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Fusion excitation functions have been measured for the first time with rather good accuracy for 32 S + 90 Zr and 32 S + 96 Zr near and below the Coulomb barrier. The sub-barrier cross sections for 32 S + 96 Zr are much larger than for 32 S + 90 Zr. A coupled-channels calculation considering the inelastic excitations is capable of describing sub-barrier enhancement only for 32 S + 90 Zr. The unexplained part for 32 S + 96 Zr is found to be correlated with the positive-Q-value intermediate neutron transfers in this system. The comparison with 40 Ca + 96 Zr suggests that couplings to the positive-Q-value neutron transfer channels may play a role in the sub-barrier fusion enhancement. Multi-neutron transfers are taken into account in Zagrebaev's semiclassical model to explain the discrepancies of the sub-barrier fusion cross sections for 32 S + 96 Zr.

The fusion excitation functions have been measured with rather good accuracy for 32 S+ 90 Zr and 32 S+ 96 Zr near and below the Coulomb barrier. The sub-barrier cross sections for 32 S+ 96 Zr are much larger compared with 32 S+ 90 Zr. Semi-classical coupled-channels calculations including two-phonon excitations are capable to describe sub-barrier enhancement only for 32 S+ 90 Zr. The remaining disagreement for 32 S+ 96 Zr comes from the positive Q-value intermediate neutron transfers in this system. The comparison with 40 Ca+ 96 Zr suggests that couplings to the positive Q-value neutron transfer channels may play a role in the sub-barrier fusion enhancement. A rather simple model calculation taking neutron transfers into account is proposed to overcome the discrepancies of 32 S+ 96 Zr.

Within the dinuclear system (DNS) conception, instead of solving Fokker-Planck Equation (FPE)analytically, the Master equation is solved numerically to calculate the fusion probability of superheavy nuclei, so that the harmonic oscillator approximation to the potential energy of the DNS is avoided. The relative motion concerning the energy, the angular momentum, and the fragment deformation relaxations is explicitly treated to couple with the diffusion process, so that the nucleon transition probabilities, which are derived microscopically, are time-dependent. Comparing with the analytical solution of FPE, our results preserve more dynamical effects. The calculated evaporation residue cross sections for one-neutron emission channel of Pb-based reactions are basically in agreement with the known experimental data within one order of magnitude.

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