Detailed characterization of neutron-proton equilibration in dynamically deformed nuclear systems

We study neutron-proton equilibration in dynamically deformed nuclear systems by investigating the correlations between the two largest fragments produced in collisions of ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$, ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$, ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ and ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Ni}$ at $35\mathrm{MeV}$ per nucleon. The extent of equilibration is investigated using the rotation angle as a clock for the equilibration. The initially dissimilar fragments converge exponentially with consistent rate constants across a wide variety of reaction partners and systems, indicating that the equilibration follows first-order kinetics.

Figure 1

Representation of dynamical deformation and decay. Panel (a) shows a projectile approaching the target. In panel (b), the projectile has rotated around the target, forming a low-density “neck” region. In panel (c), the excited PLF* and TLF* have moved further away from each other and stretched into a “string of pearls” with the smallest fragments forming out of the neck region. Panel (d) represents the breaking of the nuclear system with the PLF* separating from the TLF*. Panel (e) shows the subsequent separation of the PLF* into HF and LF. (Figures from Ref. [9].)

Figure 2

Normalized velocity distributions for the HF and the LF in the direction of the beam. The HF is represented in red and the LF in blue. The distributions correspond to the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ system for three representative combinations of HF and LF: $Z_H=14$, $Z_L=5$ (upper panel), $Z_H=14$, $Z_L=7$ (middle panel), and $Z_H=12$, $Z_L=7$ (lower panel). The dashed vertical lines (from right to left) correspond to the beam velocity (i.e., $0.27\mathrm{c}$) and mid-velocity (i.e., $0.13\mathrm{c}$), respectively.

Figure 3

Normalized yield as a function of the angular in-plane distribution ${\phi }_{\mathrm{in}}$ (top right panel), out-of-plane distribution ${\theta }_{\mathrm{out}}$ (bottom left panel), and $\alpha$ (top left panel). The bottom right panel shows the angular distribution as a function of the in-plane and out-of-plane angles simultaneously, with a linear color scale. All angular distributions shown correspond to the $Z_H=12$, $Z_L=7$ combination of HF and LF of the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ system.

Figure 4

Normalized angular distribution $\alpha$ for the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ system. Three representative combinations of HF and LF are shown: $Z_H=14$, $Z_L=5$ (upper panel), $Z_H=14$, $Z_L=7$ (middle panel), and $Z_H=12$, $Z_L=7$ (lower panel). The blue area represents the statistical contribution and the remaining area (red) represents the dynamical contribution.

Figure 5

Fractional yield as a function of $\alpha$ for the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ system. Three representative combinations of HF and LF are shown: $Z_H=14$, $Z_L=5$ (upper panel), $Z_H=14$, $Z_L=7$ (middle panel), and $Z_H=12$, $Z_L=7$ (lower panel). The circular red markers correspond to the dynamical contribution while the blue rhombic markers represent the statistical contribution.

Figure 6

Average composition $\langle \mathrm{\Delta }\rangle$ as a function of the decay alignment $\alpha$ for the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ system. Three representative combinations of HF (red circles) and LF (blue rhombi) are shown: $Z_H=14$, $Z_L=5$ (upper panel), $Z_H=14$, $Z_L=7$ (middle panel), and $Z_H=12$, $Z_L=7$ (lower panel). The black lines correspond to the exponential fits of the data.

Figure 7

Average dynamical composition, $\langle {\mathrm{\Delta }}_{\mathrm{dyn}}\rangle$, as a function of the decay alignment $\alpha$ for the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ system. Three representative combinations of HF (red circles) and LF (blue rhombi) are shown: $Z_H=14$, $Z_L=5$ (upper panel), $Z_H=14$, $Z_L=7$ (middle panel), and $Z_H=12$, $Z_L=7$ (lower panel). The black lines correspond to the exponential fit of the average composition as a function of the decay alignment.

Figure 8

Average composition $\langle \mathrm{\Delta }\rangle$ as a function of the decay alignment $\alpha$ (in full markers) and the in-plane angle ${\phi }_{\mathrm{in}}$ (in open markers) for the $Z_H=12$, $Z_L=7$ pair in the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ system.

Figure 9

Average composition $\langle \mathrm{\Delta }\rangle$ as a function of the decay alignment $\alpha$ in all thirty-two combinations used in the analysis of the ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ system. The HF is shown in red circles and the LF in blue rhombi. The black lines show exponential fits to the data, only for those $Z_H$, $Z_L$ pairs for which both fits converge.

Figure 10

gemini++ simulations show the effects of secondary decay on the composition $\langle \mathrm{\Delta }\rangle$ as a function of the alignment angle $\alpha$. Full markers show initial composition and open markers show the composition after secondary decay. The upper panel show the effect of varying the excitation energy from $1A\mathrm{MeV}$ (blue circles) to $2A\mathrm{MeV}$ (red squares). The lower panel shows the effect of varying the initial composition from neutron-rich (blue circles) to less neutron-rich (red squares).

Figure 11

Average composition $\langle \mathrm{\Delta }\rangle$ as a function of the decay alignment $\alpha$ for the $Z_H=12$, $Z_L=7$ pair in all systems studied (i.e., ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$, ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$, ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$, and ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Ni}$). The HF is represented in red circles and the LF in blue rhombi. The black lines correspond to the exponential fits of the data.

Figure 12

Equilibrium composition as a function of the atomic number. All four systems studied are represented: ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ in black squares, ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$ in red circles, ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ in yellow stars, and ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Ni}$ in green triangles. The open markers correspond to the atomic numbers of the HF and the full markers represent the atomic numbers of the LF. The different sets of data are slightly horizontally offset for clarity.

Figure 13

Rate constants (in units of inverse degrees) as a function of the atomic number. All four systems are represented: ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ (top left panel), ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ (top right panel), ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$ (lower left panel), and ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Ni}$ (lower right panel). The red circles represent the atomic numbers of the HF while the blue squares represent the atomic numbers of the LF.

Figure 14

Rate constants (in units of inverse zs) as a function of the atomic number. All four systems are represented: ${}^{70}\mathrm{Zn}+{}^{70}\mathrm{Zn}$ (top left panel), ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ (top right panel), ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Zn}$ (lower left panel), and ${}^{64}\mathrm{Zn}+{}^{64}\mathrm{Ni}$ (lower right panel). The red circles represent the atomic numbers of the HF while the blue squares represent the atomic numbers LF. The shaded areas correspond to the average rate constant per zs values for the HF and LF.