Nuclear vertex constants and asymptotic normalization coefficients for 8Be resonance states from effective-range expansions for αα scattering

Abstract

The properties of the first excited state of the 8Be* nucleus (2+) are studied. This state corresponds to the resonance in αα scattering at the energy of E α = E 2 ≈ 3 MeV. Use is made of an expansion of the effective-range function K(k 2). The function K(k 2) is sensitive to the value of E 2. A fit to experimental data on the dependence of the Coulomb-nuclear phase shift δ 2 C on the energy E α leads to an E 2 value that is smaller than the average value obtained from an analysis of various reactions. The experimental behavior of δ 2 C (E α) cannot be described satisfactorily by fixing the average value of E 2. The renormalized nuclear vertex function for the process α + α → 8Be*(2+) and the asymptotic normalization coefficient for the respectiveGamow wave function are calculated by using the set of parameter values found in the present study.