Reexamination of the neutron-to-proton-ratio puzzle in intermediate-energy heavy-ion collisions

Incorporating a newly improved isospin- and momentum-dependent interaction in the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model IBUU11, we have investigated relative effects of the density dependence of nuclear symmetry energy $E_{\mathrm{sym}}\left(\rho \right)$ and the neutron-proton effective mass splitting $m_n^{*}-m_p^{*}$ on the neutron-to-proton ratio of free nucleons and those in light clusters. It is found that the $m_n^{*}-m_p^{*}$ has a relatively stronger effect than the $E_{\mathrm{sym}}\left(\rho \right)$ and the assumption of $m_n^{*}\le m_p^{*}$ leads to a higher neutron-to-proton ratio. Moreover, this finding is independent of the in-medium nucleon-nucleon cross sections used. However, results of our calculations using the $E_{\mathrm{sym}}\left(\rho \right)$ and $m_n^{*}-m_p^{*}$ both within their current uncertainty ranges are all too low compared to the recent National Superconducting Cyclotron Laboratory double neutron-to-proton-ratio data from central ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ and ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ collisions at 50 and 120 MeV/u, thus calling for new mechanisms to explain the puzzlingly high neutron-to-proton ratio observed in the experiments.

Figure 1

Density dependence of the symmetry energy (a) and momentum dependence of the relative neutron-proton effective mass splitting in nuclear matter of the density $\rho ={\rho }_0$ and isospin asymmetry $\delta =0.2$ (b) from the ImMDI interaction with different values of $x$ and $y$.

Figure 2

Coalescence invariant double neutron-to-proton ratios DR($n/p$) in ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ collisions to ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ collisions as a function of nucleon center-of-mass energy at beam energies of (a) 120 and (b) 50 MeV/u with the impact parameter $b=2$ fm and the angular gate ${70}^{\circ }<{\theta }_{\mathrm{c}.\mathrm{m}.}<{110}^{\circ }$. The NSCL data are from Ref. [33].