Neutron Compton Scattering: from proton momentum distribution to muonium hyperfine coupling constant in the isopropyl radical

Abstract

We establish a fast and reliable benchmarking protocol for predictions of Muon Spin Resonance observables. To this end, we apply neutron Compton scattering (NCS) to study the nuclear momentum distributions of the proton and deuteron in the condensed phase of the isopropyl and d-isopropyl alcohols. By subtracting the time-of-flight NCS spectra of both compounds we demonstrate that the proton momentum distribution in the OH group of isopropanol and the deuteron momentum distribution in the OD group in d-isopropyl can be studied selectively. The site-selective application of the NCS method enables the calculation of the magnitude of the frequency isotope effect for the proton in OH along the hydrogen bond direction. By comparing the magnitude of the frequency isotope effect with values predicted for simple model potentials we are able to perform the appraisal of the degree of anharmonicity of the OH proton environment. Assuming that the effective potential felt by the OH proton along the hydrogen-bond direction can be satisfactorily described by the Morse potential, we are able to calculate its dissociation constant D and decay constant a. Finally, assuming that the same Morse potential describes the local binding of Muonium in the mioniated isopropyl radical, we are able to predict its width of momentum and position distributions and the kinetic and zero-point energy. Based on these results, we are able to provide a conservative bound for the magnitude of the isotope effect on the muonium hyperfine interaction without resorting to a complicated and computationally expensive methodology based on the application of path integrals.