Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Ab initio description of $\bar{p}+\rm{^3H}$ and $\bar{p}+\rm{^3He}$ systems in optical models

Pierre-Yves Duerinck, Rimantas Lazauskas

TL;DR

This work provides the first ab initio four-body calculations for antiproton interactions with light nuclei by solving the Faddeev–Yakubovsky equations in configuration space using realistic $NN$ and $N\bar{N}$ optical potentials. Scattering lengths and level shifts for $\bar{p}+^3H$ and $\bar{p}+^3He$ are obtained, with the level shifts computed via the Trueman expansion and annihilation densities derived from full four-body wavefunctions. The results show that $S$-wave observables are relatively insensitive to the $NN$ model, while $P$-wave observables exhibit strong model dependence on $N\bar{N}$ interactions; the experimentally measured $2p$ width is reproduced but the real part of the $2p$ shift is typically underestimated. Annihilation is demonstrated to be peripheral, supporting the PUMA approach to probing nuclear density tails and highlighting the need for improved low-energy $N\bar{N}$ constraints.

Abstract

In the context of the ongoing PUMA experiment (CERN), which investigates antiproton annihilation on atomic nuclei, we study the energy shifts and widths of Rydberg states in the $\bar{p}+\rm{^3H}$ and $\bar{p}+\rm{^3He}$ systems by performing ab initio calculations. The scattering lengths and scattering volumes are first determined by solving the Faddeev-Yakubovsky equations in configuration space. The level shifts and widths of the corresponding $\bar{p} \, \rm{^3H}$ and $\bar{p} \, \rm{^3He}$ hydrogen-like states are then obtained using the Trueman formula. A pronounced model dependence associated with the nucleon-antinucleon interaction is observed for certain states. Finally, annihilation densities are computed from the four-body wavefunctions. Comparison with the nuclear density distributions indicates that the nucleon-antinucleon annihilation is predominantly peripheral.

Ab initio description of $\bar{p}+\rm{^3H}$ and $\bar{p}+\rm{^3He}$ systems in optical models

TL;DR

This work provides the first ab initio four-body calculations for antiproton interactions with light nuclei by solving the Faddeev–Yakubovsky equations in configuration space using realistic and optical potentials. Scattering lengths and level shifts for and are obtained, with the level shifts computed via the Trueman expansion and annihilation densities derived from full four-body wavefunctions. The results show that -wave observables are relatively insensitive to the model, while -wave observables exhibit strong model dependence on interactions; the experimentally measured width is reproduced but the real part of the shift is typically underestimated. Annihilation is demonstrated to be peripheral, supporting the PUMA approach to probing nuclear density tails and highlighting the need for improved low-energy constraints.

Abstract

In the context of the ongoing PUMA experiment (CERN), which investigates antiproton annihilation on atomic nuclei, we study the energy shifts and widths of Rydberg states in the and systems by performing ab initio calculations. The scattering lengths and scattering volumes are first determined by solving the Faddeev-Yakubovsky equations in configuration space. The level shifts and widths of the corresponding and hydrogen-like states are then obtained using the Trueman formula. A pronounced model dependence associated with the nucleon-antinucleon interaction is observed for certain states. Finally, annihilation densities are computed from the four-body wavefunctions. Comparison with the nuclear density distributions indicates that the nucleon-antinucleon annihilation is predominantly peripheral.
Paper Structure (12 sections, 25 equations, 3 figures, 8 tables)

This paper contains 12 sections, 25 equations, 3 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Formalism
  3. The $N \bar{N}$ interaction
  4. Jacobi coordinates
  5. Faddeev-Yakubovsky equations
  6. Numerical resolution
  7. Results
  8. Scattering lengths
  9. Level shifts
  10. Annihilation densities
  11. Conclusion
  12. Acknowledgement

Figures (3)

  • Figure 1: Jacobi coordinates for $\mathcal{K}$ and $\mathcal{H}$ partitions including the interaction pair $(12)$.
  • Figure 2: Annihilation densities of $0^+$ (left) and $0^-$ (right) $\bar{p} \, \rm{^3H}$ states computed with the KW (red) and Jülich (blue) potentials, used in conjunction with the I-N3LO interaction. The curves are compared with the appropriately scaled density of $\rm{^3H}$ (black).
  • Figure 3: Annihilation densities of $0^+$ (left) and $0^-$ (right) $\bar{p} \, \rm{^3He}$ states computed with the KW (red) and Jülich (blue) potentials, used in conjunction with the I-N3LO interaction. The curves are compared with the appropriately scaled density of $\rm{^3He}$ (black).