.. index:: Keren
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
P_z(t) = A\exp\left[-\Gamma(t)t\right]
where the relaxation rate \Gamma(t) is
\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}
A = P_z(0) is the polarization at time zero, \nu is the fluctuation rate (inverse correlation time), \Delta is the distribution width of the local fields and \omega_L is the Larmor frequency (longitudinal field times muon gyromagnetic ratio).
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