Semimicroscopic Algebraic Cluster Model Research Articles

Geometrical interpretation of the semimicroscopic algebraic cluster model.

A geometrical mapping of the semimicroscopic algebraic cluster model is given. The geometrical variables are the relative radius vector and the quadrupole deformation parameters. The last ones correspond to absolute \ensuremath{\beta} and \ensuremath{\gamma} values, while the orientation of the deformed nucleus in the laboratory can be changed. We show that the position of the minimum of the nuclear molecular potential is determined by the minimal number of \ensuremath{\pi} bosons describing the relative motion. The minimal number of \ensuremath{\pi} bosons is determined by the implementation of the Pauli principle. Applications to simple systems ${(}^{16}$O+\ensuremath{\alpha} and $^{12}\mathrm{C}$+\ensuremath{\alpha}) are presented. \textcopyright{} 1996 The American Physical Society.

Consistent semimicroscopic algebraic description of core + α-particle systems in the A = 16 to 20 region

A standardized version of the Hamiltonian of the Semimicroscopic Algebraic Cluster Model is presented, by the use of which the spectra of several neighbouring even- and odd-mass nuclei can be parametrized in a consistent way. We extract parameters from the 12C + α, 14C + α, 15N + α and 16O + α systems and use them to construct the Hamiltonian for 13C + α by interpolation.

The semimicroscopic algebraic cluster model of atomic nuclei

The idea of the semimicroscopic algebraic cluster model of atomic nuclei was presented at the previous meeting of the same kind [1]. In this description phenomenological interactions are combined with the model space of the microscopic SU(3)cluster model, which is free from the Pauli forbidden states and spurious excitations. Here we review the present status of this approach.

Semimicroscopic Algebraic Cluster Model of Light Nuclei. I. Two-Cluster-Systems with Spin-Isospin-Free Interactions

The relation of the phenomenological algebraic cluster model, i.e., of the vibron model and its extensions, to the microscopic description is discussed. Based on this connection a semimicroscopic approach is formulated, in which the internal cluster degrees of freedom are treated in terms of the SU(3) shell model, and the relative motion is described by the vibron model. For a two-cluster system this model has a group structure of U ST C 1 (4)⊗ U C 1 (3)⊗ U R (4)⊗ U C 2 (3)⊗ U ST C 2 (4), and the phenomenological interactions are obtained in terms of the group generators. The model space is constructed to be free from the Pauli-forbidden states and spurious center of mass motion, similar to that of the SU(3) cluster model. Three examples, the 12C + α, the 12C + 12C and the 14C + α systems are presented to demonstrate various aspects of the semimicroscopic algebraic cluster model.

Semimicroscopic algebraic study of the alpha -cluster states of the 18O nucleus.

The $^{14}\mathrm{C}$+\ensuremath{\alpha} system is described in terms of the new semimicroscopic algebraic cluster model, which is based on the coupling of the SU(3) shell model to the vibron model. Molecular states of the $^{18}\mathrm{O}$ nucleus built on the $^{14}\mathrm{C}$ levels with (0,2) SU(3) quantum numbers are constructed, and the corresponding energy eigenvalues are obtained from a model Hamiltonian with SU(3) dynamical symmetry. The model is able to account for 34 experimental $^{18}\mathrm{O}$ states assigned to even- or odd-parity bands, some of which are new. Enhanced E1 and E2 transitions are also obtained.