Intersections of $\psi$ classes on Hassett Spaces for genus $0$ with all weights $\frac{1}{2}$

Hassett spaces are moduli spaces of weighted stable pointed curves. In this work, we consider such spaces of curves of genus $0$ with weights all $\frac{1}{2}$. These spaces are interesting as they are isomorphic to $\overline{M}_{0,n}$ but have different universal families and different intersection theory. We develop a closed formula for intersections of $\psi$-classes on such spaces. In our main result, we encode the formula for top intersections in a generating function obtained by applying a differential operator to the Witten-potential.