Effect of Coulomb Forces on the Position of the Pole in the Scattering Amplitude and on Its Residue

Abstract

Explicit expressions of the vertex constant for the decay of a nucleus into two charged particles for an arbitrary orbital momentum $l$ are derived for the standard expansion of the effective-range function $K_l(k^2)$, as well as when the function $K_0(k^2)$ has a pole. As physical examples, we consider the bound state of the nucleus ${}^3\mathrm{He}$ and the resonant states of the nuclei ${}^2$He and ${}^3$He in the s-wave, and those of ${}^5\mathrm{He}$ and ${}^5\mathrm{Li}$ in the p-wave. For the systems $Np$ and $Nd$ the pole trajectories are constructed in the complex planes of the momentum and of the renormalized vertex constant. They correspond to a transition from the resonance state to the virtual state while the Coulomb forces gradually decrease to zero.

arXiv comment17 pages, 5 figures

References in corpus (4)

• S-matrix and R-matrix determination of the low-energy He-5 and Li-5 resonance parameters
• The Three-Nucleon System Near the N-d Threshold
• Ground--state energies and widths of ${}^5$He and ${}^5$Li
• Search for excited states in H-3 and He-3

Cited by in corpus (7)

• {Once more about astrophysical $S$ factor for the $\alpha +d\to {}^6\mathrm{Li}+\gamma$ reaction
• Algorithm for the asymptotic nuclear coefficients calculations using phase shift data for charged particles scattering
• Asymptotic normalization coefficients of resonant and bound states from the phase shifts for $\alpha \alpha$ and ${\alpha }^{12}\mathrm{C}$ scattering
• Connection between effective-range expansion and nuclear vertex constant or asymptotic normalization coefficient
• Resonance-state properties from a phase shift analysis with the $S$-matrix pole method and the effective-range method
• Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function
• The energies and ANCs for 5Li resonances deduced from experimental p-$\alpha$ scattering phase shifts using the effective-range and $\Delta$ methods