The Intermediate Mass Fragments emission probability from Projectile-Like Fragment break-up in semi-peripheral reactions has been measured in collisions of $^{124}$Xe projectiles with two different targets of $^{64}$Ni and $^{64}$Zn at the laboratory energy of 35 amev. The two colliding systems differ only for the target atomic number Z and, consequently, for the Isospin $N/Z$ ratio. An enhancement of Intermediate Mass Fragments production for the neutron rich $^{64}$Ni target, with respect to the $^{64}$Zn, is found. In the case of one Intermediate Mass Fragment emission, the contributions of the dynamical and statistical emissions have been evaluated, showing that the increase of the effect above is due to an enhancement of the dynamical emission probability, especially for heavy IMFs (Z$gtrsim$ 7). This proves an influence of the target Isospin on inducing the dynamical fragment production from Projectile-Like Fragment break-up. In addition, a comparison of the Xe+Ni,Zn results with the previously studied $^{112,124}Sn+^{58,64}Ni$ systems is discussed in order to investigate the influence of the projectile Isospin alone and to disentangle between Isospin effects against system-size effects on the emission probability. These comparisons suggest that the prompt-dynamical emission is mainly ruled by the $N/Z$ content of, both, projectile and target; for the cases here investigated, the influence of the system size on the dynamical emission probability can be excluded.
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