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

Abstract

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 and B(E2) rates of the Bohr Hamiltonian in the γ-unstable case, as well as in an exactly separable rotational case with γ ≈ 0, called the exactly separable Morse (ES-M) solution. All medium mass and heavy nuclei with known β1 and γ1 bandheads have been fitted by using the two-parameter γ-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 and Kratzer potentials, also soluble by the AIM, are made.