  The scattering of the eletron by a domain wall in a nano-wire is studied
perturbatively to the lowest order. The correction to the thermodaynamic
potential of the electron system due to the scattering is calculated from the
phase shift. The wall profile is determined by taking account of this
correction, and the result indicates that the wall in a ferromagnet with small
exchange coupling can be squeezed to be very thin to lower the electron energy.
