Thermodynamic properties of $^{172}\rm{Yb}$ and $^{162}\rm{Dy}$ isotopes are investigated using the back-shifted Fermigas(BSFG) model with the energy-dependent level density parameter and the temperature-dependent pairing energy. The temperature dependency of pairing energy is applied using the mean order parameter of the exact Ginzburg–Landau (EGL) theory. The level density, entropy, temperature and heat capacity of $^{172}\rm{Yb}$ and $^{162}\rm{Dy}$ isotopes are calculated using these approaches and the results are compared with each other as well as with experimental data to examine the validity of these models. The results obtained by the present study indicate that the BSFG model with the temperature-dependent pairing energy is in better agreement with the experimental data, compared to the BSFG model with the energy-dependent level density parameter, for $^{172}\rm{Yb}$ and $^{162}\rm{Dy}$ isotopes.

The yrast band diagram and the reduced magnetic dipole-to-electric quadruple transitions ratio, B(M1)/B(E2), are simulated using a Fortran code and constructed based on the projected shell model (PSM). Calculations using the PSM are applied to study the back-bending phenomena of neutron-rich even–even isotopesof Sm, namely $^{150,152,154,156,158}$Sm. The obtained B(M1)/B(E2) ratios show that around the band-crossing spin, their values are decreased. This phenomenon occurs due to a change in the structure of energy bands. Calculated results reproduce well the variation of moments of inertia as a function of rotational frequency in the presented back-bending figures for the isotopes under consideration. Finally, simulated results are compared with the available experimental data. Good agreement has been achieved from this comparison.