Hyperfine Interact (2016) 237:140 DOI 10.1007/s10751-016-1360-z Nuclear electric quadrupole interactions in liquids entrapped in cavities Gregory B. Furman 1,2 · Victor M. Meerovich 1 · Vladimir L. Sokolovsky 1 © Springer International Publishing Switzerland 2016 Abstract Liquids entrapped in cavities and containing quadrupole nuclei are considered. The interaction of the quadrupole moment of a nucleus with the electric field gradient is studied. In such a system, molecules are in both rotational and translational Brownian motions which are described by the diffusion equation. Solving this equation, we show that the intra- and intermolecular nuclear quadrupole interactions are averaged to zero in cavities with the size larger than several angstroms. Keywords Nuclear quadrupole resonance · Cavity · Rotational and translational Brownian motions · Averaged quadrupole Hamiltonian PACS 76.60.Gv 1 Introduction In a crystalline solid, the electric quadrupole moment, eQ, of a nucleus possess- ing a spin greater than I > 1/2, interacts with the gradient of the electric field, ∂ 2 V ∂x i ∂x j ( x i ,x j = x, y, z ) generated by the surrounding electrons or external charges of other nuclei. The interaction results in splitting of the energy levels which are separated by distances proportional to the quadrupole coupling constant e 2 Qq h , where eq = ∂ 2 V ∂z 2 , and V is the potential of the electric field and e is the proton charge [1, 2]. This article is part of the Topical Collection on Proceedings of the International Conference on Hyperfine Interactions and their Applications (HYPERFINE 2016), Leuven, Belgium, 3–8 July 2016  Gregory B. Furman gregoryf@bgu.ac.il 1 Physics Department, Ben Gurion University of the Negev, Beer Sheva, 84105 Israel 2 Ohalo College, Katzrin, 12900 Israel