Bound, virtual, and resonanceS-matrix poles from the Schrödinger equation

Abstract

A general method, which we call the potential S-matrix pole method, is developed for obtaining the S-matrix pole parameters for bound, virtual, and resonant states based on numerical solutions of the Schrödinger equation. This method is well known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when r → ∞. Concrete calculations are performed for the 1 + ground state of 14 N, the resonance 15 F states (1/2 + , 5/2 + ), low-lying states of 11 Be and 11 N, and the subthreshold resonance in the proton-proton system. We also demonstrate that in the case of broad resonances, their energy and width can be found from the fitting the experimental phase shifts using the analytical expression for the elastic-scattering S matrix. We compare the S-matrix pole and the R matrix methods for broad resonances in the 14 O-p and in 26 Mg-n systems.A. M. MUKHAMEDZHANOV et al. PHYSICAL REVIEW C 81, 054314 (2010)

Structure and decay of the extremely proton-rich nuclei O11,12

“…At Q 2p = 4.13 MeV, the antibound state of 10 Li at E = −1.02 MeV is predicted by our model. With increasing Z c , this pole goes through the region of subthreshold resonances defined by Re(E) < 0 and Γ > 0 and located below the −45 • line in the momentum plane [74][75][76], and eventually becomes a threshold resonant state in 10 N at Z c = 6. This is not surprising as antibound states do not exists in the presence of the Coulomb interaction [77][78][79].…”

Asymptotic normalization coefficients from the14C(d,p)15Mukhamedzhanov1, Burjan2, Gulino3 et al. 2011Phys. Rev. C349560View full textAdd to dashboardCite

“…Here l = 0 and j = 1/2 are the orbital angular momentum and total angular momentum of the neutron in 15 C. This result was obtained using the resonance width of the broad state in 15 F experimentally measured in [5]. However, the value of the width of a broad resonance significantly depends on the method used to extract it [6]. Hence, the uncertainty of the ANC determined from the mirror symmetry can be large.…”

Reexamination of the astrophysicalSfactor for theα+d→6Li

“…This potential will provide the bound state wave function with the binding energy which should coincide with the value used in the extrapolation procedure. Besides, the ANC obtained from the calculated bound state wave function and from the residue of the elastic scattering S-matrix in the bound state pole must coincide [14].…”