In order to find high-probability regions of ρ nuc,rot in practice, we first draw a sufficiently large random sample from ρ(r, R). This can be achieved via Markov chain Monte Carlo (MCMC) sampling. Furthermore, a distance metric d is required for measuring the similarity of the individual labeled configurations. Two coordinate vectors can be aligned by a rotation such that their root-mean-square deviation (RMSD) in the nuclear center-of-mass frame is minimized. There exist simple equations for finding the optimal rotation matrix U opt to achieve this goal. The metric d([R] rot , [R ′ ] rot ) is defined as the RMSD after alignment.