  Based on a first principles treatment of the excitation states we show that
superfluidity of superfluid $^4$He (He II) results from a reduction in the
number of phonon wavevector $K$ states $\N2(K)$ to a level that is negligibly
low when the fluid is confined e.g. in a narrow channel, yet wider than the
helium atom correlation length, $\Lambda$. This is as a result of the $K$
discretization, a manifestation of the quantum confinement effect (QCE). The
predicted relative viscosity of a confined superfluid has the characteristic
order of magnitude of experimental data ($<10^{-6}$). Furthermore, we show that
at the edges of the resulting energy gaps, the $\N2(K)$ presents discontinuity.
When its corresponding energy exceeds the (first) gap, the superfluid flow
exhibits a critical velocity $v_c$. Our evaluation of $v_c(d)$ versus the
channel width $d$, constrained to satisfy energy conservation, is in good
quantitative agreement with experimental data for channels with $d>10^{-6}$ m.
Meanwhile, a sharp turn about $K\propto$ $ v_c$ in $\N2(K)$ resembles very well
that of the experimental overshoot data. For narrower channels of $d<10^{-6}$ m
$\le \Lambda$ in which the phonon excitation picture becomes inadequate, we
instead represent the excitation in terms of single atoms with an effective
mass, which yields a $v_c(d)$ in close agreement with experiment. Accordingly,
the reduction in the number of atomic states results in superfluidity. The
theoretical finding in this work, which can be termed the {\bf QCE
superfluidity mechanism}, provides a consistent explanation for this puzzling
phenomenon, the non-dissipative, superfluidity motion, of He II and could have
a significant impact also on the understanding of other superfluids.
