Bose-Einstein condensation in finite drops of α particles

Abstract

Ground-state properties of finite drops of $\ensuremath{\alpha}$ particles (Q-balls) are studied within a field-theoretical approach in the mean-field approximation. The strong interaction of $\ensuremath{\alpha}$'s is described by the scalar field with a sextic Skyrme-like potential. The radial profiles of scalar and Coulomb fields are found by solving the coupled system of Klein-Gordon and Poisson equations. The formation of shell-like nuclei, with vanishing density around the center, is predicted at high enough attractive strength of Skyrme potential. The equilibrium values of energy and baryon number of Q-balls and Q-shells are calculated for different sets of interaction parameters. Empirical binding energies of $\ensuremath{\alpha}$-conjugate nuclei are reproduced only if the gradient term in the Lagrangian is strongly enhanced. It is demonstrated that this enhancement can be explained by a finite size of $\ensuremath{\alpha}$ particles.