Interplay between Quantum Shells and Orientation in Quasifission

The quasifission mechanism hinders fusion in heavy systems through breakup within zeptoseconds into two fragments with partial mass equilibration. Its dependence on the structure of both the collision partners and the final fragments is a key question. Our original approach is to combine an experimental measurement of the fragments’ mass-angle correlations in ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ with microscopic quantum calculations. We demonstrate an unexpected interplay between the orientation of the prolate deformed ${}^{238}\mathrm{U}$ with quantum shell effects in the fragments. In particular, calculations show that only collisions with the tip of ${}^{238}\mathrm{U}$ produce quasifission fragments in the magic $Z=82$ region, while collisions with the side are the only ones that may result in fusion.

Figure 1

(a)–(c) Measured mass-angle distributions at center-of-mass energies $E$ near the capture barrier $B$ [55]. The logarithmic color scale is shown in the top right. The horizontal and vertical ellipsoids show the TDHF results for the axial and equatorial configurations, respectively. The values of $L$ are indicated near the points associated to the light (heavy) fragments for the axial (equatorial) orientation. (d)–(f) Projected mass ratio $M_R$ in the range $0.2<M_R<0.8$. The scale factor in panels (e) and (f) multiplies the counts scale on the left. The mass ratio distributions estimated from the TDHF results are shown with shaded areas for quasifission in the axial (ax.) and equatorial (eq.) configurations, and for fusion-fission (f.) events. The ranges of $L$ used to calculate the mass ratio distributions are given in panels (d)–(f) and correspond to events falling into the angular acceptance of the detector. The sum of these distributions is shown (solid line).

Figure 2

Time evolution of the density in ${}^{40}\mathrm{Ca}+{}^{238}\mathrm{U}$ collisions at a center-of-mass energy $E=225.4\mathrm{MeV}$. The isodensity at half the saturation density ${\rho }_0/2=0.08{\mathrm{fm}}^{-3}$ is plotted every 1.5 zs for the axial orientation at $L=100$ (top) and every 6 zs for the equatorial orientation at $L=40$ (bottom).

Figure 3

Mass-angle distributions of quasifission fragments from TDHF calculations. The common vertical linear scale corresponds to the angular differential cross section in arbitrary units.

Figure 4

(a) Mean number of protons $Z$ in the outgoing heavy fragment as a function of the angular momentum quantum number $L$. Axial and equatorial orientations are represented by thick solid and thick dashed lines, respectively. The horizontal thin solid, thin dashed, and thin dotted lines show the values of $Z$ of the initial ${}^{238}\mathrm{U}$ nucleus (quasielastic scattering), of the doubly magic ${}^{208}\mathrm{Pb}$ nucleus (mass-asymmetric fission), and of the ${}^{139}\mathrm{Ba}$ fragment formed in mass-symmetric fission, respectively. (b) Contact time between the fragments defined as the time during which the density in the neck exceeds half the saturation density ${\rho }_0/2=0.08{\mathrm{fm}}^{-3}$. The arrows indicate lower limits of the contact time.