1. Mean free path and transport parameters from Brueckner-Hartree-Fock
NNINT workshop June 18-20, 2015, Catania
Mean free path and transport parameters from Brueckner-Hartree-Fock
Hongfei Zhang
Lanzhou University

2. Collaborators:
Umberto Lombardo, Wei Zuo, Xiaojun Bao, Zenghua Li, Jianming Dong, Frances Sammarruca,

4. Contents
1 Motivation
2 Sketch of BHF with microscopic three-body force
3 In-medium nucleon-nucleon cross sections
4 Mean free path in asymmetric nuclear matter
5 Shear viscosity and thermal conductivity
in neutron stars
6 Conclusions

5. 1 Motivations
Heavy-ion collisions are theoretically described by transport-model simulations whose input data are the in-medium cross sections and the nuclear mean field. In Brueckner theory, the G matrix plays the role of the in-medium scattering amplitude . [Eur. Phys. J. A 30 III (2006)].
The mean free path is a crucial quantity, e.g. in the transport-model simulations of heavy-ion collisions and in the prediction of the nuclear transparency measured in (e, e′p) reactions. [Phys. Rev. C 45, 791 (1992)]
Gravitational radiation emitted by r-modes in rapidly rotating neutron stars drives
the instability of the system. Which dissipation mechanism tends to suppress this
instability? A good candidate is the shear viscosity. Which constituent of NS mainly
contribute to the viscosity? Neutrons, leptons, hyperons, quarks,…

6. 2 Sketch of BHF with Microscopic three-body forces
The starting point is the reaction G matrix, which satisfies the
Brueckner-Bethe Goldstone (BBG) equation,
the single-particle energy given by:
the single-particle potential:

7. In present BHF calculation, the Three-Body-Force (TBF) has been reduced
to an equivalently effective two-body interaction via a suitable average with respect to the third-nucleon degrees of freedom.
W. Zuo, A. Lejeune, U. Lombardo, and J.-F. Mathiot, Nucl. Phys. A706, 418 (2002).

8. 3 In-medium NN cross sections
In the c.m. frame, the nonrelativistic elastic differential cross section for neutron-proton (np) scattering from unpolarized beams is given by
the differential cross section can be explicitly integrated over the solid angle to give the total cross section,

9. Zhang, Li, Lombardo, Luo, Sammarruca, Zuo, Phys. Rev
Zhang, Li, Lombardo, Luo, Sammarruca, Zuo, Phys. Rev. C 76, (2007)

10. Momentum dependence of the nucleon effective mass m∗/m in symmetric nuclear matter at three densities, in the presence and absence of the 3BF effect.
Zhang, Li, Lombardo, Luo, Sammarruca, Zuo, Phys. Rev. C 76, (2007)

11. Free-space pn and NN cross sections for increasing values of the maximum angular momentum and as a function of the incident laboratory energy, E. The squares represent the experimental data.
Zhang, Li, Lombardo, Luo, Sammarruca, Zuo, Phys. Rev. C 76, (2007)

12. Total cross sections for scattering of identical nucleons with and without the effect of 3BFs. The free-space cross section is shown for comparison.
Zhang, Li, Lombardo, Luo, Sammarruca, Zuo, Phys. Rev. C 76, (2007)

13. Total cross sections for scattering of nonidentical nucleons
Zhang, Li, Lombardo, Luo, Sammarruca, Zuo, Phys. Rev. C 76, (2007)

14. Center-of-mass differential cross section for scattering of identical nucleons with and without the effect of 3BFs at E =100 and 240 MeV. The free-space cross section is also shown for comparison
Zhang, Li, Lombardo, Luo, Sammarruca, Zuo, Phys. Rev. C 76, (2007)

15. Center-of-mass differential cross section for scattering of nonidentical nucleons with and without the effect of 3BFs at E =100 and 240 MeV. The free-space cross section is also shown for comparison
Zhang, Li, Lombardo, Luo, Sammarruca, Zuo, Phys. Rev. C 76, (2007)

16. Comparison with the NN cross sections of DBHF model.
Identical nucleons
Nonidentical nucleons
Z diagram (left) and its contribution to the nuclear
matter energy (right). Upward/downward lines
represent positive/negative energy states.
Zhang, Li, Lombardo, Luo, Sammarruca, Zuo, Phys. Rev. C 76, (2007)

17. 4 Mean free path
The nucleon mean free path can be calculated from imaginary part of
the mass operator.
BHF
EBHF

18. matter. Three densities and zero temperature are considered
Mean free path versus energy with and without 3BF for symmetric nuclear
matter. Three densities and zero temperature are considered
Bao, Zhang, Lombardo, Dong, Zuo, J. Phys. G, 41 (2014)

19. Mean free path for symmetric nuclear matter in the BHF (left) and EBHF (right) approximation: three densities at zero temperature (upper panels) and three
temperatures at the saturation density are considered.
Bao, Zhang, Lombardo, Dong, Zuo, J. Phys. G, 41 (2014)

20. Bao, Zhang, Lombardo, Dong, Zuo, J. Phys. G, 41 (2014) 105101

21. Bao, Zhang, Lombardo, Dong, Zuo, J. Phys. G, 41 (2014) 105101

22. 5 Shear viscosity and thermal conductivity

23. Shear viscosity
Zhang, Lombardo, Zuo, Phys. Rev. C 82, (2010)

24. Thermal conductivity
Zhang, Lombardo, Zuo, Phys. Rev. C 82, (2010)

25. 6 Conclusions
The in-medium NN cross sections were calculated within the BHF+3BF theory, showing that Pauli principle mainly suppress the forward and backward angles whereas the mass renormalization plays the most important role.
The nucleon mean free path in isospin symmetric and asymmetric nuclear matter at finite temperature was calculated with BHF. The density, isospin and temperature dependence of the mean free path has been investigated.
Transport parameters, shear viscosity and thermal conductivity were calculated in different configurations of nuclear matter, including
beta-stable nuclear matter and neutron stars.

26. Thank you!