Analytical solutions of the Bohr Hamiltonian with the Morse potential

Abstract

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.

33 pages with 2 Tables and 2 Figures

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• Physical applications of second-order linear differential equations that admit polynomial solutions
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• Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model
• Electric quadrupole transitions of the Bohr Hamiltonian with Manning-Rosen potential
• The Asymptotic Iteration Method Revisited
• Resonant states and pseudospin symmetry in the Dirac Morse potential
• Conjunction of $\gamma$-rigid and $\gamma$-stable collective motion in the critical point of the phase transition from spherical to deformed nuclear shapes
• Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential
• Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials
• An alternative approach to Schrödinger equations with a spatially varying mass
• Polynomial solutions of certain differential equations arising in physics
• Solvable Systems of Linear Differential Equations