  We demonstrate direct measurements of the spin-orbit interaction and Land\'e
g factors in a semiconductor nanowire double quantum dot. The device is made
from a single-crystal pure-phase InAs nanowire on top of an array of finger
gates on a Si/SiO$_2$ substrate and the measurements are performed in the Pauli
spin-blockade regime. It is found that the double quantum dot exhibits a large
singlet-triplet energy splitting of $\Delta_{ST}\sim 2.3$ meV, a strong
spin-orbit interaction of $\Delta_{SO}\sim 140$ $\mu$eV, and a large and
strongly level-dependent Land\'e g factor of $\sim 12.5$. These results imply
that single-crystal pure-phase InAs nanowires are desired semiconductor
nanostructures for applications in quantum information technologies.
