Constraints on symmetry energy and the n/p effective mass splitting

Symmetry energy: Besides depending on the nuclear density, the symmetry energy also depends on the momentum or energy of a nucleon. Very different predictions for the momentum dependence of the nuclear symmetry potential. S(r,k)=K+S_loc(r)+S_nlc(r,k) For cold nuclear matter

1. Constraint on symmetry energy from N- Star is smaller than from HICs 2.Constraints from different transport models are not consistent 3.Constraints from nuclear structure studies Challenges on the constraints on symmetry energy: Addressing these challenges requires a good candidate that can connect the studies in HICs, nuclear structure and neutron-star models.

However, there are two defaults: 1. use different interaction form or parameters in HICs, structure and n-star studies 2.In the transport model simulations, E0, K0, S0, L, m*… are changed un- correlated. It could cause some mis-leading results. How to understand and solve it? 1, develop new version of transport codes, which can use the same interactions (or energy density) as in structure and n-star studies. 2, And the coefficients of E0, K0, S0, L and m* are changed consisitently. Best choice, transport model

Para.E0E0 K0K0 Q0Q0 JLK sym m*/m SLy <1 SkI <1 SkM* >1 Gs >1 NRAPR >1 Small LLarge L m_n*<m_p*SLy4SkI2 m_n*>m_p*SkM*Gs

Density dependence of symmetry energy, effective mass and Lane potential

DR(n/p) and isospin diffusion depend on: 1.Not only the local part, but also nonlocal part (effective mass splitting) in symmetry potential MDI: tends to change the momentum of nucleons from beam directions to transverse direction. Thus, we can find the MDI contributions by analyzing 1, n/p vs pt 2, n/p for transverse emitted nucleons with high kinetic energy

Charge distribution

n/p and DR(n/p) ratios as a function of kinetic energy

Isospin transport ratio SLy4, because mn*<mp*, the isospin dependent MDI drive the reaction system reach the isospin equilibrium faster.

Conclusion 1, n/p ratios of transverse emitted nucleons at high pt or high kinetic energy are sensitive to the effective mass splitting 2, calculations show that DR(n/p) not only depend on S 0 and L, but also on the n/p effective mass splitting 3, The DR(n/p) and isospin diffusion data support the SLy4 parameter set, S 0 =32, L=46, Ksym=-120, m*/m=0.69 and mn*<mp*. This conclusion is close to the results obtained from N-STAR (Steiner12),

Skz-1 is ruled out : 1. neutron effective mass increase with density increasing for PNM, 2. largest $\eta$ values in the \beta term, 3. stronger repulsive at high density region. Also has been ruled out in J Margueron, PRC66,014303(2002) Charge distribution

n/p ratios vs pt (-0.3<y^0<0.3) At high pt, the mn*<mp* cause the emitted nucleons with larger n/p ratios

DR(n/p) ratios vs pt