  We present a quantum interpretation of the heights in hysteresis of $Fe_{8}$
molecule at lower temperatures by treating the crystal as an Ising spin system
with the dipolar interaction between spins. Then we apply it to two limit cases
: rapid and adiabatic regions. Our theoretical analysis is in agreement with
the experimental observation in these regions, which indicates that the steps
in hysteresis loops of magnetization of Fe$_{8}$ at lower temperatures show a
pure quantum process.
