The real part of the polarization potential which depends on both energy and angular momentum is calculated in a simple way using dispersion relation. A barrier penetration model (BPM) has been used to explain the fusion cross-section and compound nucleus spin distribution for³²S+⁶⁴Ni system in the energy range 50–75 MeV. It is also shown that the polarization potential which only depends on energy, is not adequate to give rise to correct spin distribution even after including any radial dependence. The proposed polarization potential with implicitE andl dependences is able to explain both fusion cross-section and average spin values.

The energyE and angular momentuml dependence of optical potential for fusion of¹⁶O+²⁰⁸Pb system, observed by Christleyet al [5], is expressed as a function of radial kinetic energy (ɛ) instead of explicitE andl dependence. It is shown that the effects of different channel couplings, which result in different effective potentials, can also be parametrized as a function ofɛ. A correlation is obtained between the energy dependent part of this effective potential and the maximum of the spin enhancement around the Coulomb barrier and both these quantities depend on the details of the channel couplings.

In the optical model (OM) approach for fusion, absorption of flux occuring beyond the barrier position is presented in detail at low energies. It has been shown that the OM transmission can be well approximated as a sum of the WKB transmission and a long range absorption (LRA) contribution. Owing to absence of LRA, the fusion predictions of coupled channel codes based on transmission approach like the CCFUS code, do not agree with the predictions of complete coupled reaction channel (CRC) calculations based on OM approach using the code FRESCO. The CCFUS code with a modified transmission which includes LRA contribution is shown to be consistent with the CRC results using FRESCO. The static deformation of the colliding nuclei strongly influences the fusion imaginary potential and therefore the deep sub-barrier fusion cross sections.