Multinucleon exchange in quasifission reactions

The nucleon exchange mechanism is investigated in the central collisions of ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ systems near the quasifission regime in the framework of the stochastic mean-field (SMF) approach. Sufficiently below the fusion barrier, a dinuclear structure in the collisions is maintained to a large extent. Consequently, it is possible to describe nucleon exchange as a diffusion process familiar from deep-inelastic collisions. Diffusion coefficients for proton and neutron exchange are determined from the microscopic basis of the SMF approach in the semiclassical framework. Calculations show that after a fast charge equilibration the system drifts toward symmetry over a very long interaction time. Large dispersions of proton and neutron distributions of the produced fragments indicate that the diffusion mechanism may help to populate heavy transuranium elements near the quasifission regime in these collisions.

Figure 1

Density profiles in units of $\mathrm{nucleon}/\mathrm{fm}{}^3$ in the reaction plane near maximum overlap in the central collisions of ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ (a) and ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ (b) systems at energies $E_{\text{c.m.}}=202.0$ MeV and $E_{\text{c.m.}}=198.7$ MeV, respectively, obtained in TDHF calculations. Red lines indicate the position of window planes.

Figure 2

Mean drift paths of projectile-like fragments in $\left(N,Z\right)$ plane in the central collision of ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ (a) and ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ (b) systems at energies $E_{\text{c.m.}}=202.0$ MeV and $E_{\text{c.m.}}=198.7$ MeV, respectively, obtained in TDHF calculations.

Figure 3

Proton drift $v_Z$ (dashed line) and neutron drift $v_N$ (solid line) coefficients in the central collisions of ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ (a) and ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ (b) systems at energies $E_{\text{c.m.}}=202.0$ MeV and $E_{\text{c.m.}}=198.7$ MeV, respectively, obtained in TDHF calculations.

Figure 4

Proton diffusion $D_{ZZ}$ (dashed line) and neutron diffusion $D_{NN}$ (solid line) coefficients in the central collisions of ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ (a) and ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ (b) systems at energies $E_{\text{c.m.}}=202.0$ MeV and $E_{\text{c.m.}}=198.7$ MeV, respectively, obtained in the semiclassical framework of the SMF approach.

Figure 5

Proton dispersion ${\sigma }_{ZZ}$ (dashed line), neutron dispersion ${\sigma }_{NN}$ (solid line), and mixed dispersion ${\sigma }_{ZN}$ (dotted line) of the fragment distributions (projectile-like or target-like) in the central collisions of ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ (a) and ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ (b) systems at energies $E_{\text{c.m.}}=202.0$ MeV and $E_{\text{c.m.}}=198.7$ MeV, respectively.

Figure 6

Equal probability lines for populating target-like elements with $C=0.5,1.0,1.5$ in the central collisions of ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ (a) and ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ (b).

Figure 7

Total mass dispersion ${\sigma }_{AA}$ of the fragment distributions (projectile-like or target-like) in the central collisions of ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ (a) and ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ (b) systems at energies $E_{\text{c.m.}}=202.0$ MeV and $E_{\text{c.m.}}=198.7$ MeV, respectively.