We study the neutrino-induced production of nuclides in explosive supernova nucleosynthesis for progenitor stars with solar metallicity and initial main sequence masses between 15 M$_odot$ and 40 M$_odot$. We improve previous investigations i) by using a global set of partial differential cross sections for neutrino-induced charged- and neutral-current reactions on nuclei with charge numbers $Z < 76 $ and ii) by considering modern supernova neutrino spectra which have substantially lower average energies compared to those previously adopted in neutrino nucleosynthesis studies. We confirm the production of $^7$Li, $^{11}$B, $^{138}$La, and $^{180}$Ta by neutrino nucleosynthesis, albeit at slightly smaller abundances due to the changed neutrino spectra. We find that for stars with a mass smaller than 20 M$_odot$, $^{19}$F is produced mainly by explosive nucleosynthesis while for higher mass stars it is produced by the $ u$ process. We also find that neutrino-induced reactions, either directly or indirectly by providing an enhanced abundance of light particles, noticeably contribute to the production of the radioactive nuclides $^{22}$Na and $^{26}$Al. Both nuclei are prime candidates for gamma-ray astronomy. Other prime targets, $^{44}$Ti and $^{60}$Fe, however, are insignificantly produced by neutrino-induced reactions. We also find a large increase in the production of the long-lived nuclei $^{92}$Nb and $^{98}$Tc due to charged-current neutrino capture.
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