  We present 3D simulations of supernova (SN) explosions of nonrotating stars,
triggered by the neutrino-heating mechanism with a suitable choice of the
core-neutrino luminosity. Our results show that asymmetric mass ejection caused
by hydrodynamic instabilities can accelerate the neutron star (NS) up to recoil
velocities of more than 700 km/s by the "gravitational tug-boat mechanism",
which is enough to explain most observed pulsar velocities. The associated NS
spin periods are about 100 ms to 8 s without any correlation between spin and
kick magnitudes or directions. This suggests that faster spins and a possible
spin-kick alignment might require angular momentum in the progenitor core prior
to collapse. Our simulations for the first time demonstrate a clear correlation
between the size of the NS kick and anisotropic ejection of heavy elements
created by explosive burning behind the shock. In the case of large NS kicks
the explosion is significantly stronger opposite to the kick vector. Therefore
the bulk of the Fe-group elements, in particular nickel, is ejected mostly in
large clumps against the kick direction. This contrasts with the case of low
recoil velocity, where the Ni-rich lumps are more isotropically distributed.
Intermediate-mass nuclei heavier than Si (like Ca and Ti) also exhibit a
significant enhancement in the hemisphere opposite to the direction of fast NS
motion, while the distribution of C, O, and Ne is not affected, and that of Mg
only marginally. Mapping the spatial distribution of the heavy elements in SN
remnants with identified pulsar motion may offer an important diagnostic test
of the kick mechanism. Different from kick scenarios based on anisotropic
neutrino emission, our hydrodynamical acceleration model predicts enhanced
ejection of Fe-group elements and of their nuclear precursors in the direction
opposite to the NS recoil. (abridged)
