We have made detailed calculations of the composition of magnetically driven jets ejected from a collapsar, based on long-term, magnetohydrodynamic simulations of a rapidly rotating, massive (40 M☉) star during core collapse. We follow the evolution of the abundances of about 4000 nuclides from the collapse phase to the ejection phase and through the jet generation phase using two large nuclear reaction networks. We find that the r-process successfully operates in the jets, so that U and Th are synthesized abundantly when the progenitor has a large magnetic field (1012 G) and a rapidly rotating core. The abundance pattern inside the jets is similar to that of the r-elements in the solar system. About 0.01 M☉ of heavy, neutron-rich nuclei can be ejected from the collapsar. The detailed abundances depend on the nuclear properties of the mass model, β-decay rate, and fission, for nuclei near the neutron drip line. Furthermore, we find that p-nuclei are produced without seeds: not only can light p-nuclei, such as 74Se, 78Kr, 84Sr, and 92Mo, be abundantly synthesized in the jets, but also heavy p-nuclei, 113In, 115Sn, and 138La. The amounts of p-nuclei in the ejecta are much greater than those in core-collapse supernovae. In particular, 92Mo, 113In, 115Sn, and 138La, which are deficient in these supernovae, are produced significantly in the collapsar ejecta.
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