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The dynamic coupling effects on fusion cross sections for reactions $^{32}$S+ $^{94,96}$Zr and $^{40}$Ca + $^{94,96}$Zr are studied with the universalfusion function formalism and an empirical coupled channel (ECC) model. Anexamination of the reduced fusion functions shows that the total effect ofcouplings to inelastic excitations and neutron transfer channels on fusion in$^{32}$S + $^{94}$Zr ($^{40}$Ca + $^{94}$Zr) is almost the same as that in$^{32}$S + $^{96}$Zr ($^{40}$Ca + $^{96}$Zr). The enhancements of the fusioncross section at sub-barrier energies due to inelastic channel coupling andneutron transfer channel coupling are evaluated separately by using the ECCmodel. The results show that effect of couplings to inelastic excitationschannels in the reactions with $^{94}$Zr as target should be similar as that inthe reactions with $^{96}$Zr as target. This implies that the quadrupoledeformation parameters $\beta_2$ of $^{94}$Zr and $^{96}$Zr should be similarto each other. However, $\beta_2$'s predicted from the finite-range dropletmodel, which are used in the ECC model, are quite different. Experiments on$^{48}$Ca + $^{94}$Zr or $^{36}$S + $^{94}$Zr are suggested to solve thepuzzling issue concerning $\beta_2$ for $^{94}$Zr.

Theoretical study of fusion reactions $^{32}$S + $^{94,96}$Zr and $^{40}$Ca + $^{94,96}$Zr and quadrupole deformation of $^{94}$Zr