Study of the Level Density and Thermodynamic Quantities for 256Cf98 and 290Fl114 Heavy and Superheavy Isotopes based on TD(P-E_shell)-BSFGM Considering the Effects of Spin, Parity, Rotation and Vibration

Nuclear level density is a critical parameter in nuclear physics as it represents the number of energy levels per unit of energy (MeV) in a nucleus. This study calculates the level density and level density parameter for heavy and super heavy isotopes and based on the back-shifted Fermi gas method. The level density parameter is determined through a semi-classical approach using the nuclear Woods-Saxon potential. This research investigates the influence of pairing energy, and temperature-dependent shell effects on level density and thermodynamic quantities such as entropy, nuclear temperature, and nuclear-specific heat. Furthermore, the research explores the effects of nuclear spin, parity, rotational, and vibrational motion on these quantities. A graphical representation is used to illustrate the variations in nuclear level density, entropy, temperature, and specific heat as a function of nuclear excitation energy, highlighting the influence of nuclear spin, parity, and rotational and vibrational motions on them. The results show that considering these effects leads to changes in the parameters studied without altering the overall trends. Additionally, a specific heat diagram demonstrates the effects of vibrational and rotational motions, spin and parity effects, shell effects, and temperature-dependent pairing energy on excitation energy, revealing the breaking of the first nucleon pair at energies of E=2.948 MeV and E=3.04 MeV for isotopes and , respectively.