Muon Spin Diffusion Fit Function

[robertapplin]

Blocked: waiting on test data from scientists, and documentation description

Is your feature request related to a problem? Please describe.
Adam Berlie would like a fit function implemented in Mantid. This is the info I currently have:

Attached is a scanned copy of the relevant function from the muon text book. 
1.	What I'm trying to fit is equation 8.29 to a plot of lambda vs longitudinal field.
2.	In my case, I only need to worry about the first term, A^2/4 J(we). J(we) = eqn 8.31 in the notes
3.	you feed into it S(t) from equation 8.30
4.	The exact product function is defined by eqns 8.32...
5.	and in this case omega = B (LF) *gamma_mu.
It all get confusing, but you should get the outputs to look like Fig 8.9. You then fit your data as a Fourier transform of S(t) to extract different values of the diffusion rates, Di, for the different scenarios, 1D, 2D or 3D.

I've tried to write some Python scripts to model these functions, but not sure if I have got it quite right. I am not convinced that I am getting the right shape for J(w) vs B.

scan_lvr68513_2024-04-11-12-36-56.zip

Describe the solution you'd like
Implement a fit function for 8.29 in Mantid