Accretion heats the neutron star crust thereby decreasing the electric conductivity in the solid region. This leads to a rapid field decay when the currents supporting the field are concentrated in the solid crust (Geppert & Urpin 1994, Urpin & Geppert 1995). Depending on the duration of the accretion phase and on the total mass accreted the field can be decreased by 3 − 4 orders of magnitude after 106− 107years. This mechanism explains the low magnetic fields of many pulsars entering

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... nary systems.However, there exist both low–mass (e.g. Her X–1, 4U 1626–67) and high–mass (e.g. Cen X–3, SMC X–1) systems, where the neutron star deserves strong accretion and the magnetic field is still large.