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# 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

$P_z(t) = A\exp\left[-\Gamma(t)t\right]$

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).

## Properties (fitting parameters)¶

Name

Default

Description

A

1.0

Polarization at time zero

Delta

0.2

Distribution width of local fields (MHz)

Field

50.0

Longitudinal field (Gauss)

Fluct

0.2

Hopping rate (inverse correlation time, MHz)

Categories: FitFunctions | Muon\MuonSpecific