Mesoscopic chemical potentials across the (hyper)nuclear landscape

TL;DR

This work defines mesoscopic chemical-potential analogs $\{\mu_B,\mu_Q,\mu_S\}$ as discrete derivatives of the strong-force energy $\tilde{E}$ with respect to the QCD charges $\{B,Q,S\}$, extracted directly from experimental nuclear and hypernuclear masses after Coulomb subtraction. By applying controlled finite-difference stencils on the discrete nuclear chart up to $\mathcal{O}(h^4)$, shell and pairing oscillations are suppressed to reveal smooth local slopes that approximate grand-canonical responses in a mesoscopic, near-$T=0$ regime. The results reveal a large negative $\mu_S$ and a near-zero $\mu_Q$ at isospin symmetry, with $\mu_B$ spanning roughly $920$–$940$ MeV, providing data-driven EOS constraints near saturation and a concrete calibration target for strangeness-enabled dense-matter models. The work also outlines targeted hypernuclear measurements to sharpen these constraints and links canonical nuclear data to the grand-canonical framework used in dense-matter theory, offering a direct empirical test for hyperon-inclusive EOSs.

Abstract

Finite nuclei constrain the dense-matter equation of state (EOS), yet they are self-bound quantum droplets far from the thermodynamic limit. Motivated by an analogy to quantum dots, we show that the nuclear chart nevertheless defines a mesoscopic regime in which mesoscopic chemical-potential analogs $\{μ_B,μ_Q,μ_S\}$ can be extracted directly from nuclear and hypernuclear binding energies after consistent Coulomb subtraction. These are discrete finite-difference response functions -- local slopes of the strong-interaction energy landscape -- not equilibrium grand-canonical chemical potentials. The nuclear chart itself supplies an "ensemble of nearby droplets": finite differences across neighboring nuclei suppress shell- and pairing-scale oscillations while retaining the smooth bulk trend, producing robust slopes without a macroscopic limit. Thus, the data provide empirical local derivatives that any strangeness-enabled EOS must reproduce near saturation. Mapping the measured (hyper)nuclear landscape at $T\simeq 0$, we find smooth, numerically stable responses, including a large, negative strangeness chemical-potential analog, and we identify specific hypernuclear measurements that can directly test and sharpen these EOS constraints.

Figures (14)

• Figure 1: We show the left-hand side of Eq. (\ref{['eqn:Gibb_ps']}), $(p-sT)/n_B$, plotted versus $A$ for different slices of $Y_Q$. We find values of approximately $\sim -3$ MeV (with error bars often consistent with zero) that do not appear to vary with $A$ or $Z$. This residual is much smaller than the extracted effective chemical potentials, so it represents a small correction relative to the extracted values.
• Figure 2: Results for $\mu_B(A,Y_Q)$ vs isospin asymmetry. We compare a specific chain of isotopes at fixed $Z$ and their corresponding error bars. Calculations are performed at different orders of accuracy, using the Euler method $\mathcal{O}(h)$, mid-point method $\mathcal{O}(h^2)$, and $\mathcal{O}(h^4)$.
• Figure 3: Averaged mesoscopic chemical potentials (top: baryon, middle: electric charge, bottom: strangeness), binned across the isospin asymmetry term. Statistical errors are shown in black/blue and systematic errors are in red/yellow.
• Figure 4: Scatter plot demonstrating the availability of experimental measurements of the mass of nuclei Huang:2021nwkWang:2021xhn (red) versus when both the mass of nuclei and their corresponding charge radii are available (black).
• Figure 5: Comparison of the experimentally measured nuclear charge radii from Angeli:2013epw to our fit in Eq. (\ref{['eqn:Rcfit']}).