  The r-process nucleosynthesis in core-collapse supernovae (CC-SNe) is
studied, with a focus on the explosion scenario induced by rotation and strong
magnetic fields. Nucleosynthesis calculations are conducted based on
magneto-hydrodynamical explosion models with a wide range of parameters for
initial rotation and magnetic fields. The explosion models are classified in
two different types: i.e., prompt-magnetic-jet and delayed-magnetic-jet, for
which the magnetic fields of proto-neutron stars (PNSs) during collapse and the
core-bounce are strong and comparatively moderate, respectively. Following the
hydrodynamical trajectories of each explosion model, we confirmed that
r-processes successfully occur in the prompt-magnetic-jets, which produce heavy
nuclei including actinides. On the other hand, the r-process in the
delayed-magnetic-jet is suppressed, which synthesizes only nuclei up to the
second peak ($A \sim 130$). Thus, the r-process in the delayed-magnetic-jets
could explain only "weak r-process" patterns observed in metal-poor stars
rather than the "main r-process", represented by the solar abundances. Our
results imply that core-collapse supernovae are possible astronomical sources
of heavy r-process elements if their magnetic fields are strong enough, while
weaker magnetic explosions may produce "weak r-process" patterns ($A \lesssim
130$). We show the potential importance and necessity of magneto-rotational
supernovae for explaining the galactic chemical evolution, as well as
abundances of r-process enhanced metal-poor stars. We also examine the effects
of the remaining uncertainties in the nature of PNSs due to weak interactions
that determine the final neutron-richness of ejecta. Additionally, we briefly
discuss radioactive isotope yields in primary jets (e.g., $^{56}$Ni), with
relation to several optical observation of SNe and relevant high-energy
astronomical phenomena.
