  The effects of strong magnetic field on superconducting Nb and MoGe nanowires
with diameter $\sim10$ nm have been studied. We have found that the
Langer-Ambegaokar-McCumber-Halperin (LAMH) theory of thermally activated phase
slips is applicable in a wide range of magnetic fields and describes well the
temperature dependence of the wire resistance, over eleven orders of magnitude.
The field dependence of the critical temperature, $T_{c}$, extracted from the
LAMH fits is in good quantitative agreement with the theory of pair-breaking
perturbations that takes into account both spin and orbital contributions. The
extracted spin-orbit scattering time agrees with an estimate $\tau_{so}\simeq
\tau(\hbar c/ Ze^{2})^{4}$, where $\tau$ is the elastic scattering time and $Z$
is the atomic number.
