Nature of excited helium atoms in liquid helium: A theoretical model

A model is developed in which excited helium atoms in liquid helium may exist in stable cavities of diameter 10 Å and larger. A repulsive effective interaction between the excited atom and the remaining atoms in the ground state is responsible for cavity formation. The equilibrium shape of the cavity is determined by minimizing the total energy, which is the sum of the electronic perturbation due to the surrounding liquid and the energy required to form the cavity. Each of these can be evaluated separately as a function of the cavity size and shape. The energy required to form a near-spherical cavity of radius $R$ is approximated by the classical expressions for work done against the surface tension $\gamma$ of liquid helium, and against the external pressure $p$ on the liquid. For a particular cavity size, the liquid may be represented by a perturbing potential, and the response of the electronic wave function explicitly determined using the variational method. The calculations indicate that the optical spectra of helium atoms in these cavities are only slightly perturbed, and agreement with observed spectra lends strong support to the cavity model. Agreement has been obtained with the observed emission transitions $2{}_{}{}^3{}_{}{}^{}P\to 2{}_{}{}^3{}_{}{}^{}S$ and $3{}_{}{}^{1,3}{}_{}{}^{}S\to 2{}_{}{}^{1,3}{}_{}{}^{}P$, and also with the absorption $2{}_{}{}^3{}_{}{}^{}S\to 2{}_{}{}^3{}_{}{}^{}P$, at saturated vapor pressure. Recently, the pressure dependence of the position and width of these spectral lines has been measured up to 25 atm. The pressure dependence predicted by the model is in good agreement with the data for all lines in which the initial state is spherically symmetric.