  In this paper, we present new analytical solutions of the Bohr Hamiltonian
problem that we derived with the Tietz-Hua potential, here used for describing
the {\beta}-part of the nuclear collective potential plus harmonic oscillator
one for the {\gamma}-part. Also, we proceed to a systematic comparison of the
numerical results obtained with this kind of {\beta}-potential with others
which are widely used in such a framework as well as with the experiment. The
calculations are carried out for energy spectra and electromagnetic transition
probabilities for {\gamma}-unstable and axially symmetric deformed nuclei. In
the same frame, we show the effect of the shape flatness of the
{\beta}-potential beyond its minimum on transition rates calculations.
