Muon spin motion at the crossover regime between Gaussian and Lorentzian distribution of magnetic fields

The muon spin relaxation method is a powerful microscopic tool for probing the electronic states of materials by observing local magnetic field distributions on the muon. It often happens that a distribution of local magnetic fields shows an intermediate state between Gaussian and Lorentzian shapes. In order to generally describe these intermediate field distributions, we considered the convolution of two isotropic distributions in three dimensions and derived exact muon-spin relaxation functions which can be applied to all crossover regimes between Gaussian and Lorentzian.