3 Free-space cross sections Argonne V 14 is used The total cross sections converge rapidly to the corresponding experimental values with increasing number of partial waves

4. Total cross sections for identical nucleons Up to the saturation density, the effect of the 3BF is small, and the medium suppression is mainly controled by the reduction of density of state due to Pauli blocking. At the higher density, the 3BF produces a larger reduction of the cross section, which persists up to high energy. The latter is mainly due to the strong 3BF renormalization of the effective mass. The scattering amplitude is also affected by the 3BF

5. Differential cross section for identical nuc leons The reduction of the cross sections is more sizable in the forward and backward directions, since low momentum transfers are strongly suppressed by the Pauli principle. This effect leads to distributions that are almost flat at high density. This feature justifies the frequency practice of adopting isotropic cross sections in HIC simulations.

6. Total cross sections for nonidentical nucleons In scattering of distinguishable nucleons, the T=0 component of the interaction is also included. As a consequence, the free cross sections for unlike particle is larger than the one for like particles, a property which remains true in the medium. The 3Bf effect on the cross section is evident, especially in high density.

7. Differential cross section for nonidentical nuc leons The differential cross section is strongly asymmetric. The in-medium values exhibit similar asymmetry although less pronounced.

8. Comparison with DBHF predictions The cross sectios from 2BF+3BF are in good agreement with thevalues from DBHF, with the exception of the highest density. Energy and density dependent appear quite consistent among the two cases, although the cross sectios from 2BF+3BF is somewhat larger than the values from DBHF across the broad.

Examination of the last column in the left table clearly suggests that 3BF other than Z diagrams are the main cause of the discrepancies between the DBHF and BHF+3BF predictions of the EOF and, consequently, of the respective cross sections.

9. nucleon-nucleon cross section in asymmetry nuclear Bonn B potential and a new version of three-body Force are used, Dr. Z.H. li will give a talk on the improvement for the previous BHF with 3BF !

Isospin dependent of total nucleon-nucleon cross sections The lowering (rising) proton (neutron) Fermi mementum and the reduced (increased) proton (neutron) effective mass tend to move the cross section in opposite direction. With pauli blocking applied to intermediate and final states, the final balance is that The neutron-neutron effective cross section is more strongly suppressed.

Ⅳ. Summary The TBF provides a repulsive contribution to the EOS and improves remarkably the predicted saturation properties, which suppress the magnitude of cross sections. The TBF from the Z-diagram provides the saturation mechanism and gives the main relativistic effect in DBHF approach.