Clusters and halos in light nuclei

The fermionic molecular dynamics approach uses Gaussian wave packets as single-particle basis states. Many-body basis states are Slater determinants projected on parity, angular momentum and total linear momentum. The wave-packet basis is very flexible – FMD contains harmonic oscillator shell model and Brink-type cluster states as special cases. The parameters of the wave packets are obtained by variation. A realistic effective interaction derived from the Argonne V18 interaction by means of the unitary correlation operator method is employed. We discuss the fully microscopic calculation of the ³He(α, γ)⁷Be capture reaction within the FMD approach. The model space contains frozen cluster configurations at large distances and polarized configurations in the interaction region. The polarized configurations are essential for a successful description of the ⁷Be bound state properties and for the S- and D-wave scattering states. The calculated cross section agrees well with recent measurements regarding both the absolute normalization and the energy dependence. We also discuss the structure of the cluster states, including the famous Hoyle state, in ¹²C. From the two-body densities we conclude that the Hoyle state has a spatially extended triangular α-cluster structure, whereas the third 0⁺ state features a chain-like obtuse triangle structure. We also calculate the NħΩ decomposition of our wave functions to illuminate the challenges of no-core shell model calculations for these cluster states.