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

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

2011-06-23

arxiv.org/abs/1106.4688v1

Phys. At. Nucl. 73, 757 (2010)

Physics

Nuclear Physics

Nuclear Theory

17 pages, 5 figures

Scientific paper

10.1134/S1063778810050042

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 ${}^3\rm{He}$ and the resonant states of the nuclei ${^2}$He and ${^3}$He in the s-wave, and those of ${}^5\rm{He}$ and ${}^5\rm{Li}$ 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.

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