Spin dephasing in a magnetic dipole field

Transverse relaxation by dephasing in an inhomogeneous field is a general mechanism in physics, for example, in semiconductor physics, muon spectroscopy, or nuclear magnetic resonance. In magnetic resonance imaging the transverse relaxation provides information on the properties of several biological tissues. Since the dipole field is the most important part of the multipole expansion of the local inhomogeneous field, dephasing in a dipole field is highly important in relaxation theory. However, there have been no analytical solutions which describe the dephasing in a magnetic dipole field. In this work we give a complete analytical solution for the dephasing in a magnetic dipole field which is valid over the whole dynamic range.