C12(02+)+α molecular states in a microscopic four α model

The 16O nucleus is investigated within a C12+α four α multicluster model. The generator coordinate method combined with the microscopic R-matrix method is used to determine bound and resonant states. The 12C nucleus is described by 3 α clusters located at the apexes of isosceles triangles. We optimize the generator coordinates to get a reasonable description of the 02+-01+ energy gap, where the 02+ is the so-called Hoyle state, considered as a 3 α state. Our calculations mainly focus on resonances located near the C12(02+)+α threshold. We emphasize the difficulty to interpret broad resonant states and we show that bound state approximation methods are not well adapted in the context of our study. An R-matrix analysis suggests the existence of 0+, 2+ and 4+ molecular states which present a significant C12(02+)+α structure, and which may form a rotational band.