Recent advancements in the strongly coupled many-body theory for nuclear spectral computation

Abstract

Some recent advancements of the nuclear many-body theory and selected results on nuclear giant and pygmy resonances are presented. The theory is compactly reviewed, with a special focus on the emergent scale of the quasiparticle-vibration coupling (qPVC), which carries the order parameter associated with the qPVC vertex, and an efficient treatment of the nuclear many-body problem organized around the qPVC hierarchy. Self-consistent numerical solutions of the relativistic Bethe-Salpeter-Dyson equation for the nuclear response function in medium-heavy nuclei are discussed. The presented update on the pygmy dipole resonance focuses on establishing the formation of its two-component structure as a result of the fragmentation of the low-energy dipole mode due to the qPVC and its mixing with the similarly fragmented giant dipole resonance. The centroid of the isoscalar giant monopole resonance is also linked to qPVC effects, particularly to its sensitivity to the coupling of the collective breathing mode to the lowest quadrupole vibrations, which is enhanced by quadrupole collectivity. The resolution of the long-standing "fluffiness" puzzle regarding the compressibility of open-shell tin isotopes is summarized. The recently developed thermal variant of the superfluid response theory is briefly introduced and continuously linked to the description of the isoscalar monopole response at finite temperature with the prospect of refining the temperature-dependent nuclear equation of state.

Figures (4)

• Figure 1: LEDS in $^{120}$Sn calculated in RQRPA and RQTBA/REOM$^2$ with $\Delta =$ 20 keV smearing (top panel). The radial neutron ($\nu$) and proton ($\pi$) transition densities $\rho^{(\nu,\pi)}(r)$ extracted from the RQRPA (middle) and RQTBA (bottom) calculations in the $6 \leq E \leq 10$ MeV energy range. The energies of the states are indicated in the boxes in the bottom-left corners of each panel displaying the transition densities. The dotted box in the top panel encloses the energy interval dominated by the intruder RQTBA states. The figure is reprinted from Ref. Markova2025.
• Figure 2: The $\cal Z$-values exceeding 0.01% for the characteristic LEDS states of RQRPA (top) and RQTBA (bottom): ${\cal Z}_{ij} = |{\cal X}^n_{ij}|^2 - |{\cal Y}^n_{ij}|^2$, where $\{i,j\}$ stand for the quasiparticle orbits in the mean-field basis of Dirac-Hartree-Bogoliubov spinors LitvinovaRingTselyaev2008. ${\cal X}^{n}_{jk} = \langle 0|\alpha_k\alpha_j|n\rangle$ and ${\cal Y}^{n}_{jk} = \langle 0|\alpha^{\dagger}_{j}\alpha^{\dagger}_k|n\rangle$, where $\{\alpha^{\dagger}_j,\alpha_j\}$ are the operators of the Bogoliubov quasiparticles, and $|0\rangle$ and $|n\rangle$ are the ground and excited states, respectively. The dotted box encloses the characteristic proton-dominant state. The figure is reprinted from Ref. Markova2025.
• Figure 3: (a): ISGMR centroids in nickel isotopes $^{56-70}$Ni compared to data of Refs. Monrozeau2008 ($^{56}$Ni), Lui2006 ($^{58,60}$Ni), and Vandebrouck2014 ($^{68}$Ni). Empty symbols stand for three separate peaks above 10 MeV determined in Vandebrouck2014. (b): the downward shifts $\Delta\langle E \rangle_{\text{ISGMR}}$ of the ISGMR centroids in the RQTBA with respect to the RQRPA ones (circles) in comparison with the E(2$^{+}_1$) values (diamonds). (c,d): The isoscalar monopole response in $^{120}$Sn and $^{208}$Pb as RQRPA and RQTBA strength distributions compared to experimental data Li2007 ($^{120}$Sn) and Garg2018 ($^{208}$Pb). The figure is adapted from Ref. Litvinova2023.
• Figure 4: Evolution of the monopole response of $^{120}$Sn with temperature. Dashed curves: RQRPA at $T = 0$ and finite-temperature RRPA (FT-RRPA) at $T > 0$. A continuous limit of vanishing superfluidity at the critical temperature $T_c$ in the interval $0 \leq T_c \leq 1$ MeV is assumed following Ref. Litvinova2021, for both RQTBA and FT-RTBA. The color code of the dashed curves (REOM$^1$) follows that of the solid curves.