Thermal Properties of ⁴He, ¹⁶O and ⁴⁰Ca Isotopes Using Harmonic Oscillator Nuclear Potential

In this paper, we investigate the thermal properties of  16O and 40Ca Isotopes using an independent quasi-particle model in the three-dimensional harmonic oscillator potential as a mean-filed potential. The calculations are based on quantum statistics in the canonical ensemble scheme, from which we construct the partition function. The partition functions are constructed using two different models: (1) considering nucleons as a fermion gas and utilizes an antisymmetric partition function recursion formula accounting for bulk spin pairings using Hund’s rule, (2) considering the nucleon system consists of isoscalar clusters of spin vector bosons. Hence, we calculate the thermal energy and heat capacity as a function of temperature. We then compute the level density and compare it with the available experimental data. The results are favorable and show excellent agreement with the experimental level densities.