There are plenty of theoretical work in the literature dedicated to explaining measured g_R-factors of even-even deformed nuclei, however g_R-factor calculations are limited for odd-mass deformed nuclei. In the works mentioned above, particle number conservstion, residual interactions, renormalizations of orbital matrix elements, which effect the g_R, have been neglected. Either core polarizations have been avoided or not considered. Besides, in these works only g_R-factors calculated for ^155,157Gd, ^161,163Dy, ¹⁶⁷Er, ^171,173Yb, ^177,179Hf, ¹⁸³W and ¹⁵³Eu, ¹⁵⁹Tb, ¹⁶⁵Ho, ¹⁶⁹Tm, ¹⁷⁵Lu, ¹⁸¹Ta, ^185,187Re deformed nuclei. However, the magnetic moments and g-factors have been measured for several odd-A deformed nuclei in the periodic table, and g_R-factor calculations are needed to explain them theoretically. On the other hand, even though the systematic of g-factor for even-even nuclei is well known, the systematics of g-factor in odd-mass nuclei is unknown.

In the present project, we are aiming to calculate gR- and g-factors for odd-mass nuclei in the rare earth and transition region of nuclear periodic table using Particle Number Conserving Rotational Invariant (PNCRI) Quasiparticle Phonon Nuclear Model (QPNM) formulated in the project for the first time and to investigate the systematic behavior of these factors in different mass regions. In the project, we will employ Pyatov-Salamov method to restore broken symmetries of QPNM Hamiltonian. The superiority of this method is that choosing effective restoring forces in coherent with the mean field, which let us not to add a free parameter to the theory.

A computer code in the Fortran programming language for the PNCRI-QPNM formulas was obtained within the project's scope. The project was completed in two stages. The first stage calculated g_R- and g-factors for the deformed nuclei with experimental data and compared the results with the measured values. In the second stage, g_R- and g-factors for ^123-147La, ^125-153Ce, ^125-153Pr, ^131-155Nd, ^131-155Pm, ^135-155Sm,^135-155Eu, ^153-165Gd, ^153-165Tb, ^153-165Dy, ^153-165Ho, ^157-171Er, ^157-171Tm, ^159-177Yb, ^159-177Lu, ^163-181Hf, ^163-181Ta, ^169-189W, ^169-189Re, ^173-193Os, ^173-193Ir, ^177-199Pt, and ^177-199Au odd-mass isotopic chains in the rare earth and transition region of the nuclear periodic table was calculated and thus to obtain the systematic of these factors in different mass regions. The effect of particle number conservation and restoration of rotational symmetry of microscopic Hamiltonian, spin-spin residual interactions, and renormalization of orbital matrix elements on g_R- and g factors were investigated for the first time.