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In this article, we study a second-order expansion for the effect induced ona large quantum particle which undergoes a single scattering with a low-massparticle via a repulsive point interaction. We give an approximation withthird-order error in $\lambda$ to the map $G\to \Tr_{2}[(I\otimes\rho)S_{\lambda}^{*}(G\otimes I)S_{\lambda}]$, where $G\in \Bi(L^{2}(\R^{n}))$is a heavy-particle observable, $\rho\in \Bi_{1}(\R^{n})$ is the density matrixcorresponding to the state of the light particle, $\lambda=\frac{m}{M}$ is themass ratio of the light particle to the heavy particle, $S_{\lambda}\in\Bi(L^{2}(\R^{n})\otimes L^{2}(\R^{n}))$ is the scattering matrix between thetwo particles due to a repulsive point interaction, and the trace is over thelight-particle Hilbert space. The third-order error is bounded in operator normfor dimensions one and three using a weighted operator norm on $G$.

The reduced effect of a single scattering with a low-mass particle via a point interaction