Data on nuclear level densities extracted from transmission data or gamma energy spectrum store the basic statistical information about nuclei at various temperatures. Generally this extracted data goes through model fitting using computer codes like CASCADE. However, recently established semiclassical methods involving no adjustable parameters to determine the level density parameter for magic and semi-magic nuclei give a good agreement with the experimental values. One of the popular ways to paramaterize the level density parameter which includes the shell effects and its damping was given by Ignatyuk. This damping factor is usually fitted from the experimental data on nuclear level density and it comes around 0.05 M eV −1 . In this work we calculate the Ignatyuk damping factor for various nuclei using semiclassical methods.

Semiclasically derived shell structure and pairing correlation energies have been included in the recently developed formula by Royer et al to evaluate the binding energies of several well known α−radioactive nuclei after appending the effects of deformation as well. Exploiting single-particle level density for spherically symmetric harmonic oscillator potential with spin–orbit interactions within the microscopic-macroscopic framework, Qα-values and the penetration probabilities are determined. This method has been extended to several recently detected superheavy elements, experimentally unknown ones and, also to four α−decay chains in Z = 120 isotopes. The obtained results have been compared with the available experimental and theoretical ones. A stability analysis for such nuclei has been done on the basis of the obtained half-lives (T1/2-values) as well.

We demonstrate that pairing phase transition (superfluid to normal) can be described quite generally in terms of the thermodynamical properties after verifying the obtained level densities with the available experimental data for [Formula: see text]- isotopes. Periodic-orbit theory conveniently connects the oscillatory part of level density to the underlying classical periodic orbits and hence, leads to the shell effects in the single-particle level density. Such methods incorporated with pairing effects can be used effectively to study the phase transitions in [Formula: see text]-isotopes. In addition to this, an interplay between pairing correlations and the shell effects has been understood by analyzing the results obtained for the critical temperatures and shell structure energies for [Formula: see text] isotopes. A relation between variation in critical temperatures caused by shell effects and the shell structure energies determined with and without pairing effects has been established. Furthermore, the systematics of the heat capacity (giving a clear signature of pairing phase transition) as function of temperature for these nuclei are investigated as well.

In this work, we calculate the level density parameter for several nuclei by deploying the semiclassical trace formula for spherically symmetric harmonic oscillator potential with spin-orbit interactions, which describes the quantum shell effects in terms of the classical periodic orbits. With the usage of recently proposed Laplace like formula of level density parameter by Canbula et al., the effects of collective rotations and vibrations as well as deformations in nuclei are incorporated. The comparison of our results with the experimental ones show a good agreement. Later on, the study is also extended to the calculation of nuclear level density and survival probability in several superheavy nuclei (SHN).

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