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. E0 K0 Q0 J L Ksym m*/m

SLy4 0.16 -15.97 229.91 363.11 32 46 -120 0.69 <1

SkI2 0.158 -15.78 240.93 339.70 33 104 71 0.68 <1

SkM* 0.16 -15.77 216.61 386.09 30 46 -156 0.79 >1

Gs 0.158 -15.59 237.29 348.79 31 93 14 0.78 >1

NRAPR 0.16 -15.85 225.65 362.54 33 60 -123 0.69 >1

Small L Large L

m_n*<m_p* SLy4 SkI2

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 pt2, 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 S0 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, S0=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