Alternatively, we could write it as $$ H_{\mathrm{HO}}= H_{\mathrm{CoM}}+\frac{1}{2mA}\sum_{i < j}(\boldsymbol{p}_i-\boldsymbol{p}_j)^2 +\frac{m\omega^2}{2A}\sum_{i < j}(\boldsymbol{r}_i-\boldsymbol{r}_j)^2, $$

The center-of-mass term is defined as $$ H_{\mathrm{CoM}}= \frac{\boldsymbol{P}^2}{2mA}+\frac{mA\omega^2\boldsymbol{R}^2}{2}. $$