In this paper, analytical solution of the Bohr model with Mie potential for even–even and odd–even nuclei are evaluated in the Bose alone symmetry [E(5)−Mie] and a new class of Bose–Fermi dynamical symmetry [E(5)−Mie⊗U(4)], respectively. The excitation energy spectra as well as electromagnetic transition strengths, quadrupole moments and dipole moments are investigated near the critical point of shape phase transition between the spherical and deformed γ-unstable nuclei. To show our results are compatible with experiment, some examples are tested.
