Imaging two-body correlations in atomic nuclei via low- and high-energy processes

TL;DR

This paper tackles imaging two-body nucleon correlations in nuclei by linking high-energy ground-state fluctuations to ground-state density-density correlations and contrasting this with traditional low-energy Kumar operator interpretations. It develops an ab initio framework using PHFB/PGCM with χEFT Hamiltonians to compute the mean-square eccentricity ⟨ε^2_ℓ⟩ and its decomposition into one- and two-body parts, introducing the high-energy quantity B^2_ℓ(HE) proportional to the two-body component. The results show that low-energy Kumar-based measures ⟨Q^(2)_2⟩ (via B^2_LE) do not reliably reflect intrinsic deformation, while HE-based imaging correlates with β^2_{20} after accounting for Pauli offsets; PGCM shape fluctuations further enhance two-body correlations, achieving agreement with NLEFT/QMC benchmarks in light nuclei. The Hoyle state in 12C and other 0^+_2 states exhibit especially large two-body correlations, and the work points to pursuing three-nucleon correlations in future studies.

Abstract

Characterizing the correlated behavior of nucleons inside atomic nuclei constitutes a long-standing challenge, both experimentally and theoretically. It has recently been understood that two-particle correlations in the azimuthal distribution of final hadrons emitted in ultra-relativistic ultra-central ion-ion collisions can be used to quantify ground-state two-body correlations. Performing systematic ab initio nuclear structure calculations of light nuclei, we demonstrate that such an observable does provide a meaningful imaging of nuclear ground states, naturally leading to a robust interpretation of the various categories of two-nucleon correlations at play. This is at variance with the low-energy approach relying on Kumar operators whose traditional interpretation in terms of deformation parameters is shown to be inoperative. A future interesting development will consist of targeting specific three-particle correlations to isolate three-nucleon correlations in which additional nuclear structure information of interest leave their fingerprint.

Figures (11)

• Figure 1: Projected HFB ground-state (a) mean-square quadrupole anisotropy $\langle \epsilon^2_2 \rangle$ and (b) its rescaled two-body contribution $\mathcal{B}^2_2(\text{HE})$ for all even-even nuclei between carbon and nickel. Proton (neutron) magic numbers are indicated by horizontal (vertical) lines.
• Figure 2: Projected HFB ground-state $\langle \epsilon^2_2 \rangle$, $\langle \epsilon^2_2 \rangle^{1\text{b}}$ and $\langle \epsilon^2_2 \rangle^{2\text{b}}$ as a function of $A$ for all even-even nuclei between carbon and nickel.
• Figure 3: Rescaled PHFB two-body ground-state quadrupole mean-square eccentricity $\mathcal{B}^2_{2}(\text{HE})$ and Kumar quadrupole second moment $\mathcal{B}^2_{2}(\text{LE})$ against the squared intrinsic quadrupole deformation parameter $\beta^2_{20}$ of the underlying dHFB state. For consistency, the dHFB (PHFB) one-body radius is used to compute $\beta_{20}(\text{dHFB})$ ($\mathcal{B}^2_{2}(\text{LE})$) instead of $R_0$ using the connection detailed in the SM.
• Figure 4: Same as Fig. \ref{['fig: systematic comparison of Beta^2 versus standard beta^2']} for both PHFB and PGCM calculations of $^{12}$C, $^{16}$O and $^{20,22}$Ne.
• Figure 5: Convergence plot of $\mathcal{B}^2_2(\mathrm{HE})$ in $^{12}$C, $^{16}$O and $^{20,22}$Ne as a function of the one-body basis dimension. Calculations are performed within the PHFB approximation.