Nucleon Resonances in Nuclear Matter and Finite Nuclei

TL;DR

The paper develops an extended energy-density-functional (EDF) framework to describe nuclear excitations involving nucleon resonances, treating them as $NN^{-1}$ and $N^*N^{-1}$ particle–hole configurations and solving a generalized $N^*RPA$ Dyson equation at one-loop order. It systematically builds the theory from microscopic interactions (Dirac-Brueckner G-matrices and three-body terms) to a density-functional description, and then to a coupled-channels response formalism that includes in-medium self-energies and channel mixing. The authors apply this to asymmetric nuclear matter and finite nuclei, deriving CC response functions, in-medium $N^*$ spectral distributions, and local-density-approximation results that can be directly compared with high-energy heavy-ion data. The approach yields insights into the transition from quasi-elastic to resonance-dominated excitations and has potential implications for neutrino-matter interactions and upcoming facilities, with clear paths for extending the resonance spectrum and improving quantitative predictions. The work provides a thermodynamically consistent, self-contained framework that links ground-state properties to dynamical response across a broad energy range via $N^*$-coupled configurations.

Abstract

The theory of nuclear excitations involving nucleon resonances is revisited and significantly extended to asymmetric nuclear matter and higher P- and S-wave $N^*$ resonances. Excited states of are described as superpositions of particle-hole configurations including $NN^{'-1}$ and $N^*N^{-1}$ configurations. Configuration mixing is taken into account on the one-loop level by solving the generalized $N^*RPA$ Dyson equation. The underlying coupled channels formalism is derived and response functions is discussed. Applications of the approach are illustrated for charge-exchange modes of asymmetric nuclear matter and finite nuclei. The spectral gross structures of corresponding excitations in finite nuclei are investigated in local density approximation. Applications of the approach to resonance studies by high-energy heavy ion reactions are recapitulated.

Figures (12)

• Figure 1: Missing energy spectrum obtained in a $^{112}$Sn$\to{}{}^{112}$In reaction on a proton and a carbon target, in the latter case showing clearly separated quasi-elastic and resonance peaks. Note the shift in the resonance peak for the two targets (from Ref. Rodriguez-Sanchez:2020hfh).
• Figure 2: Binding energy per nucleon of symmetric nuclear matter obtained with the GiEDF without (blue line/green symbols) and with many-body corrections (red line/purple symbols) of the Urbana model UIX as used in Akmal:1998cf. The ladder and three-body resonance contributions are indicated.
• Figure 3: Schematic illustration of spectrum relative to the chemical potential $\lambda$ of hole state and particle states which are located to the left and to the right of $\lambda$, respectively. In cold degenerate matter the chemical potential is given by the Fermi energy $\varepsilon_{Fq}$ of baryon type $q=p,n\ldots$. In momentum space the hole occupation numbers are given by the Heaviside distribution $n(\mathbf{k})=n^<(\mathbf{k})=\Theta(k^2_{Fq}-\mathbf{k}^2)$ while particle states are populated complementary, $n(\mathbf{k})=n(\mathbf{k})^>=1-n^<(\mathbf{k})=\Theta(\mathbf{k}^2-k^2_{Fq})$.
• Figure 4: In-medium interactions of a baryon resonance $N^*$ via the static mean-field (left) and the dispersive polarization self-energies (center) indicated here by the decay into intermediate nucleon-meson configurations. Moreover, in nuclear matter the coupling to $NN^{-1}$ excitations contributes a spreading width (right). Wavy lines indicate the exchange mesons $\pi,\eta,\sigma,\delta/a0(980),\rho,\omega$.
• Figure 5: The RPA polarization propagator. The $N^{-1}N\to N^{-1}N$ (left), the mixed $N^{-1}N\to N^{-1}\Delta$ and the $N^{-1}\Delta\to N^{-1}\Delta$ components are displayed. Also the bare particle-hole type propagators are indicated. External fields are shown by wavy lines, the residual interactions are denoted by dashed lines. Only part of the infinite RPA series is shown.