Spinodal instability in nuclear matter with light cluster degrees of freedom

Abstract

We investigate the thermodynamical stability of low-density isospin-symmetric nuclear matter at finite temperature, explicitly including light clusters as degrees of freedom. Within a generalized mean-field framework, we compute the curvature matrix of the free-energy density and determine the spinodal region, identifying the conditions under which mechanically unstable modes may develop in the presence of clustering. Particular attention is devoted to the formal consequences of introducing an infrared momentum cutoff in the density and current moments, which effectively accounts for Pauli-blocking effects and the associated reduction of low-momentum quasiparticle states in the medium. We show that when the cutoff is density dependent, thermodynamic consistency requires additional contributions to the chemical potentials and extra terms also appear in the first hydrodynamic moment, influencing both the stability analysis and the location of the spinodal boundary. We further examine the character of the unstable modes and find that a sufficiently stiff density dependence of the cutoff may drive clusters to fluctuate out of phase with nucleons, pushing them toward low-density regions while nucleonic instabilities grow, in contrast with the in-phase pattern obtained when in-medium effects are neglected. Our results shed new light on the role of light clusters in the phase dynamics of warm, dilute nuclear matter, with implications for heavy-ion collisions and for the physics of neutron-star crusts.

Figures (12)

• Figure 1: Deuteron mass fraction $X_{d}$ as a function of the total baryon density $\rho_{b}$ for different values of $\gamma_{d}$ (top panel) and $\xi_{d}$ (bottom panel). The insets show the density dependence of the corresponding infrared cutoff parametrizations.
• Figure 2: Eigenvalue $\ell_{S_1}^{d}$ (see text) as a function of the total baryon density $\rho_{b}$ for different values of $\gamma_{d}$ (top panel) and $\xi_{d}$ (bottom panel). The full calculations (solid lines) are compared with the case in which the density dependence of the cutoff parameterizations is neglected $\left(\partial \lambda_{d}/\partial \rho_{b} = 0\right)$ (dashed lines) and with the pure nucleonic case (SNM, grey dotted line). The insets show the corresponding behavior of the density derivative of the infrared cutoff parametrizations, expressed in the same units as in the main panels.
• Figure 3: The quantity $\Delta_{d}$ (see text) as a function of the total baryon density $\rho_b$ for different values of $\gamma_{d}$ (top panel) and $\xi_{d}$ (bottom panel). The full calculations (solid lines) are compared with the case in which the density dependence of the cutoff parameterizations is neglected $\left(\partial \lambda_{d}/\partial \rho_{b} = 0\right)$ (dashed lines). The insets show the corresponding behavior of the isoscalar-cluster component of the free-energy curvature matrix $\mathbb{C}_{12}$.
• Figure 4: Spinodal border in the $(\rho_{b},T)$ plane for nuclear matter with deuterons under different prescriptions: (i) density-independent cutoff, $\partial\lambda_{d}/\partial\rho_{b}=0$ (dashed lines); (ii) "hybrid" case (dash-dotted lines); and (iii) full inclusion of in-medium effects (solid lines). The red curves correspond to the linear-response (Vlasov) results of Ref. WangPRC2024, while the blue curves represent the present thermodynamic stability analysis. The spinodal boundary for pure nucleonic matter (SNM, gray) is shown for reference.
• Figure 5: The quantity $\Delta_{d}$ (see text) as a function of the total baryon density $\rho_{b}$ for nuclear matter with deuterons, obtained by neglecting (dashed lines) or fully including (solid lines) in-medium effects, at three different temperatures. The red curves, drawn only inside the spinodal region, correspond to the linear-response (Vlasov) results of Ref. WangPRC2024, while the blue curves represent the thermodynamic stability analysis. The shaded areas indicate the extent of the corresponding spinodal regions in the two approaches when in-medium effects are fully included. The dotted lines, shown for reference, correspond to $|\Delta_{d}| = 1$.