Three-body nuclear molecular states

Abstract

A formalism for the calculation of three-body nuclear molecules has been developed. Assuming a system of three structureless clusters all six collective degrees of freedom have been taken into account. By a transformation to suitable coordinates in the body-fixed system the different modes (rotation, bending mode, symmetric and antisymmetric radial vibration modes) approximately decouple. The problem is then reduced to a one-dimensional Schrödinger equation for the bending mode. As results we obtain three-body resonance energies, wave functions and average bending angles, which give information on the most probable internal structure: For low angular momenta L a triangular configuration is realized, while states with higher angular momenta L > L cr = 3 to 8 ħ have a stretched configuration. However, ideal linear configurations do not exist. Calculations have been performed for the systems α- 12C-α, α- 16O-α, 12C-α- 12C, 16O-α- 16O, 12C- 16O- 12C and 16O- 12C- 16O. A comparison with selected experimental data has been done for the systems α- 12C-α ( 20Ne), 12C-α- 12C ( 28Si), 12C- 16O- 12C ( 40Ca) and 16O- 12C- 16O ( 44Ti). All two-body and three-body decay data of the E c.m. = 19.7 MeV 14 + resonance in the 16O+ 12C reaction can be well understood assuming a 12C-α-12C three-body admixture in the wave function of this resonance.