6.1

\(\renewcommand\AA{\unicode{x212B}}\)

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.

(Source code, png, hires.png, pdf)

../../_images/StandardSC-1.png

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

Source

Python: StandardSC.py (last modified: 2021-01-08)