The interaction of an unpolarized electron beam with a counterpropagating ultraintense linearly polarized laser pulse is investigated in the quantum radiation-dominated regime. We employ a semiclassical Monte Carlo method to describe spin-resolved electron dynamics, photon emissions and polarization, and pair production. Abundant high-energy linearly polarized gamma photons are generated intermediately during this interaction via nonlinear Compton scattering, with an average polarization degree of more than 50%, which further interacting with the laser fields produce electron-positron pairs due to nonlinear Breit-Wheeler process. The photon polarization is shown to significantly affect the pair yield by a factor beyond 10%. The considered signature of the photon polarization in the pairs yield can be experimentally identified in a prospective two-stage setup. Moreover, the signature can serve also for the polarimetry of high-energy high-flux gamma photons with a resolution well below 1% with currently achievable laser facilities.
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