Improved bounds for interatomic distance in Morse clusters

We improve the best known lower bounds on the distance between two points of a Morse cluster in $\mathbb{R}^3$, with $\rho \in [4.967,15]$. Our method is a generalization of the one applied to the Lennard-Jones potential in~\cite{Schac}, and it also leads to improvements of lower bounds for the energy of a Morse cluster. Some of the numerical results have been announced in~\cite{AS}.