## Q-balls, clouds and shells of alpha particles

After reviewing some facts regarding the various sources of alpha clusters in nuclei and nuclear matter, I introduce, within the Relativistic Mean-Field, a Lagrangian for a complex scalar massive field φ describing alpha particles interacting with scalar σ and vector ω mesons. In close analogy to the scalar meson field, this Lagrangian is supplemented by a nonlinear scalar potential containing quartic and sextic self-interactions.

It was conjectured by Coleman in the eighties that due to the occurence of non-linear self-interactions, the classical solutions of the equation of motion describing the complex scalar field φ correspond to stable non-topological solitons, called Q-balls. From mathematical point of view these objects are localized, coherent superposition of bosons similar to Bose-Einstein condensates in magnetic traps. For some selections of the non-linear potential, there is another branch of solutions giving an unstable class of configurations that approach the plane-wave (dissipated solution) at large charge and are dubbed Q-clouds.

For a gauged Lagragian (e.g. scalar complex field coupled to the electromagnetic field) another class of solutions may arise where the radial scalar profile does not form a ball but rather a shell (bubble). These Q-shells arise in many, if not all, potentials that produce Q-balls.

On the other hand, in the middle of the nineties, Walter Greiner conjectured that some superheavy elements (e.g. the double magic Z=120, N-172 as predicted by the RMF) assume, mostly in their peripheral regions, a fullerene-like structure. I apply the above concepts rooted in the non-topological model to describe finite nuclei composed of alpha-particles and show that this model predicts the density depletion in the central region of a superheavy nucleus (Q-shell solution) for a range of model parameters. For other parameters selections Q-ball and Q-cloud solutions are obtained.