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 $[E (5) - Mie \otimes U (4)]$ , 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.

Keywords:

PACS: 21.60.Ev, 21.10.Ky, 21.10.Re, 21.60.Fw

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