Imaging nuclei by smashing them at high energies: how are their shapes revealed after destruction?

Abstract

High-energy nuclear collisions have recently emerged as a promising ``imaging-by-smashing'' approach that may reveal the intrinsic shapes of atomic nuclei. Here, I outline a conceptual framework for this technique, explaining how nuclear shapes are encoded during quark-gluon plasma formation and evolution, and how they can be decoded from final-state particle distributions. I highlight the method's potential to advance our understanding of both nuclear structure and quark-gluon plasma physics.

Figures (5)

• Figure 1: Connections between initial and final state in various "smashing" experiments: (a) Deformed water droplet colliding with a hydrophobic surface, producing an expansion pattern that inverts the initial shape asymmetry Yun:2017; (b) Expansion of a strongly-coupled Fermi gas released from an optical trap OHara:2002pqs, whose geometry leaves imprints in the subsequent dynamics of the gas due to the ultra-fast switch-off of the confining potential; (c) Coulomb-explosion imaging of a small molecule stripped of electrons, in which nuclear positions are inferred by reversing the repulsive expansion ceiceinature; (d) Pressure-driven expansion of the quark-gluon plasma produced in high-energy nuclear collisions madai. In each case, the final state can be reverse-engineered to extract the initial condition, provided the expansion dynamics, represented by the system's energy-momentum tensor $T_{\mu\nu}$, are sufficiently well understood (e). Note that panel-e draws an analogy in their response patterns rather than a direct comparison of the physics.
• Figure 2: Energy dependence of nuclear structure. Different degrees of freedom become relevant at different energies, affecting the apparent shape of the nucleus. Due to quantum fluctuations at nucleon and subnucleonic level, even a nominally spherical nucleus such as $^{208}$Pb exhibits a deformed nucleon distribution in the transverse plane at high energies.
• Figure 3: Relation between initial- and final-state of high-energy nuclear collisions. The features of collision geometry are characterized by its shape and size parameters, $\mathcal{E}_n$ and $d_{\perp}$ (${\bf a}$). They are linearly related to observables that describe the transverse momentum $p_{\mathrm{T}}$ spectra in each event, i.e., the anisotropic flow coefficients $V_n$ and the average transverse momentum $[p_{\mathrm{T}}]$ (${\bf b}$). The event-to-event variations of these initial- and final-state quantities are linearly related.
• Figure 4: Three steps in the imaging-by-smashing method. Illustrated here are collisions of spherical nuclei (${\bf a1}$--${\bf a3}$) and prolate-deformed nuclei with $\beta_2=0.28$ (${\bf b1}$--${\bf b3}$) for two representative collision events: (${\bf a1}$ and ${\bf b1}$) initial configurations of the colliding nuclei, (${\bf a2}$ and ${\bf b2}$) initial geometry in the transverse plane, and (${\bf a3}$ and ${\bf b3}$) final-state distribution of particles in azimuthal angle and $p_{\mathrm{T}}$. The event-to-event variation in the initial-state geometry and final-state distributions is quantified by the moments involving $\varepsilon_n$ and $d_{\perp}$ of the initial state and $v_n$ and $[p_{\mathrm{T}}]$ of the final state, as indicated in the middle row. Parameter $a$ represents the nuclear surface diffusivity. The nucleon positions are simulated in a Monte-Carlo Glauber model with $R_0=6.81$ fm, $a=0.55$ fm, and $A=238$. Imaging involves reconstructing the initial geometry from final-state particles (Step 1), relating it to the nuclear shape, which is affected by both global deformation and quantum fluctuations (Step-2), and comparing different collision systems to isolate the global deformation (Step-3).
• Figure 5: Implementation of the imaging method. The iterative processes of calibration, validation, and prediction to establish connections between nuclear structure and final-state flow observables or initial conditions structure, as well as the traditional approach of constraining initial conditions and QGP properties via hydrodynamic or transport model description of final state flow.