Nuclear shape dynamics in low-energy heavy-ion reactions

TL;DR

The paper surveys theoretical advances in low-energy heavy-ion reactions with a focus on probing nuclear shapes through reaction dynamics. It develops a GOE-based microscopic model for the imaginary part of the optical potential to capture absorption across resonance regimes, and introduces a Fourier-imaging approach to visualize quantum interferences in elastic scattering. It then analyzes multi-channel fusion with barrier distributions to extract deformation parameters, and presents an emulator based on eigenvector continuation to enable rapid Bayesian inference in coupled-channels calculations. Finally, it connects to relativistic heavy-ion collisions by showing how eccentricity distributions can distinguish static deformations from dynamical surface vibrations, illustrating a cross-scale view of nuclear shape dynamics across energy regimes.

Abstract

We discuss recent theoretical developments in low-energy heavy-ion reactions. To this end, we put emphasis on a viewpoint of probing nuclear shapes with heavy-ion reactions. We first discuss a single-channel problem with an optical potential model. We particularly discuss a microscopic modeling of the imaginary part of an optical potential as well as a visualization of quantum interference phenomena observed in heavy-ion elastic scattering. We then discuss multi-channel scattering problems, and demonstrate that heavy-ion fusion reactions at energies around the Coulomb barrier are sensitive to the shape of colliding nuclei, providing a powerful tool to probe nuclear shapes. We finally point out that relativistic heavy-ion collisions have large similarities to low-energy heavy-ion reactions in the context of nuclear shape dynamics.

Figures (10)

• Figure 1: A schematic illustration of the schematic model proposed in Ref. hagino2025 for a microscopic modeling of an imaginary part of an optical potential. In this model, the entrance channel Hamiltonian in the discrete basis representation couples to compound nucleus states described with the random matrix based on the Gaussian Orthogonal Ensemble (GOE). $\gamma$ and $d$ are the decay width and the mean level spacing of the compound nucleus states, respectively.
• Figure 2: Transmission coefficients $T$ as a function of the incident energy $E$ obtained with the schematic model introduced in Ref. hagino2025 (see Fig. \ref{['fig:schematic']}). The blue dashed line is for $\gamma/d=20$, while the red solid line for $\gamma/d=1$.
• Figure 3: (Upper panel) A schematic illustration of a setup of the double-slit problem. (Lower panel) The imaging of the double-slit problem with Eq. (\ref{['eq:imaging']}) on the two-dimensional $(X,Y)$ plane. The parameters are taken to be $l=1,k=30$, $\theta_0=0$, and $\Delta\theta=\Delta\varphi=$ 15 degree.
• Figure 4: (Upper panel) Differential cross sections for $^{16}$O+$^{16}$O elastic scattering at $E_{\rm c.m.}$ = 26.5 MeV obtained with the optical potential model. The anti-symmetrization between the projectile and the target nuclei is ignored for simplicity. The solid line shows the result of the optical potential model calculation, while the dashed and the dotted lines show its decomposition to the near-side and the far-side components, respectively. (Lower panel) The visualization of $^{16}$O+$^{16}$O elastic scattering at $E_{\rm c.m.}$ = 26.5 MeV on a two-dimensional screen, whose coordinates are specified by $X$ and $Y$. The left and the right peaks correspond to the far-side and the near-side components, respectively.
• Figure 5: Fusion cross sections for the $^{16}$O+$^{154}$Sm system as a function of the incident energy in the center of mass frame, which is measured with respect to the height of the Coulomb barrier, $V_b$=60.35 MeV. The dashed line is obtained with a single-channel calculation, while the solid line takes into account the deformation effect of the $^{154}$Sm nucleus with the orientation average formula, Eq. (\ref{['fusion']}). The experimental data are taken from Ref. leigh1995.