constraints on symmetry energy and the n/p effective mass splitting
Post on 24-Feb-2016
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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
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