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

Abstract

Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing an important role in nuclear physics and astrophysics. We derive a new useful relationship between ANC of the Gamow radial wave function and the renormalized (due to the Coulomb interaction) Coulomb-nuclear partial scattering amplitude. We use an analytical approximation in the form of a series for the nonresonant part of the phase shift which can be analytically continued to the point of an isolated resonance pole in the complex plane of the momentum. Earlier, this method which we call the S-matrix pole method was used by us to find the resonance pole energy. We find the corresponding fitting parameters for the

Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function

“…We emphasize that the renormalized scattering amplitude does not include the Coulomb term h(η) (8) which is part of the ERF in Eq. (7). The function h(η) forms a background for the nuclear term and obviously leads to a wrong ANC for 'large' charges of colliding nuclei.…”

“…There is a fairly good agreement between the fitting curves and the experimental data in the energy intervals considered. 7 Be ↔ α+ 3 H. Calculation method, J π , resonance energy E0 and its width Γ, corresponding values of ANCs |C l | and |C a l | calculated by Eq. (19) for narrow resonances.…”

“…In the S-matrix pole method (SMP) (see Ref. [7]), an analytical continuation to the resonance pole is accomplished for the so-called 'potential' (or no resonant) phase shift in the complex k plane. Having found the ANC, we now know the asymptotic part of the Gamow wave function.…”

Extrapolation of scattering data to the negative-energy region

“…The ERF method has been successfully employed to determine the ANCs for bound (as well as resonant) nuclear states in a number of works (see, e.g. [9][10][11] and references therein).…”

“…The following procedure is usually used (see, e.g. [10,11]). The values of the ERF K l (E) at E > 0 obtained by the phase-shift analysis of experimental data are approximated by some analytic function, say, by several first terms of the effective-range expansion or by the Padé approximant.…”