A set of global optical potential parameters, DA1p, for deuterons with the $1p$-shell nuclei is obtained by simultaneously fitting 67 sets of experimental data of deuteron elastic scattering from uc{6}{Li}, uc{9}{Be}, uc{10}{B}, uc{11}{B}, uc{12}{C}, uc{13}{C}, uc{14}{N}, uc{16}{O} and uc{18}{O} with incident energies between 5.25 and 170 MeV. DA1p improves the description of the deuteron elastic scattering from the $1p$-shell nuclei with respect to the existing systematic deuteron potentials and can give satisfactory reproduction to the experimental data with radiative nuclei such as uc{9}{Li}, uc{10}{Be}, uc{14}{C} and uc{14}{O}.
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