Approximate resolution convolution function for fitting a dispersion gap measured on a triple-axis spectrometer

We present an analytical convoluted gap function for fitting dispersion gaps measured on a triple-axis spectrometer (TAS). At the gap, the instrumental resolution skews the signal, producing a high-energy tail that complicates fitting. Our function assumes an instrumental Q resolution with two equal wide directions and one narrow direction (typical of focused TAS instruments) and a parabolic dispersion at the gap, which is exact for quadratic and accurate for linear dispersions if the resolution is moderate. We demonstrate that our function outperforms previous methods of fitting a gap by giving a better fit and more accurate gap determination. Here, the antiferromagnetically gapped material MnF₂ is simulated in a double-focusing TAS instrument. We also tested our function on experimental data on MnF₂ from a TAS-like instrument, where we reproduced the gap size from previous accurate measurements determined experimentally. The function is simple to implement and converges reliably, and we recommend its use for future gap fitting on TAS data.