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Abstract
In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three α-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13C.
Highlights
Cluster degrees of freedom are very important for the description of light nuclei, in particular kα and kα + x nuclei, due to the large binding energy of the 4He nucleus
We present a study of cluster states in 12C and 13C in the framework of the algebraic cluster model and the cluster shell model, respectively
Cluster states are described in terms of a system of N interacting bosons with angular momentum and parity LP = 1− and LP = 0+
Summary
Cluster degrees of freedom are very important for the description of light nuclei, in particular kα and kα + x nuclei, due to the large binding energy of the 4He nucleus. The relevant degrees of freedom of a system of k-body clusters are given by the k − 1 relative Jacobi coordinates and their conjugate momenta. The building blocks of the ACM consist of a vector boson for each relative coordinate and a scalar boson. Cluster states are described in terms of a system of N interacting bosons with angular momentum and parity LP = 1− (vector bosons) and LP = 0+ (scalar bosons). The 3(k − 3) components of the vector bosons together with the scalar boson span a (3k − 2)dimensional space with group structure U (3k−2). Since one does not consider the excitations of the α particles themselves, the allowed cluster states have to be symmetric under the permutation group Sk
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