The model that is being fitted is that of a delta-function (elastic component) of amplitude A(0) and Lorentzians of amplitude A(j) and HWHM W(j) where j = 1, 2, 3. The whole function is then convolved with the resolution function. The -function and Lorentzians are intrinsically normalised to unity so that the amplitudes represent their integrated areas.
For a Lorentzian, the Fourier transform does the conversion: 1/(x2 + δ2) ⇔ exp[ − 2π(δk)]. If x is identified with energy E and 2πk with t/ℏ where t is time then: 1/[E2 + (ℏ/τ)2] ⇔ exp[ − t/τ] and σ is identified with ℏ/τ. The program estimates the quasielastic components of each of the groups of spectra and requires the resolution file and optionally the normalisation file created by ResNorm.
For a Stretched Exponential, the choice of several Lorentzians is replaced with a single function with the shape : ψβ(x) ⇔ exp[ − 2π(σk)β]. This, in the energy to time FT transformation, is ψβ(E) ⇔ exp[ − (t/τ)β]. So sigma is identified with (2π)βℏ/τ. The model that is fitted is that of an elastic component and the stretched exponential and the program gives the best estimate for the β parameter and the width for each group of spectra.
This routine was originally part of the MODES package.