Characterizing Neutron-Proton Equilibration in Nuclear Reactions with Subzeptosecond Resolution

We study neutron-proton equilibration in dynamically deformed atomic nuclei created in nuclear collisions. The two ends of the elongated nucleus are initially dissimilar in composition and equilibrate on a subzeptosecond time scale following first-order kinetics. We use angular momentum to relate the breakup orientation to the time scale of the breakup. The extracted rate constant is $3{\mathrm{zs}}^{-1}$, which corresponds to a mean equilibration time of 0.3 zs. This technique enables new insight into the nuclear equation of state that governs many nuclear and astrophysical phenomena leading to the origin of the chemical elements.

Figure 1

Illustration of dynamical deformation and decay. Panel (a) shows the deformed ${\mathrm{PLF}}^{*}$ and ${\mathrm{TLF}}^{*}$ system before rupture of the neck. Panel (b) shows a later time after the ${\mathrm{PLF}}^{*}$ and ${\mathrm{TLF}}^{*}$ system has separated. The ${\mathrm{PLF}}^{*}$ has rotated relative to the ${\mathrm{TLF}}^{*}$ separation axis (${\overrightarrow{v}}_{\mathrm{CM}}$) and is itself about to break up into two fragments ($\mathbf{H}\mathbf{F}$ and $\mathbf{L}\mathbf{F}$). The time the ${\mathrm{PLF}}^{*}$ lives before breaking up is measured by the angle $\alpha$. The color denotes the composition with blue indicating neutron richness and red indicating relative neutron deficiency.

Figure 2

Normalized angular distributions for select $Z_H$ and $Z_L$ pairings. Emission of the lighter charged fragment in the backward direction (toward the target) corresponds to $\cos (\alpha )=1$.

Figure 3

Composition as a function of decay alignment showing equilibration. As the angle of rotation increases ($\alpha$ increases from 0° to 180°), the $⟨N-Z/A⟩$ initially decreases rapidly for ${\mathrm{Z}}_L$ and increases for ${\mathrm{Z}}_H$ before plateauing. The majority of equilibration occurs between 0° and 80°.

Figure 4

Out-of-plane $\alpha$-particle distribution comparing experimental data and the gemini++ model to evaluate the spin ($22\hslash$).