Classical HWHM Workflow

Use this workflow for atomic or ionic systems where rotational broadening is absent. It extracts Γ(Q) per Q-bin then fits a translational model.

Full Script

from qens import (
    Config, load_dataset, fit_elastic_peak, assign_resolution,
    extract_hwhm, save_hwhm_csv,
)
from qens.models    import fickian_hwhm, ce_hwhm
from scipy.optimize import curve_fit
import numpy as np

cfg = Config(
    files_to_fit    = ["benzene_260_360_inc.nxspe",
                       "benzene_290_360_inc.nxspe"],
    primary_file    = "benzene_290_360_inc.nxspe",
    resolution_file = "benzene_260_360_inc.nxspe",
    q_min=0.3, q_max=2.5,
    energy_window=0.8,
    n_q_bins=13
)

# Load and pre-process
dataset = load_dataset(cfg.files_to_fit, data_dir="data/",
                       critical_files=[cfg.primary_file])
for d in dataset.values():
    fit_elastic_peak(d)
assign_resolution(dataset, cfg)

target = dataset[cfg.primary_file]

# Extract HWHM per Q-bin
q, gamma, gerr, eisf = extract_hwhm(target, cfg)
save_hwhm_csv(q, gamma, gerr, eisf, save_dir="results/")

# Fit Fickian model
p_fick, cov_fick = curve_fit(
    fickian_hwhm, q, gamma, sigma=gerr,
    p0=[0.15], bounds=([1e-3], [3.0])
)
print(f"Fickian  D = {p_fick[0]:.4f} ± {cov_fick[0,0]**0.5:.4f} Ų/ps")

# Fit Chudley-Elliott model
p_ce, cov_ce = curve_fit(
    ce_hwhm, q, gamma, sigma=gerr,
    p0=[0.15, 2.0], bounds=([1e-3, 0.1], [3.0, 6.0])
)
print(f"CE       D = {p_ce[0]:.4f} ± {cov_ce[0,0]**0.5:.4f} Ų/ps"
      f"   ℓ = {p_ce[1]:.3f} Å")

# Plot
import qens.plotting as qp
qp.plot_hwhm_classical(q, gamma, gerr,
                       fits={"Fickian": (fickian_hwhm, p_fick),
                             "CE":      (ce_hwhm,      p_ce)},
                       save_path="results/hwhm_classical.png")

Interpreting the Dispersion Plot

Feature	Interpretation
Linear at low Q²	Slope = ħD. Consistent with continuous Fickian diffusion.
Plateau at high Q²	Jump-diffusion saturation. CE or SS model applies.
Below resolution line	Spectral resolution too coarse for this sample/Eᵢ combination.
Non-monotonic dip	Likely coherent contamination near de Gennes peak.

Warning

If the HWHM plateau looks identical to the CE jump-diffusion saturation and the sample is a molecular liquid, the broadening may be rotational rather than translational. Use the joint forward-model workflow (usage_joint) to distinguish them. See Physical Models for the “Lost in Translation” degeneracy.