The spectrum of $^{18}$O in terms of the multiconfigurational dynamical symmetry

Abstract

Background: The experimental study of the $^{6}$Li-transfer reaction and alpha-scattering resulted in a rich spectrum of $^{18}$O, including some strong indication for band structure. Different configurations are proposed for the structural interpretation of different energy domains. Purpose: We intend to investigate whether a uniform description is possible for the complete spectrum, including the high-lying states from scattering measurement. Methods: We apply the multiconfigurational dynamical symmetry for the determination of the shape isomers and for the calculation of the spectrum obtained from different reactions. Results: The shape isomers of $^{18}$O is obtained from the study of the stability and self-consistency of the SU(3) symmetry, which is in the intersection of the shell and different cluster configurations. The $^{14}$C+$^{4}$He spectrum is calculated, and its connection to other configurations is revealed. A very simple Hamiltonian is applied, including only a harmonic oscillator term, a quadrupole interaction and an $L^2$ term. Conclusions: The spectrum (from the ground state up to the high-lying states) can be reasonably well described by a $^{14}$C+$^{4}$He cluster configuration. All the state allows the $^{12}$C+$2n$+$^{4}$He clusterization as well, and has definite shell model content. For the lowest-lying three bands the shell configuration is unique, and the overlap of the shell and the different cluster configurations is 100%.