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

中文翻译：

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磁场高斯分布与洛伦兹分布交叉状态下的介子自旋运动

介子自旋弛豫方法 (μSR) 是一种强大的微观工具，用于探测材料的电子状态，观察介子上的局部磁场分布。经常发生局部磁场的分布显示介于高斯和洛伦兹形状之间的中间状态。为了一般性地描述中间场分布，我们处理了三个各向同性分布的卷积，并导出了精确的μ子自旋弛豫函数，该函数可以应用于高斯和洛伦兹之间的所有交叉状态。