deerlab.bg_hom3d_phase#

bg_hom3d_phase = <deerlab.model.Model object>#

Phase shift from a homogeneous distribution of spins in a 3D medium

Parameters:
tarray_like

Time vector, in microseconds.

concscalar

Spin concentration

lamscalar

Pathway amplitude

Returns:
Bndarray

Dipolar background vector.

Notes

Parameter Table

Name

Lower

Upper

Type

Frozen

Unit

Description

conc

0.01

5e+03

nonlin

No

μM

Spin concentration

lam

0

1

nonlin

No

Pathway amplitude

Model

This model describes the phase shift due to inter-molecular interactions between one observer spin with a 3D homogenous distribution of spins of concentration c_s

The expression for this model is

B(t) = \mathrm{exp}\left(\mathrm{i}\frac{8\pi}{9\sqrt{3}}(\sqrt{3} + \mathrm{ln}(2-\sqrt{3}))\lambda c_s D t\right)

where c_s is the spin concentration (entered in spins/m3 into this expression) and D is the dipolar constant

D = \frac{\mu_0}{4\pi}\frac{(g_\mathrm{e}\mu_\mathrm{B})^2}{\hbar}