Double pole $S$-matrix singularity in the continuum of $^7$Be

TL;DR

This paper investigates whether exceptional points (EPs) can occur in nuclear open quantum systems and how they manifest in observables. Using the Gamow Shell Model in coupled-channel form (GSM-CC), the authors describe bound, resonant, and continuum states with a Berggren basis while tracking the $5/2^-$ doublet in $^7$Be as a function of spin–orbit strengths. They identify an EP where the two $5/2^-$ resonances coalesce in energy and total width, the phase rigidity $r_i$ vanishes, and single-state spectroscopic factors and $B(E2)$ values diverge, though their sum remains finite. The results demonstrate tangible signatures of EPs in nuclear open quantum systems and reveal how non-Hermitian continuum coupling qualitatively alters reaction-channel observables.

Abstract

The double pole singularity of the $S$-matrix, the so-called exceptional point, associated with the $5/2^-$ doublet of resonances in the spectrum of $^{7}$Be has been identified in the framework of the Gamow shell model. The exceptional point singularity is demonstrated by the coalescence of wave functions and spectral functions of the two resonances, as well as by the singular behavior of spectroscopic factors and electromagnetic transitions.

Figures (6)

• Figure 1: The experimental spectrum of $^7\text{Be}$ is compared with the GSM-CC spectrum. The widths (in keV) of resonances are given in brackets. On the right-hand side, one shows the spectrum for a Hamiltonian $H(\lambda_{EP})$ for which the two $5/2^-$ states coalesce.
• Figure 2: The energy eigenvalue trajectories (left panel) and the partial widths of the proton and $^3$He resonances (right panel) are shown as a function of the spin-orbit potential strength $l=1$ for protons. Near EP, a characteristic square root dependence of the energy and width can be observed.
• Figure 3: The phase rigidity of $5/2^-$ resonances is plotted as a function of their separation energy. The phase rigidity becomes equal zero at the EP.
• Figure 4: Spectral function of both $5/2^-$ resonances for different values of the phase rigidity.
• Figure 5: Evolution of the real part (upper panels) and imaginary part (bottom panels) of the $\langle {}^7 \text{Be}(5/2^-_n) ||{}^4 \text{He}(0^+)\otimes{}^3 \text{He}(F_{5/2})\rangle$ (left panels) and $\langle {}^7 \text{Be}(5/2^-_n) ||{}^6 \text{Li}(1^+)\otimes\text{p}(p_{3/2})\rangle$ (right panels) spectroscopic factors for the $5/2^-_n$ ($n=1,2$) doublet of resonances in ${}^7 \text{Be}$ when approaching the EP as a function of the energy separation between these states.