Nuclear collectivity and the harmonic spectrum of two-body correlations

TL;DR

This paper proposes a horizontal, ground-state diagnostic of nuclear collectivity by analyzing angular correlations in the two-body density in the transverse plane, which can be accessed in high-energy nucleus-nucleus collisions. Using ab initio QMC and NLEFT calculations for $^{20}$Ne and $^{16}$O, it performs a harmonic (Fourier) decomposition of the two-body density $\rho^{(2)}_ot(r_\perp, \Delta\phi)$ to extract deformation moments $\mathfrak{B}_n$ and $\langle \hat{\mathcal{E}}_n\rangle$. The results reveal a dominant $\cos(2\Delta\phi)$ quadrupole modulation in $^{20}$Ne consistent with a bowling-pin quadrupole deformation and a strong $\cos(3\Delta\phi)$ octupole modulation in $^{16}$O signaling alpha-cluster structure, with arrangement effects becoming pronounced toward the nuclear surface. These findings link intrinsic nuclear shapes to the harmonic content of microscopic ground-state correlations and suggest that collider measurements of ultra-central collisions can probe ab initio nuclear structure and constrain low-energy constants in chiral EFTs.

Abstract

High-energy nuclear collisions have opened a new experimental method to reveal collective behavior in nuclear ground states through the lens of many-body correlations of nucleons. Using ab initio lattice and variational calculations of $^{20}$Ne and $^{16}$O, we study how emergent phenomena such as deformation or clustering can be identified in these systems from the dependence of their two-body density distributions on the relative azimuthal angle of nucleon pairs. A harmonic analysis of the correlation functions reveals in particular a dominant quadrupole component in $^{20}$Ne, consistent with a bowling-pin picture, and a prominent triangular modulation in $^{16}$O, possibly indicative of alpha-cluster correlations. Given that such structures can be accurately identified in high-energy collider experiments, these findings open a new paradigm for analyzing emergent collective behavior in atomic nuclei, relating their intrinsic shapes to the harmonic spectrum of microscopic correlations.

Figures (5)

• Figure 1: $^{16}$O nucleus in its rest frame (left). Probed in the laboratory frame following an acceleration to ultrarelativistic energies, the nucleus appears flattened in the $(x,y)$ plane (right), leading to a marginalization of the $z$ coordinates of its nucleons (the beam direction). In this work we are concerned with the two-body density $\rho^{(2)}(r_{1\perp}=r_\perp,r_{2\perp}=r_\perp,\Delta\phi=\phi_1-\phi_2)$, obtained from the projection of a large number of nuclei (snapshots), and how it varies as a function of the relative azimuthal angle, $\Delta\phi$, in a circle of radius $r_\perp$.
• Figure 2: Emergent collective behavior of nucleons in the ground states of $^{20}$Ne (upper row) $^{16}$O (second, third, and fourth row). The two-body azimuthal correlation is plotted as a function of $\Delta\phi = \phi_1 - \phi_2$, for radial slices $r_\perp = R_A/2$ (first column), $R_A/1.5$ (second column) $R_A$ (third column), and $1.5 R_A$ (fourth column). Different rows indicate different ab initio nuclear structure input: NLEFT configurations with a soft SU(4)-symmetric potential are for $^{20}$Ne and $^{16}$O (first and second row, respectively); QMC calculations employing either a pion-less EFT Hamiltonian (third row), or the phenomenological AV6P+UIX potential (fourth row). For $^{20}$Ne, a dominant $\cos(2\Delta\phi)$ quadrupole modulation emerges as one approaches $r_\perp=R_A$, consistent with a quadrupole-deformed rotor picture. In $^{16}$O, a $\cos(3\Delta\phi)$ modulation emerges as we approach the nuclear surface ($r_\perp \sim R_A$), indicating an effect akin to an octupole deformation. The observed dips at $\Delta\phi=0$ for small $r_\perp$ are a consequence of short-range repulsion among nucleons. This is showcased by the results in the fifth row, obtained for a mean-field configuration (Slater determinant) of $^{16}$O, where correlations are solely induced by Pauli exclusion.
• Figure 3: Fourier series decomposition of the two-body correlation of $^{20}$Ne as a function of $\Delta\phi$ for $r=R_A$. The solid black histogram corresponds to the curve shown in the upper row of Fig. \ref{['fig:2']}. The decomposition is of the form $a_0+\sum_{n=1}^4 a_n \cos(n\Delta\phi)$, with $a_0=-0.0289$, $a_1=-0.0130$, $a_2=0.147$, $a_3=0.0322$, $a_4=0.0389$. The purple dashed line corresponds to the Fourier series including only $a_1$, $a_2$, and $a_4$. The red solid line shows the effect of including $a_3$, which notably shifts the minima of the curve to their true location.
• Figure 4: Angular correlation analysis for the mean field configurations of $^{16}$O. Upper: recentered configurations. Lower: with a fluctuating center-of-mass, corresponding to the fifth row in Fig. \ref{['fig:2']}.
• Figure 5: Same as Fig. \ref{['fig:COM_MF']} but for the QMC calculations of $^{16}$O employing the AV6P+UIX potential. The lower panel corresponds to the fourth row in Fig. \ref{['fig:2']}.