  We calculate the reaction cross-sections for the fusion of hydrogen and
deuterium in strong magnetic fields as are believed to exist in the atmospheres
of neutron stars. We find that in the presence of a strong magnetic field ($B
\gsim 10^{12}$G), the reaction rates are many orders of magnitude higher than
in the unmagnetized case. The fusion of both protons and deuterons are
important over a neutron star's lifetime for ultrastrong magnetic fields ($B
\sim 10^{16}$G). The enhancement may have dramatic effects on thermonuclear
runaways and bursts on the surfaces of neutron stars.
