Exploring Zeptosecond Quantum Equilibration Dynamics: From Deep-Inelastic to Fusion-Fission Outcomes in ${}^{58}\mathrm{Ni}+{}^{60}\mathrm{Ni}$ Reactions

Energy dissipative processes play a key role in how quantum many-body systems dynamically evolve toward equilibrium. In closed quantum systems, such processes are attributed to the transfer of energy from collective motion to single-particle degrees of freedom; however, the quantum many-body dynamics of this evolutionary process is poorly understood. To explore energy dissipative phenomena and equilibration dynamics in one such system, an experimental investigation of deep-inelastic and fusion-fission outcomes in the ${}^{58}\mathrm{Ni}+{}^{60}\mathrm{Ni}$ reaction has been carried out. Experimental outcomes have been compared to theoretical predictions using time dependent Hartree-Fock and time dependent random phase approximation approaches, which, respectively, incorporate one-body energy dissipation and fluctuations. Excellent quantitative agreement has been found between experiment and calculations, indicating that microscopic models incorporating one-body dissipation and fluctuations provide a potential tool for exploring dissipation in low-energy heavy ion collisions.

Figure 1

Mass ratio distributions from the ${}^{58}\mathrm{Ni}+{}^{60}\mathrm{Ni}$ reaction for a range of $E/V_B$. In (a), a $65°<{\theta }_{\mathrm{c}.\mathrm{m}.}<115°$ gate has been used to ensure full detector coverage. The thin vertical lines indicate the expected mass ratios for the projectile and target nuclei. The inset shows an enlarged version of the $E/V_B=0.83$ mass ratio distribution on a linear scale. In (b), a gate has been placed on TKE that excludes 99% of the Rutherford scattered events, together with an $85°<{\theta }_{\mathrm{c}.\mathrm{m}.}<95°$ gate that isolates mass ratios corresponding to the region where fusion-fission events are expected to be found. The orange line shows ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ data at $E/V_B=0.83$ without angle or TKE gate. No background subtraction has been applied to any of these mass distributions.

Figure 2

Scattering angle ${\theta }_{\mathrm{c}.\mathrm{m}.}$ vs TKE differential cross section distributions $d^2\sigma /(d{\theta }_{\mathrm{c}.\mathrm{m}.}d\mathrm{TKE}$) for ${}^{58}\mathrm{Ni}+{}^{60}\mathrm{Ni}$ at (a) $E/V_B=1.14$, (b) $E/V_B=1.27$, and (c) $E/V_B=1.40$ overlaid with (${\theta }_{\mathrm{c}.\mathrm{m}.}$, TKE) impact parameter trajectories calculated with TDHF. (Diamond symbols) ${}^{58}\mathrm{Ni}+{}^{60}\mathrm{Ni}$, where black diamonds are projectilelike fragments (PLF), white diamonds are targetlike fragments (TLF); (Dotted lines) ${}^{60}\mathrm{Ni}+{}^{60}\mathrm{Ni}$. Differential cross sections are only a lower limit outside of the range of $65°<{\theta }_{\mathrm{c}.\mathrm{m}.}<115°$ due to detector angular coverage. The impact parameter $b$ for selected points along the TDHF trajectories are shown.

Figure 3

(a) TDRPA and observed ${\sigma }_{\mathrm{MR}}$ values are plotted as a function of calculated impact parameter $b$ for $E/V_B=1.40$. For the experimental data, ${\sigma }_{\mathrm{MR}}$ is obtained from a Gaussian fit of the mass ratio within a (${\theta }_{\mathrm{c}.\mathrm{m}.}$,TKE) gate corresponding to the equivalent trajectory given by the symmetric calculation; the impact parameter for each point is assigned based on the symmetric trajectory. The error bars on the experimental points and the gray dashed line show the detector mass resolution obtained from the ${\sigma }_{\mathrm{MR}}$ of the below-barrier ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ data, corresponding to the detector mass ratio resolution for a single atomic mass. Because data points have been selected along the projectilelike branch of the trajectory, points at high TKE values (large $b$) are expected to approach the resolution limit. (b) TDHF contact time versus ${\sigma }_{\mathrm{MR}}$ from TDRPA. The dotted line indicates maximum ${\sigma }_{\mathrm{MR}}$ from experiment with the shaded region representing the detector mass ratio resolution.