Model selection in neutron Compton scattering - a Bayesian approach with physical constraints

This work analyses the performance of the maximum-likelihood estimation approach in fitting Gram-Charlier expansion curves to nuclear momentum distributions with non-negativity constraints. The presented approach guarantees that the most likely model selected to describe the recorded data is also a physically meaningful one, i.e., corresponds to a non-negative probability distribution function. For the case of the most popular momentum distribution model, containing the information about the variance and excess kurtosis of the distribution, we derive a simple and easy to implement non-negativity criterion. We test the performance of the newly developed approach by applying it to interpret proton momentum distribution obtained from neutron Compton scattering from solid phosphoric acid, a system in which nuclear quantum tunnelling was proposed in the limit of low temperature. From a methodological point of view, this work provides a screening tool in the search for systems exhibiting the so-called 'non-trivial nuclear quantum effects'.