An exact form for the magnetic field density of states for a dipole
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We present an analytical form for the density of states for a magnetic dipole in the center of a spherical voxel. This analytic form is then used to evaluate the signal decay as a function of echo time for different volume fractions and susceptibilities. The decay can be considered exponential only in a limited interval of time. Otherwise, it has a quadratic dependence on time for short echo times and an oscillatory decaying behavior for long echo times.
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