Isospin splitting of nucleon effective mass and symmetry energy in isotopic nuclear reactions

Within an isospin and momentum dependent transport model, the dynamics of isospin particles (nucleons and light clusters) in Fermi-energy heavy-ion collisions are investigated for constraining the isospin splitting of nucleon effective mass and the symmetry energy at subsaturation densities. The mass splitting of $m^{*}_{n}>m^{*}_{p}$ and $m^{*}_{n}<m^{*}_{p}$ in nuclear matter and the different stiffness of symmetry energy are used in the model. The single and double neutron to proton ratios of free nucleons and light particles are thoroughly investigated in the isotopic nuclear reactions of $^{112}$Sn+$^{112}$Sn and $^{124}$Sn+$^{124}$Sn at the incident energies of 50 and 120 MeV/nucleon, respectively. It is found that the both effective mass splitting and symmetry energy impact the kinetic energy spectra of the single ratios, in particular at the high energy tail (larger than 20 MeV). Specific constraints are obtained from the double ratio spectra, which are evaluated from the ratios of isospin observables produced in $^{124}$Sn+$^{124}$Sn over $^{112}$Sn+$^{112}$Sn collisions. A mass splitting of $m^{*}_{n}<m^{*}_{p}$ is constrained from the available data at the energy of 120 MeV/nucleon. A soft symmetry energy with the stiffness of $gamma_{s}=$0.5 is close to the experimental double ratio spectra at both energies.