LAUSR

We prove lower bounds for energy in the Gaussian core model, in which point particles interact via a Gaussian potential. Under the potential function $t \mapsto e^{-\alpha t^2}$ with $0 \pi e$. As a consequence of our results, we obtain bounds in $\mathbb{R}^n$ for the minimal energy under inverse power laws $t \mapsto 1/t^{n+s}$ with $s>0$, and these bounds are sharp to within a constant factor as $n \to \infty$ with $s$ fixed.