Neutron spatial distribution in nuclei and the impact-parameter dependence of the ${\pi }^{+}\text{−}{\pi }^{-}$ asymmetry in heavy-ion collisions

The theoretical nuclear physics predictions and experimental results on antiprotonic atoms lead to different proton and neutron spatial distributions. At CERN SPS energies production of positive and negative pions differs for $pp,pn,np$, and $nn$ scattering. These two facts lead to an impact-parameter dependence of the ${\pi }^{+}$ to ${\pi }^{-}$ ratio in ${}^{208}\mathrm{Pb}+{}^{208}\mathrm{Pb}$ collisions. A recent experiment at CERN seems to qualitatively confirm these predictions. The results for two models considered are almost identical. This may open a new possibility for determination of the neutron density distribution in nuclei.

Figure 1

(Color online) Neutron-to-proton ratio $Z{\rho }_n\left(r\right)∕N{\rho }_p\left(r\right)$ for ${}^{208}\mathrm{Pb}$. The experimental point is taken from [3] and the experimental gray band from [19]. The result of the HFB calculation [10] is shown by the thin solid line.

Figure 2

(Color online) $d\sigma ∕d{x}_F$ as a function of Feynman $x_F$ for $\alpha \beta \to {\pi }^{+}$ (left panel) and $\alpha \beta \to {\pi }^{-}$ (right panel) for different subcollisions: $pp$ (black solid), $nn$ (gray solid), $pn$ (black dashed), and $np$ (gray dashed).

Figure 3

The ratio $R_{+∕-}$ as a function of the Feynman $x_F$ for the model with binary collision (left panel) and for the model with the scaling with number of wounded nucleons (right panel) for selected values of impact parameters. Elementary cross sections are taken from HIJING model (solid lines) or from our fit to NA49 experimental $p+p$ and $p+n$ data (dashed lines). Also shown are the preliminary NA49 experimental data for $\mathrm{Pb}+\mathrm{Pb}$ from Ref. 14. Solid circles correspond to central and open circles to peripheral events.

Figure 4

The ratio $R_{+∕-}$ as a function of impact parameter for the model with binary collision (left panel) and for the model with the scaling with number of wounded nucleons (right panel) for selected values of $x_F$. Elementary cross sections are taken from HIJING model (solid lines) or from our fit to NA49 experimental $p+p$ and $p+n$ data (dashed lines).