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Gamow shell model description of exceptional point in $^7$Li

David Cardona Ochoa, Marek Płoszajczak, Nicolas Michel

TL;DR

This work identifies an exceptional point (EP) within the Gamow Shell Model in the Coupled Channels representation (GSM-CC) for the $^7$Li spectrum, specifically among the $5/2^-$ doublet. By tuning proton and neutron spin-orbit strengths, the two states coalesce in energy and width at the EP, accompanied by vanishing phase rigidity and a double pole in the S-matrix. The EP imprint appears in reaction observables: the elastic cross section shows a split-peak structure and the phase shift exhibits a single $2\pi$ jump. The results establish GSM-CC as a powerful framework to explore EP phenomena in nuclei and point to indirect experimental signatures via cross sections, phase shifts, and widths.

Abstract

We report the first identification of an exceptional point (EP) within the Gamow Shell Model in the Coupled Channels representation (GSM-CC). In the spectrum of $^{7}$Li, an EP is found for the $5/2^-$ doublet, where the two states coalesce in both energy and width, the phase rigidity vanishes, and the S-matrix develops a double pole. These features manifest directly in observables: the elastic cross section acquires a split-peak structure, and the phase shift shows a single $2π$ jump. This work demonstrates that GSM-CC provides a powerful framework to explore EP phenomena in nuclei and their experimental signatures.

Gamow shell model description of exceptional point in $^7$Li

TL;DR

This work identifies an exceptional point (EP) within the Gamow Shell Model in the Coupled Channels representation (GSM-CC) for the Li spectrum, specifically among the doublet. By tuning proton and neutron spin-orbit strengths, the two states coalesce in energy and width at the EP, accompanied by vanishing phase rigidity and a double pole in the S-matrix. The EP imprint appears in reaction observables: the elastic cross section shows a split-peak structure and the phase shift exhibits a single jump. The results establish GSM-CC as a powerful framework to explore EP phenomena in nuclei and point to indirect experimental signatures via cross sections, phase shifts, and widths.

Abstract

We report the first identification of an exceptional point (EP) within the Gamow Shell Model in the Coupled Channels representation (GSM-CC). In the spectrum of Li, an EP is found for the doublet, where the two states coalesce in both energy and width, the phase rigidity vanishes, and the S-matrix develops a double pole. These features manifest directly in observables: the elastic cross section acquires a split-peak structure, and the phase shift shows a single jump. This work demonstrates that GSM-CC provides a powerful framework to explore EP phenomena in nuclei and their experimental signatures.

Paper Structure

This paper contains 7 sections, 15 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. GSM-CC
  4. Exceptional points in a 2x2 Matrix
  5. S-matrix
  6. Results
  7. Conclusions

Figures (4)

  • Figure 1: Spectrum of $^7\text{Li}$ obtained in from the GSM-CC calculation showing the relevant particle emission thresholds, the energies are reproduced perfectly, with a slight underestimation of the experimental widths. On the right, the position of the found EP where the two $5/2^-$ states coalesce.
  • Figure 2: Trajectories of the $5/2^-$ doublet towards the EP, exhibiting the characteristic square-root behavior of energies and widths."
  • Figure 3: On the left, the elastic cross section as a function of the center of mass energy for $^4\text{He}(^3\text{H},^3\text{H})^4\text{He}$ showing the characteristic split peak behavior at the energy of the state related to the EP. On the right, the phase shift of the $F_{5/2}$ partial wave of the $^3\text{H}$ projectile showing the $2\pi$ jump related to having a double pole in the S-matrix.
  • Figure :