.. _func-Keren: ============ Keren ============ .. index:: Keren Description ----------- Keren's generalization of the Abragam relaxation function to a longitudinal field, for fitting the time-dependent muon polarization. The function is derived in `*Phys Rev B, vol. 50, 14, 10039-42 (1994)* `_ and is given by .. math:: P_z(t) = A\exp\left[-\Gamma(t)t\right] where the relaxation rate :math:`\Gamma(t)` is .. math:: \Gamma(t)t = 2\Delta^2 \frac{\left\{\left(\omega_L^2 + \nu^2\right)\nu t + \left(\omega_L^2-\nu^2\right)\left(1-e^{-\nu t}\cos(\omega_L t)\right) - 2\nu\omega_L e^{-\nu t}\sin(\omega_L t)\right\}}{\left(\omega_L^2 + \nu^2\right)^2} :math:`A = P_z(0)` is the polarization at time zero, :math:`\nu` is the fluctuation rate (inverse correlation time), :math:`\Delta` is the distribution width of the local fields and :math:`\omega_L` is the Larmor frequency (longitudinal field times muon gyromagnetic ratio). .. attributes:: .. properties:: .. categories:: .. sourcelink::