A test of K-matrix formulae

Abstract

Abstract R -matrix and K -matrix fits to elastic scattering and reaction data involving low-lying 0 + states of 8 Be are compared. Three-level R -matrix formulae give good simultaneous fits to the ground-state energy and width, the α + α s-wave phase shift and a 9 Be(p, d) 8 Be deuteron spectrum that shows the 8 Be ground-state ghost. The values of the α + αf channel radius are reasonable (about 6 fm), and the third level representing the background lies above the energy range being fitted. The corresponding K -matrix formulae, with a background level lying above the fitted energy range, cannot give good fits to the same data. It seems necessary to introduce an echo pole just below the 8 Be ground state, and then the data can be well fitted. Inclusion of such a pole means, however, that 8 Be ground-state properties are not well determined by extrapolation of the high-energy data alone. It therefore seems that K -matrix formulae should be used with caution in other cases where high-energy data are extrapolated to the low energies of interest in astrophysics.