Probing effective nucleon masses with heavy-ion collisions

It has been generally accepted that momentum-dependent potentials for neutrons and protons at energies well away from the Fermi surface cause both to behave as if their inertial masses are effectively 70% of the vacuum values. This similarity in effective masses may no longer hold in dense neutron-rich regions within neutron stars, core-collapse supernovas, and nuclear collisions. There differences in the momentum-dependent symmetry potentials may cause neutron and proton effective masses to differ significantly. We investigate this effect by measuring the energy spectra of neutrons, protons, and charged particles emitted in ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions at $E_{\mathrm{beam}}/A=50$ and 120 MeV with precision sufficient to distinguish, in principle, between effective interactions with very different values of the neutron and proton effective masses. These data and model comparisons point the way towards future advances in our capabilities to understand the density and momentum dependence of the nuclear symmetry energy.

Figure 1

(a) Free neutron, (d) free proton, (b) CI neutron, (e) CI proton spectra from the ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reaction at 50 MeV, (c) CI neutron, and (f) CI proton spectra from the ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ reaction at $E_{\mathrm{beam}}/A=120\mathrm{MeV}$ (black data points) compared to ImQMD-Sky calculations (solid and dashed lines).

Figure 2

Neutron to proton double ratio [Eq. (3)] for $\mathrm{Sn}+\mathrm{Sn}$ collisions at (a) $E_{\mathrm{beam}}/A=50\mathrm{MeV}$ and (b) 120 MeV.