Heavy-ion fusion reactions at extreme sub-barrier energies

Recent years have witnessed an increase in interest in the study of fusion reactions at extreme sub-barrier energies, despite the fact that it is challenging to measure them due to their extremely small cross sections. Such reactions are essential to understand the creation of heavy elements in varied settings. In the present thesis work, the status of the field is reviewed involving all the related theoretical and experimental works carried out so far. The unexpected behavior seen in the steep falloff of measured cross-sections at low incident energies is explained in detail using new physics concepts related to the fusion process of atomic nuclei. Besides that, the framework of the sudden and adiabatic approaches using different potential structures especially shallow and deep potentials is discussed through the supersymmetric phase equivalent potential concept in quantum theory.