Bohr Hamiltonian for collective low-lying vibrational states of well deformed nuclei

It is shown that the Bohr Hamiltonian in the intrinsic frame used for the description of the low-lying vibrational states in the well-deformed nuclei can be presented in two different forms. In the first form the Hamiltonian has three different mass coefficients but the quadrupole transition operator has a standard form with one parameter only. The second form of the Hamiltonian can be derived by a transformation from $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ to the new variables. In this form the Hamiltonian contains only one mass coefficient but the quadrupole operator takes a different form with three parameters. It is shown also that this Hamiltonian can describe a situation when a collectivity of the vibrational states is rather low, but their excitation energies are relatively small, while the $E2$ transitions inside the bands are very strong.