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We study the (near or close to) ground state distribution of N softlyrepelling particles trapped in the interior of a spherical box. The chargesmutually interact via an inverse power law potential of the form $1/r^\gamma$.We study three regimes in which the charges form an single spherical shell atthe edge of the box ($\gamma=1$), a series of concentric shells of increasingdensity ($\gamma=2$) and $\gamma=12$ for which the charges form shells with amore uniform charge distribution. We conduct numerical simulations for clusterscontaining up to 5000 charges and compare charge density across the system withcontinuum limit results. The agreement between numerical (discrete) results andthe continuum limit is found to improve with increasing N.

Packing of softly repulsive particles in a spherical box - a generalised Thomson problem