Energy transfer in the collision of two scalar wave packets in spherical symmetry

We study the collisions of two scalar wave packets in the asymptotically flat spacetime and asymptotically anti-de Sitter spacetime in spherical symmetry. An energy transfer formula is obtained, $y=C{m}_i{m}_o\mathrm{/}r$, where $y$ is the transferred energy in the collisions of the two wave packets, $m_i$ and $m_o$ are the Misner-Sharp energies for the ingoing and outgoing wave packets, respectively, $r$ is the areal radius and collision place, and $C=1.873$ and $C=1.875$ for the asymptotically flat spacetime and asymptotically anti-de Sitter spacetime circumstances, respectively. The formula is universal, independent of the initial profiles of the scalar fields.