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# StandardSC¶

## Description¶

Sinusoidal function damped with Gaussian relaxation and a non-decaying oscillation:

$A(t)=A_0e^{-\frac{\sigma^2t^2}{2}}\cos(\omega_\text{SC}t+\phi) + A_\text{bg}\cos(\omega_\text{BG}t+\phi)$

where,

$$A_\text{bg}$$ is the amplitude of the background field oscillation,

$$A_0$$ is the amplitude of the decaying oscillation due to internal field,

$$\omega_\text{SC}$$ (rad/s) is the angular frequency of internal field,

$$\omega_\text{BG}$$ (rad/s) is the angular frequency of background field,

$$\sigma$$ is the depolarization rate,

and $$\phi$$ is the phase.

The relationship between $$\omega$$ and magnetic field B is given by:

$\omega = 2 \pi \nu = \gamma_\mu \text{B}$

where,

$$\gamma_\mu$$ is the gyromagnetic ratio of muon.

## Properties (fitting parameters)¶

Name

Default

Description

A0

0.16

Amplitude of interal field oscillation

Sigma

0.2

Gaussian decay rate

FieldSC

300.0

Internal Field (G)

FieldBG

300.0

External Field (G)

Phi

0.0

Phase

Abg

0.1

Amplitude of external field oscillation

## References¶

Categories: FitFunctions | Muon\MuonGeneric

## Source¶

Python: StandardSC.py