  Quantum tunneling of domain walls out of an impurity potential in a
mesoscopic ferromagnetic sample is investigated. Using improved expressions for
the domain wall mass and for the pinning potential, we find that the cross-over
temperature between thermal activation and quantum tunneling is of a different
functional form than found previously. In materials like Ni or YIG, the
crossover temperatures are around 5 mK. We also find that the WKB exponent is
typically two orders of magnitude larger than current estimates. The sources
for these discrepancies are discussed, and precise estimates for the transition
from three-dimensional to one-dimensional magnetic behavior of a wire are
given. The cross-over temperatures from thermal to quantum transitions and
tunneling rates are calculated for various materials and sample sizes.
