Reexamining the isospin-relaxation time in intermediate-energy heavy-ion collisions

Isospin-relaxation times characterizing isospin transport processes between the projectile and the target with different $N/Z$ ratios and that between the neck and the spectator with different isospin asymmetries and densities in intermediate-energy heavy-ion collisions are studied within an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model using the lattice Hamiltonian approach. The respective roles and timescales of the isospin diffusion and drift as the major mechanisms of isospin transport in intermediate-energy heavy-ion collisions are discussed. Effects of nuclear symmetry energy and neutron-proton effective mass splitting on the isospin relaxation times are examined.

Figure 1

Time evolution of the ratio of the particle number in the resides (${\mathrm{A}}_{\mathrm{res}}$) to the total particle number ($A_{\mathrm{targ}}+A_{\mathrm{proj}}$) in ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ collisions at different beam energies using the parametrization ($x=0,y=-115$ MeV) for the ImMDI interaction.

Figure 2

Time evolution of the isospin equilibration meter $\left[\lambda \right(t)-1]/\left[\lambda \right(0)-1]$ in ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ collisions and beam energies of 25 (a), 100 (b), 200 (c), and 300 AMeV (d) from calculations using different symmetry energies and neutron-proton effective mass splittings.

Figure 3

Beam energy dependence of the isospin relaxation time in ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ collisions from calculations using different symmetry energies and neutron-proton effective mass splittings.

Figure 4

Contours of the isospin asymmetry $\delta =({\rho }_n-{\rho }_p)/\rho$ in the reaction plane ($x-o-z$) at different times in ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ collisions at the beam energy of 35 AMeV and the impact parameter of 4 fm with ($L=60$ MeV, $m_n^{*}>m_p^{*}$) (first row), ($L=60$ MeV, $m_n^{*}<m_p^{*}$) (second row), and ($L=90$ MeV, $m_n^{*}>m_p^{*}$) (third row). The fourth row is for testing purposes by setting ($L=90$ MeV, $m_n^{*}>m_p^{*}$) at $t=0-170$ fm/c and ($L=60$ MeV, $m_n^{*}>m_p^{*}$) at $t=170-300$ fm/c.

Figure 5

Correlation between the isospin asymmetry $\delta$ and the reduced nucleon number density $\rho /{\rho }_0$ at $t=170$ fm/c in noncentral ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ collisions at the beam energy of 35 AMeV from calculations using different symmetry energies and neutron-proton effective mass splittings, corresponding to the reactions in Fig. 4.

Figure 6

Time evolution of the magnitude of the isovector dipole moment for the projectile-like fragment in the later stage of noncentral ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ collisions from simulations using different symmetry energies and neutron-proton effective mass splittings corresponding to the four scenarios in Fig. 4. The scatters are results from simulations, while the solid lines are from the fit according to Eq. (20).