  Models for supernovae (SNe) arising from thermonuclear explosions of white
dwarfs (WDs) have been extensively studied over the last few decades, mostly
focusing on the single degenerate (accretion of material of a WD) and double
degenerate (WD-WD merger) scenarios. In recent years it was suggested that
WD-WD direct collisions provide an additional channel for such explosions. Here
we extend the studies of such explosions, and explore the role of Helium-shells
in affecting the thermonuclear explosions. We study both the impact of low-mass
helium ($\sim0.01$ M$_{\odot})$ shells, as well as high mass shells ($\ge0.1$
M$_{\odot}$). We find that detonation of the massive helium layers precede the
detonation of the WD Carbon-Oxygen (CO) bulk during the collision and can
change the explosive evolution and outcomes for the cases of high mass
He-shells. In particular, the He-shell detonation propagates on the WD surface
and inefficiently burns material prior to the CO detonation that later follows
in the central parts of the WD. Such evolution leads to larger production of
intermediate elements, producing large yields of $^{44}{\rm Ti}$ and $^{48}{\rm
Cr}$ relative to the pure CO-CO WD collisions. Collisions of WDs with a
low-mass He-shell do not give rise to helium detonation, but helium burning
does precede the CO bulk detonation. Such collisions produce a high velocity,
low-mass of ejected burned material enriched with intermediate elements, with
smaller changes to the overall explosion outcomes. The various effects arising
from the contribution of low/high mass He layers change the kinematics and the
morphological structure of collision-induced SNe and may thereby provide unique
observational signatures for such SNe, and play a role in the chemical
enrichment of galaxies and the production of intermediate elements and
positrons from their longer-term decay.
