bg_hom3d

Background due to a homogeneous spin distribution in 3D

Syntax

info = bg_hom3d()
P = bg_hom3d(t,param)
P = bg_hom3d(t,param,lambda)
Inputs
  • t – Time axis (N-array)
  • param – Model parameters
  • lambda – Modulation amplitude (between 0 and 1)
Outputs
  • B – Model background (N-array)
  • info – Model information (struct)

Model

This model describes the inter-molecular interaction of one observer spin with a 3D homogenous distribution of pump-spins of concentration c_p

../_images/model_scheme_bg_hom3d.png

The expression for this model is

B(t) = \mathrm{exp}\left(-\frac{8\pi^2}{9\sqrt{3}}\lambda c_p D |t|\right)`

where c_p is the pumped-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}

Variable Symbol Default Lower bound Upper bound Description
param(1) c_p 50 0.01 5000 Pumped spin concentration (μM)

Description

info = bg_hom3d()

Returns an info structure containing the specifics of the model:

  • info.model – Full name of the parametric model.
  • info.nparam – Total number of adjustable parameters.
  • info.parameters – Structure array with information on individual parameters.
B = bg_hom3d(t,param)

Computes the background model B from the axis t according to the parameters array param for a modulation amplitude lambda=1. The required parameters can also be found in the info structure.

B = bg_hom3d(t,param,lambda)

Computes the background model B for a given modulation amplitude lambda (between 0 and 1).