Analytical solutions of the Bohr Hamiltonian are obtained in the $\gamma$-unstable case, as well as in an exactly separable rotational case with $\gamma\approx 0$, called the exactly separable Morse (ES-M) solution. Closed expressions for the energy eigenvalues are obtained through the Asymptotic Iteration Method (AIM), the effectiveness of which is demonstrated by solving the relevant Bohr equations for the Davidson and Kratzer potentials. All medium mass and heavy nuclei with known $\beta_1$ and $\gamma_1$ bandheads have been fitted by using the two-parameter $\gamma$-unstable solution for transitional nuclei and the three-parameter ES-M for rotational ones. It is shown that bandheads and energy spacings within the bands are well reproduced for more than 50 nuclei in each case.Comment: 33 pages with 2 Tables and 2 Figure

Eigenfunctions of the collective Bohr Hamiltonian with the Morse potential have been obtained by using the Asymptotic Iteration Method (AIM) for both γ-unstable and rotational structures. B(E2) transition rates have been calculated and compared to experimental data. Overall good agreement is obtained for transitions within the ground state band, while some interband transitions appear to be systematically underpredicted in γ-unstable nuclei and overpredicted in rotational nuclei.

In this paper, the Morse potential is used in the β-part of the collective Bohr Hamiltonian for triaxial nuclei. Energy eigenvalues and eigenfunctions are obtained in a closed form through exactly separating the Hamiltonian into its variables by using an appropriate form of the potential. The results are applied to generate the nuclear spectrum of 192 Pt , 194 Pt and 196 Pt isotopes which are known to be the best candidate exhibiting triaxiality. Electric quadrupole transition ratios are calculated and then compared with the experimental data and the Z(5) model results.

The effect of the potential well size on the spectra and B(E2) transition rates of the Z(5) solution of the Bohr Hamiltonian, corresponding to triaxial shapes, has been studied. Convergence to the Z(5) solution is obtained for large well sizes. The results are compared to the infinite well, the harmonic oscillator and the rigid triaxial rotor results. The relevance of this solution to the prolate to oblate shape/phase transition in neutron-rich nuclei in the W-Os-Pt region is discussed.