Influence of neutron-skin thickness on the ${\pi }^{-}/{\pi }^{+}$ ratio in Pb + Pb collisions

Within an isospin- and momentum-dependent transport model (IBUU11) using as an input nucleon density profiles from Hartree-Fock calculations based on a modified Skyrme-like (MSL) model, we study the influence of the uncertainty of the neutron skin thickness on the ${\pi }^{-}/{\pi }^{+}$ ratio in both central and peripheral Pb + Pb collisions at beam energies of 400 MeV/nucleon and 1000 MeV/nucleon. Within the current experimental uncertainty range of neutron skin in ${}^{208}\mathrm{Pb}$, while the neutron skin effect on the ${\pi }^{-}/{\pi }^{+}$ ratio is negligible in central reactions at both energies, it increases gradually with increasing impact parameter and becomes comparable with or even larger than the symmetry energy effect in peripheral collisions especially at 400 MeV/nucleon. Moreover, we find that while the ${\pi }^{-}/{\pi }^{+}$ ratio is larger with a softer $E_{\mathrm{sym}}\left(\rho \right)$ in central collisions, above certain impact parameters depending on the size of the neutron skin, a stiffer $E_{\mathrm{sym}}\left(\rho \right)$ can lead to a larger ${\pi }^{-}/{\pi }^{+}$ ratio as most of the pions are produced at densities below the saturation density in these peripheral reactions. Therefore, a clear impact parameter selection is important to extract reliable information about the $E_{\mathrm{sym}}\left(\rho \right)$ at suprasaturation densities (size of neutron skin) from the ${\pi }^{-}/{\pi }^{+}$ ratio in central (peripheral) heavy-ion collisions.

Figure 1

The density dependence of the symmetry energy.

Figure 2

The neutron and proton density profiles for ${}^{208}\mathrm{Pb}$ with neutron-skin thicknesses of 0.1 and 0.3 fm, respectively.

Figure 3

Evolution of the size of neutron skin initially set at 0.1 fm in the ground state of ${}^{208}\mathrm{Pb}$, and in the target/projectile in typical central and peripheral ${}^{208}\mathrm{Pb}$ + ${}^{208}\mathrm{Pb}$ collisions at beam energies of 400 and 1000 MeV/nucleon, respectively.

Figure 4

Evolution of the charged pion multiplicities in ${}^{208}\mathrm{Pb}$ + ${}^{208}\mathrm{Pb}$ collisions at impact parameters of 5 and 11 fm and a beam energy of 1000 MeV/nucleon, respectively.

Figure 5

Evolution of the ${({\pi }^{-}/{\pi }^{+})}_{\mathrm{like}}$ ratio from midcentral to peripheral Pb + Pb reactions at beam energies of 400 (left) and 1000 MeV/nucleon (right). The $x$ parameter is 1 (red [gray]) and 0 (black), and the size of neutron skin is 0.1 fm in all cases.

Figure 6

Rapidity distributions of the ${\pi }^{-}/{\pi }^{+}$ ratio from midcentral to peripheral Pb + Pb collisions at 400 MeV/nucleon with two sizes of neutron skin of 0.1 and 0.3 fm.

Figure 7

Same as Fig. 6 but for the beam energy of 1000 MeV/nucleon.

Figure 8

Rapidity distributions of the ${\pi }^{-}/{\pi }^{+}$ ratio with the soft symmetry energy $(x=1)$ in Pb + Pb collisions with an impact parameter of 11 fm and the beam energies of 400 and 1000 MeV/nucleon with and without the Coulomb fields, respectively. The blue (gray) lines are used to guide the eye.

Figure 9

Transverse momentum dependence of the ${\pi }^{-}/{\pi }^{+}$ ratio with the stiff symmetry energy $(x=0)$ in Pb + Pb collisions with an impact parameter of 11 fm and a beam energy of 1000 MeV/nucleon with the two sizes of neutron skin of 0.1 and 0.3 fm, respectively.