We have developed a special computing code for calculation of nuclear shape changes and quadrupole moments ( Q) of Gadolinium Isotopes. It has been shown from these calculations that by increasing neutron number, deformation parameter also increase for more heavier isotopes which means more deformation from spherical shape. By comparison with Nilsson level diagrams we can infer quadrupole deformation parameter (β 2 ) and calculate quadrupole moments of these isotopes.

Back-bending phenomenon is one of the important phenomena usually seen at high spin states of even -even heavy nuclei. As a result, any changes in the behavior of nuclear rotation, such as increase in moment of inertia versus rotational frequency can be shown in the usual back-bending plots which have been studied in many papers before. In this paper we show for the first time that these changes can be seen in the ratio of electromagnetic reduced transition probabilities B (E2) and B (M1) in even -even [152][153][154][155][156][157][158][159][160][161][162][163][164] Dy isotopes using the Projected Shell Model (PSM) theory. The electric quadrupole transition probability B (E2) and the magnetic dipole transition probability B (M1) moments are sensitive to nuclear shape deformation and nuclear charge distribution, respectively. Our findings confirm the well-known back-bending previously seen and are in good agreement with experimental results. While intrinsic quadrupole moments are constant for each Dy isotope, the new findings show that spectroscopic quadrupole moments are increasing with spin.