  We investigate whether the magnetic field of an accreting neutron star may be
diamagnetically screened by the accreted matter. We assume the freshly
accumulated material is unmagnetized, and calculate the rate at which the
intrinsic stellar magnetic flux is transported into it by Ohmic diffusion. We
calculate the one-dimensional steady-state magnetic field profiles, and show
that the magnetic field strength decreases as one moves up through the outer
crust and ocean by roughly (Mdot/0.02 Mdot_Edd) orders of magnitude, where Mdot
is the accretion rate and Mdot_Edd the Eddington accretion rate. We show that
buoyancy instabilities set a limit to the strength of any buried field of
roughly 10^10-10^11 G.
  Our results show that magnetic screening is ineffective for Mdot<0.01
Mdot_Edd, so that, no matter how the accreted material joins onto the star, the
underlying stellar field should always be evident. In this respect, we point
out the only known persistently-pulsing accreting X-ray millisecond pulsar, SAX
J1808.4-3658, has an accretion rate of 10^-3 Mdot_Edd, far below the regime
where magnetic screening can play a role.
  Most steadily accreting neutron stars in low-mass X-ray binaries in our
Galaxy accrete at rates where screening would be effective if the simplified
magnetic and accretion geometry we adopt were correct. If screened, then the
underlying field will emerge after accretion halts, on a timescale of only
100--1000 years, set by the Ohmic diffusion time across the outer crust. It
thus seems unlikely that screening alone can explain the low magnetic fields of
the millisecond radio pulsars.
