Solution of the Bohr Hamiltonian for the Davidson potential in the 𝛾~unstable region for odd-even nuclei

Protons and neutrons, called nucleons, form the nucleus of the atom, and the structure of the nucleus changes depending on the number of nucleons it has. When the experimental excitation energy data of the nuclei were examined, it was seen that there could be three different structures. Geometrically, these structures are harmonic oscillator, gamma-unstable and prolate (oblate) deformed rotor. One of the subjects that nuclear structure physicists have been working on intensively in recent years is the shape phase transitions that occur between these limit structures depending on the number of nucleons. Firstly, even-even nuclei were investigated because of the regularity of the experimental excitation energy spectra. At the critical points where phase transitions take place, properties such as excitation energies and electric quadrupole transition ratios of even-even nuclei are obtained. When the experimental data were examined, it was seen that except for a few nuclei, the others exhibited structures around the critical point. Odd-even nuclei, on the other hand, have not been studied much because of the complexity of their excitation energy spectra. In this study, the unstable odd-even nuclei has been thought as the single nucleon moving in a j=3/2 orbit without breaking the unstablitiy of even core. Since the system is deformed, the observables of such a system can be obtained by the collective Bohr Hamiltonian. In the Hamiltonian, the potential energy was assumed to be of the form of Davidson potential, which has two free parameters. Then the corresponding Schrödinger equation has been solved analytically by using the Nikiforov-Uvarov method. The energy equation has been obtained in a closed form as functions of Davison potential free parameters. In this study, (_^(187-195))Ir isotopes having gamma-unstable structure have been selected to test the ability of Davidson potential. To predict the experimental spectra of these nuclei, a code has been written in Mathematica programme and the Davidson potentail parameters for each isotope have been determined. It is found that theoretical predictions are in good aggreement with the experimental data.