Investigating the structures of odd-mass deformed nuclei is one of the most complex and least studied topics in nuclear physics. Almost all existing theoretical and experimental studies have focused on investigating the Gallagher-Maszkowski splitting, and Newby shifts in the energy levels of odd-odd nuclei, for which the interactions between the valance neutron and valance proton are responsible. Although the ground state magnetic moments of many odd-odd deformed nuclei in the rare earth and actinide regions have been measured, no satisfactory and comprehensive theoretical study on their calculations stands out as a significant deficiency in understanding the complex structure. Because magnetic moments are sensitive to single-particle and collective motion of nucleons, they provide useful information about the nature of nuclear forces and constitute an important testing area for nuclear models. Existing theoretical studies are based on Nilsson, Hartree-Fock and Macroscopic-Microscopic Model calculations. They were used to calculate the observed magnetic moments of only one or a few odd-odd isotopes and have not applied to all nuclei for which experimental data are available. For some nuclei within the same isotope chain, these models give results that are compatible with the experiment, but for some, the results differ approximately twice from the experiment or have opposite signs. Due to these inconsistencies, it is unknown how successful these models will be in all deformed nuclei in any region of the periodic table. Besides, in these studies, the details of wave functions and Hamiltonians are not given, interactions (for example, neutron and proton interactions, which are known to be of critical importance for odd-odd nuclei) are not considered, and effective spin and collective gyromagnetic factors (g_R) are arbitrarily chosen. These damage the reliability and general validity of these models. In addition, although the magnetic moment of many odd-odd deformed nuclei has been measured since these pioneering studies, a new theoretical approach has not been developed for their calculations.
The proposal's subject is to formulate a new theory (Doubly-Odd QPNM) based on the Quasiparticle Phonon Nuclear Model (QPNM) for the first time and to code it in the FORTRAN programming language. This theory will allow calculating the magnetic moments of deformed odd-odd nuclei (^130-154Pr, ^144-154Pm, ^138-158Eu, ^140-168Tb, ^152-170Ho, ^154-174Tm, ^156-180Lu, ^212,214Ac, ^228-236Pa, ^236-244Np, ^236-246Am) in the rare earth and actinide regions. It will also make it possible to investigate the systematic properties of the magnetic moments of these nuclei. We aim to take into account new terms such as spin-spin interactions, interactions between single neutron and single proton, and interactions between valance nucleons and core phonons, which are not included in existing theories, and to eliminate the arbitrariness in the selection of the spin polarization factor and g_R-factor. Thus, a compact theory that eliminates the previous theoretical deficiencies reveals the effects of ignored interactions, eliminates the arbitrariness in and g_R-factor selections and can be applied to the magnetic moment calculation of all deformed odd-odd nuclei will be introduced to the literature. It is aimed to determine the systematics of the magnetic moments of odd-odd nuclei in the rare earth and actinide regions and to present first predictions for the magnetic moments of odd-odd ^{130-140,144-154}Pr, ^146,150-156Pm, ^156,160Eu, ^{140-146,154,162-168}Tb, ^164-170Ho, ^172-174Tm, ^{156-160,170,180}Lu, ^216-224Ac, ^232-236Pa, ^236-244Np, ^{236-240,244,246}Am.