Cluster excitation and single-nucleon excitation in ¹²C

We propose a new method for the classification of excitations of nuclei. Taking ¹²C as an example, we determine whether a given excited state is more of an α-cluster excitation or a single-nucleon excitation. Using the so-called pinhole algorithm in the framework of nuclear lattice effective field theory, we study the distance between any two α clusters in the nucleus, and the separations of arbitrarily chosen nucleons inside an α cluster. For a state which is predominantly a cluster-type excitation (such as the Hoyle state) the distribution of α - α separations is very different from that of the ground state. For states that are predominantly single-nucleon excitations, the two-nucleon separation inside an α cluster is in general increased.