Nucleon exchange in heavy-ion collisions within a stochastic mean-field approach

Nucleon exchange mechanism is investigated in deep-inelastic symmetric heavy-ion collisions in the basis of the stochastic mean-field approach. By extending the previous work to off-central collisions, an analytical expression is deduced for the diffusion coefficient of the nucleon exchange mechanism. Numerical calculations are carried out for ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ and ${}^{90}\mathrm{Zr}+{}^{90}\mathrm{Zr}$ systems and the results are compared with the phenomenological nucleon exchange model. Also, calculations are compared with the available experimental results of deep-inelastic collisions between calcium nuclei.

Figure 1

Snapshots of density profiles on the reaction plane, $\rho (x,y,z=0,t)$, at different times are plotted in units of $\mathrm{fm}{}^{-3}$ for the ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ reaction at $E_{\text{cm}}=110$ MeV and initial orbital angular momentum $l=70\hslash$. The panels (a), (b), and (c) correspond respectively to time before, during, and after contact.

Figure 2

A plot of the reduced phase-space distribution of one of the fragments $\overline{f}(x=0,y=0,p_x,p_y=0)$ versus $p_x$ at time $t={10}^{-21}$ s for the ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ reaction at $E_{\text{cm}}=110$ MeV and $l=70\hslash$. The solid line and dashed line show unsmoothed and smoothed phase-space distributions, respectively.

Figure 3

Diffusion coefficients for nucleon exchange are plotted versus time in ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ collisions at bombarding energy $E_{\text{cm}}=110$ MeV and four different initial angular momenta.

Figure 4

Diffusion coefficients for nucleon exchange are plotted versus time in ${}^{90}\mathrm{Zr}+{}^{90}\mathrm{Zr}$ collisions at bombarding energy $E_{\text{cm}}=300$ MeV and three different initial angular momenta.

Figure 5

Widths of fragment mass distributions in collisions of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ at $E_{\text{cm}}=110$ MeV and four different initial angular momenta. Lines are found by integral of diffusion coefficient, and symbols are results of empirical relation.

Figure 6

Widths of fragment mass distributions in collisions of ${}^{90}\mathrm{Zr}+{}^{90}\mathrm{Zr}$ at $E_{\text{cm}}=300$ MeV and three different initial angular momenta. Lines are found by integral of diffusion coefficient, and symbols are results of empirical relation.

Figure 7

Asymptotic values of ${\sigma }_{\mathrm{AA}}$ as a function of the orbital angular momentum obtained with SMF (red filled circles) and TDHF (blue filled squares). The asymptotic value $\sqrt{N_{\mathrm{exc}}\left(\infty \right)}$ is also shown by black open squares. The blue area indicates the fusion region while the yellow area indicates the “orbiting” region where the two nuclei stick together for a long time and then reseparate.