The problem of the structure (state of helium) in small He N -CO clusters

A second-order perturbation theory, developed for calculating the energy levels of the He-CO binary complex, is applied to small He N -CO clusters with N = 2−4, the helium atoms being considered as a single bound object. The interaction potential between the CO molecule and HeN is represented as a linear expansion in Legendre polynomials, in which the free rotation limit is chosen as the zero approximation and the angular dependence of the interaction is considered as a small perturbation. By fitting calculated rotational transitions to experimental values it was possible to determine the optimal parameters of the potential and to achieve good agreement (to within less than 1%) between calculated and experimental energy levels. As a result, the shape of the angular anisotropy of the interaction potential is obtained for various clusters. It turns out that the minimum of the potential energy is smoothly shifted from an angle between the axes of the CO molecule and the cluster of θ = 100° in He-CO to θ = 180° (the oxygen end) in He3-CO and He4-CO clusters. Under the assumption that the distribution of helium atoms with respect to the cluster axis is cylindrically symmetric, the structure of the cluster can be represented as a pyramid with the CO molecule at the vertex.