Isospin diffusion in heavy-ion collisions and the neutron skin thickness of lead

The correlation between the thickness of the neutron skin in ${}^{208}\mathrm{Pb}$ and the degree of isospin diffusion in heavy-ion collisions is examined. The same equation of state is used to compute the degree of isospin diffusion in an isospin-depedent transport model and the neutron skin thickness in the Hartree-Fock approximation. We find that skin thicknesses less than 0.15 fm are excluded by the isospin diffusion data.

Figure 1

(Color online) Symmetry energies as a function of baryon number density, ρ, in units of the saturation density, ${\rho }_0$, for three of the equations of state considered in this work.

Figure 2

(Color online) Time evolutions of $R_i$ and average central density for MDI and SBKD interactions with $x=-1$.

Figure 3

Results of fitting the MDI EOS for $x=-1$ (solid curves) to a Skyrme EOS (dashed curves). Plotted is the energy per baryon as a function of the baryon density, ρ. The dashed curves are barely visible because of the high quality of the fit.

Figure 4

(Color online) Skin thickness in lead, $\delta R$, versus the isospin diffusion parameter $1-R_i$ for the four equations of state in this work. A sample measurement with an uncertainty corresponding to a 1% measurement of the neutron radius is included, as well as the present acceptable experimental range.