Fragmentation patterns of nuclear response: low-spin giant resonances and soft modes

TL;DR

The paper develops a relativistic nuclear field theory (RNFT) framework with beyond-QRPA quasiparticle–phonon coupling (qPVC) to describe fragmentation and spectral strength of low-spin giant resonances and soft modes. It formulates the response via a two-time Bethe-Salpeter–Dyson equation with static and dynamical kernels, and implements a controlled subtraction to avoid double counting while progressively including complex npnh configurations (e.g., $2q\otimes\text{phonon}$ and beyond to REOM$^3$). The leading-order qPVC is shown to shift and fragment the isoscalar monopole strength (ISGMR) by roughly 1–2 MeV through coupling to low-lying quadrupole phonons, enabling a parameter-free description across Ni, Sn, and Pb when using a self-consistent interaction, and the isovector dipole response in Sn isotopes proves highly sensitive to the pairing gap, affecting both the GDR and pygmy strength. Overall, the work provides a unified, beyond-mean-field pathway to connect nuclear matter properties (e.g., incompressibility) with finite-nucleus spectroscopy, while highlighting remaining uncertainties in pairing and complex configurations that motivate further ab initio grounding and scheme refinement.

Abstract

Nuclear resonances provide a rich and versatile testbed for exploring fundamental aspects of physics, particularly within the domain of strongly correlated many-body systems. The overarching goal of the theory is to develop a consistent and predictive framework that is (i) capable of a spectroscopically accurate description and (ii) sufficiently general to be applied across different energy scales and transferable to a wide range of complex systems. Thoroughly capturing emergent collective phenomena that arise in nuclear media is the central challenge for the theory, which is discussed in this contribution. It concentrates on the themes inspired and influenced by Angela Bracco's research, in particular, on the fragmentation patterns of the monopole and dipole responses of medium-heavy nuclei and associated open problems.

Figures (8)

• Figure 1: Schematic structure of the fermionic response theory. The rectangular blocks marked with $\rho$ stand for exact two-fermion densities, and those with $G^{(4)}$ denote correlated four-fermion, or $2p2h$, GF.
• Figure 2: Schematic structure of the fermionic response theory, truncated on the two-body level via the cluster decomposition and mapped to qPVC. $\tilde{R}$ stands for the correlated part of the response function.
• Figure 3: Isoscalar monopole response of selected medium-mass and heavy nuclei: RQRPA and RQTBA strength distributions compared to experimental data Lui2000 ($^{58}$Ni), Gupta2016 ($^{90}$Zr), Li2007 ($^{120}$Sn), and Garg2018 ($^{208}$Pb). RQTBA strength distributions with $\Delta =$ 35 keV and $\Delta =$ 0.5 MeV are shown.
• Figure 4: Isoscalar monopole response of $^{56-70}$Ni isotopes.
• Figure 5: (a) The ISGMR centroids in nickel isotopes $^{56-70}$Ni, compared to data of Refs. Monrozeau2008 ($^{56}$Ni), Lui2006 ($^{58,60}$Ni), and Vandebrouck2014 ($^{68}$Ni). The three separate peaks above 10 MeV reported in Vandebrouck2014 are denoted by empty circles with error bars. (b) The downward shifts $\Delta\langle E \rangle_{\text{ISGMR}}$ of the ISGMR centroids obtained in the RQTBA relative to the RQRPA centroids (circles) and the energies of the lowest quadrupole states E(2$^{+}_1$) (diamonds). The figure is reproduced from Ref. Litvinova2023.