Effects of symmetry energy and effective $k$-mass splitting on central ${}^{96}\mathrm{Ru}\left({}^{96}\mathrm{Zr}\right)+{}^{96}\mathrm{Zr}\left({}^{96}\mathrm{Ru}\right)$ collisions at 50 to 400 MeV/nucleon

The isospin mixing between projectile and target in central ${}^{96}\mathrm{Ru}\left({}^{96}\mathrm{Zr}\right)+{}^{96}\mathrm{Zr}\left({}^{96}\mathrm{Ru}\right)$ collisions at 50 to 400 MeV/nucleon is investigated within the isospin-dependent quantum molecular dynamics model in combination with the statistical decay code gemini. Four groups of parameters, which provide different density dependences of symmetry energy and effective $k$-mass splitting, are applied in the model. Calculations within the same effective $k$-mass splittings show that the isospin mixing is more likely to take place for soft symmetry energy than hard symmetry energy. Calculations within similar symmetry energies show that the isospin mixing is more likely to take place for $m_n^{*}<m_p^{*}$ than $m_n^{*}>m_p^{*}$. Significantly, the effects of effective $k$-mass splitting on the isospin mixing become stronger with increasing incident energies, while those of symmetry energy are similar at different incident energies.

Figure 1

Potential part of symmetry energies as a function of density at (a) zero temperature and (b) temperature of 50 MeV.

Figure 2

(a) Number of $np, nn$, and $pp$ collisions as a function of time in the central reaction of ${}^{96}\mathrm{Ru}+{}^{96}\mathrm{Zr}$ with a beam energy of 400 MeV/nucleon. (b) Observable $R(n/p)$, calculated from the neutrons and protons in the rapidity region $0.5<y^{\left(0\right)}<1.0$, as a function of time in the same reaction.

Figure 3

Observable $R(n/p)$, calculated from the free neutrons and protons, as a function of rapidity in central ${}^{96}\mathrm{Ru}+{}^{96}\mathrm{Zr}$ reactions at (a) 50 MeV/nucleon and (b) 400 MeV/nucleon.

Figure 4

Observable $R(n/p)$ calculated from the free neutrons and protons in the rapidity region $0.5<y^{\left(0\right)}<1.0$ in the central reactions of ${}^{96}\mathrm{Ru}+{}^{96}\mathrm{Zr}$ at 50, 100, 200, and 400 MeV/nucleon. Lines are used for guiding the eyes.

Figure 5

(a) Observable $R\left(p\right)$, calculated from the free protons, as a function of rapidity in central ${}^{96}\mathrm{Ru}+{}^{96}\mathrm{Zr}$ reaction at 400 MeV/nucleon. (b) Observable $R_{4y}$ as a function of rapidity in central reactions with different combinations of ${}^{96}\mathrm{Ru}$ and ${}^{96}\mathrm{Zr}$ nuclei at 400 MeV/nucleon.