Pauli blocking is carefully investigated for the processes of $NN rightarrow N Delta$ and $Delta rightarrow N pi$ in heavy-ion collisions, aiming at a more precise prediction of the $pi^-/ pi^+$ ratio which is an important observable to constrain the high-density symmetry energy. We use the AMD+JAM approach, which combines the antisymmetrized molecular dynamics for the time evolution of nucleons and the JAM model to treat processes for $Delta$ resonances and pions. As is known in general transport-code simulations, it is difficult to treat Pauli blocking very precisely due to unphysical fluctuations and additional smearing of the phase-space distribution function, when Pauli blocking is treated in the standard method of JAM. We propose an improved method in AMD+JAM to use the Wigner function precisely calculated in AMD as the blocking probability. Different Pauli blocking methods are compared in heavy-ion collisions of neutron-rich nuclei, ${}^{132}mathrm{Sn}+{}^{124}mathrm{Sn}$, at 270 MeV/nucleon. With the more accurate method, we find that Pauli blocking is stronger, in particular for the neutron in the final state in $NN rightarrow N Delta$ and $ Delta to Npi$, compared to the case with a proton in the final state. Consequently, the $pi^-/pi^+$ ratio becomes higher when the Pauli blocking is improved, the effect of which is found to be comparable to the sensitivity to the high-density symmetry energy.
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