A long sought result: Closed analytical solutions of the Bohr Hamiltonian with the Morse potential

The determination of closed analytical solutions of the Morse potential for nonzero angular momenta has been an open problem for decades, solved recently by the Asymptotic Iteration Method (AIM) for solving differential equations. Closed analytical expressions have been obtained for the energy eigenvalues of the Bohr Hamiltonian in the gamma-unstable case, as well as in an exactly separable rotational case with gamma approximate to 0, called the exactly separable Morse (ES-M) solution. 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. Comparisons to the fits provided by the Davidson potential, also soluble by the AIM, are made.