The excited state of the $\alpha$-particle: a benchmark study

Abstract

A benchmark study is performed for the excited state of ${}^4$He. When the Coulomb interaction is switched off, the ${}^4$He nucleus exhibits a bound excited state in the vicinity of $p-{}^3$H threshold. As the Coulomb interaction is gradually introduced, the excited state crosses the threshold and eventually becomes a resonant state. Using three numerical methods, we track the evolution of this excited state and determine the resonance energy and width. Comparisons of the theoretical predictions reveal a significant discrepancy with commonly used $R$-matrix values based on the analysis of the experimental data. We explain the origin for this discrepancy. Additionally, the two-level energy spectrum of ${}^4$He in the absence of the Coulomb force exhibits characteristics linked to Efimov physics, suggesting a reduced sensitivity to interaction details.

References in corpus (26)

• Chiral effective field theory and nuclear forces
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Quantum Monte Carlo Calculations of $A\le 6$ Nuclei
• Benchmark Test Calculation of a Four-Nucleon Bound State
• A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
• Few-nucleon systems in translationally invariant harmonic oscillator basis
• Momentum-space treatment of Coulomb interaction in three-nucleon reactions with two protons
• Modern nuclear force predictions for the alpha particle
• Universal Properties of the Four-Body System with Large Scattering Length
• The Four-Boson System with Short-Range Interactions
• Testing Non-local Nucleon-Nucleon Interactions in the Four-Nucleon Systems
• Four-nucleon scattering: Ab initio calculations in momentum space
• Calculation of the Alpha--Particle Ground State within the Hyperspherical Harmonic Basis
• Ab initio four-body calculation of n-3He, p-3H, and d-d scattering
• Benchmark calculation of n-3H and p-3He scattering
• Linear correlations between 4He trimer and tetramer energies calculated with various realistic 4He potentials
• Efimov Physics and Connections to Nuclear Physics
• Description of Four- and Five-Nucleon Systems by Solving Faddeev-Yakubovsky Equations in Configuration Space
• $N$-boson spectrum from a Discrete Scale Invariance
• Pade approximation of the S-matrix as a way of locating quantum resonances and bound states
• Embedding nuclear physics inside the unitary window
• Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei
• Benchmark calculation of p-3H and n-3He scattering
• Three-neutron resonance study using transition operators
• From few to many bosons inside the unitary window: a transition between universal to non-universal behavior
• Tetraneutron resonance in the presence of a dineutron

Cited by in corpus (1)

• Possible Existence of ${}_{\varphi }^3$H, ${}_{\varphi }^4$H, ${}_{\varphi }^4$He, and ${}_{\varphi }^5$He Nuclei