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 K0(k 2 ) has a pole. As physical examples, we consider the bound state of the nucleus 3 He and the resonant states of the nuclei 2 He and 3 He in the s-wave, and those of 5 He and 5 Li in the p-wave. For the systems N p and N d 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.

Resonance-state properties from a phase shift analysis with theS-matrix pole method and the effective-range method

“…According to Refs. [4,12,13], we renormalize the partial amplitude of the elastic scattering multiplying it by the function…”

Reexamination of the astrophysicalSfactor for theα+d→6Li

“…In this procedure the elastic scattering phase shift is analytically approximated in the physical region with the subsequent analytical continuation to the bound state pole. This analytical approximation in the physical region can be done using different approaches: Pade approximation [2], effective range expansion [3][4][5]. There is also a possibility to solve N/D equations, which take into account the right unitary cut and the left dynamical singularities.…”

Analytic continuation of scattering data as a method of obtaining characteristics of bound states

“…The ANC values for the α+d system determine the cross section of the radiative capture 4 He(d,γ) 6 Li, which is the only process of 6 Li formation in the Big Bang model. The available data on the values of the ANCs C l and the NVCs G l for that channel are characterized by a large spread, especially for l = 2 (l = 0, 2 is the channel orbital angular momentum).…”

“…The most effective way of realization of that procedure is the analytic continuation of the scattering (or effective range) function. This approach was employed in papers [3][4][5] for one-channel scattering to get the ANC and NVC values for several light nuclei. In papers [6] the method of the analytic continuation of the effective range function was generalized to the two coupled elastic channels what is important for the scattering of two particles with spins ½ or spins 1 and 0.…”