A simple description of the states $0^{+}$ and $2^{+}$ in ${}^{168}Er$

A sixth-order quadrupole boson Hamiltonian is used to describe 26 states $0^{+}$ and 67 states $2^{+}$ which have been recently identified in ${}^{168}Er$. Two closed expressions are alternatively used for energy levels. One corresponds to a semi-classical approach while the other one represents the exact eigenvalue of the model Hamiltonian. The semi-classical expression involves four parameters, while the exact eigenvalue is determined by five parameters. In each of the two descriptions a least square fit procedure is adopted. Both expressions provide a surprisingly good agreement with the experimental data.