Intense fluxes of neutrinos are emitted by the hot neutron star produced in a supernova .
The average supernova neutrino energies satisfy a robust hierarchy \langle E _ { \nu _ { e } } \rangle < \langle E _ { \bar { \nu } _ { e } } \rangle < \langle E _ { \nu _ { % \mu ( \tau ) } } \rangle \approx \langle E _ { \bar { \nu } _ { \mu ( \tau ) } } \rangle .
The \nu _ { e } and \bar { \nu } _ { e } capture reactions on neutrons and protons , respectively , provide heating to drive a wind from the hot neutron star .
The same reactions also determine the neutron-richness of the wind material .
Nucleosynthesis via rapid neutron capture , the r -process , may occur in the wind material as it expands away from the neutron star .
The neutron-richness of the wind material , and hence , the r -process nucleosynthesis therein , are sensitive to mixing between \nu _ { \mu ( \tau ) } / \bar { \nu } _ { \mu ( \tau ) } and \nu _ { e } / \bar { \nu } _ { e } ( or sterile neutrinos \nu _ { s } / \bar { \nu } _ { s } ) at the level of \sin ^ { 2 } 2 \theta \ > \lower 1.72 pt \hbox { $ \stackrel { \scriptstyle < } { \scriptstyle \sim% } $ } \ > 10 ^ { -4 } for \delta m ^ { 2 } \ > \lower 1.72 pt \hbox { $ \stackrel { \scriptstyle > } { \scriptstyle \sim } $ } \ > 1 eV ^ { 2 } .
Indirect arguments and direct tests for the supernova origin of the r -process elements are discussed with a goal to establish supernova r -process nucleosynthesis as an important probe for neutrino mixing .