The application of the real Weinberg state method to unbound levels in13C formed by neutron scattering and (d,p) on12C

Abstract

The real Weinberg state method devised to calculate a suitable form factor of the resonant final state in a stripping reaction is applied to elastic resonance scattering of neutrons by 12C. The purpose is to establish the methodological accuracy of the theory. Some important adjustments to the theory are incorporated. The phase shifts of the different total angular momentum and parity (Jpi =1/2+,3/2+,5/2+) channels are compared with the exact solution obtained from a coupled-channel method. The agreement is generally satisfactory. The parameters of the resonances yielded by the respective methods are also compared. The Weinberg method describes the levels as mixtures of discrete configurations which are either BSEC (bound states embedded in the continuum) or single-particle resonances treated as Weinberg states. The wavefunctions of the respective methods are used as form factors in 12C(d,p)13C stripping calculations, again with satisfactory agreement. The role of Weinberg method as a schematic way of solving a coupled-channel problem is briefly discussed.