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Deuteron Peak Fit for NMR Signal Analysis

Fitting routine for spin-1 NMR signals with quadrupolar splitting Pake doublets, based on C code by C. Dulya. [1]

Uses Non-Linear Least-Squares Minimization and Curve-Fitting for Python (LMFIT), https://lmfit.github.io/lmfit-py/

Usage

May be called as object "DFits" which requires passing a list of frequency points, a list signal magnitudes at each point, and a parameter dictionary.

fit_results = DFits(freqs, sweep, params)

r = fit_results.result.params['r'].value
pol = (r * r - 1) / (r * r + r + 1)

The return is a LMFIT ModelResult object (https://lmfit.github.io/lmfit-py/model.html#lmfit.model.ModelResult).

The success of the fit is highly dependent on the initial parameters passed. The parameter dictionary is label based on Dulya's convention:

  • A: Width due to dipolar broadening
  • G: Scale factor
  • r: Asymmetry parameter, representing relative sizes of two peaks
  • wQ: Quadrupolar splitting frequency width
  • wL: Nuclear Larmor frequency (in same units as the passed frequency list)
  • eta: Peak width factor
  • xi: False asymmetry correction from mistuning

Example Fit of 42% Polarized Deuteron Signal at 5T

Example Fit of 42% Polarized Deuteron Signal at 5T taken on ND3 during Run Group C at Jefferson Lab.

Example

An example signal is included for fitting. Script example.py gives an example usage which will plot this signal to test your installation.

Author

Written in 2021 by J. Maxwell (https://orcid.org/0000-0003-2710-4646).

References

[1] Dulya, C. et. al. "A line-shape analysis for spin-1 NMR signals" NIM A, 398, 109-125 (1997). (https://doi.org/10.1016/S0168-9002(97)00317-3)