  The dynamic interactions between pairs of swimming microorganisms underpin
the collective behaviour of larger suspensions, but accurately calculating
pairwise collisions has typically required the use of numerical simulations in
which hydrodynamic interactions are fully resolved. In this paper, we utilise
analytical expressions for forces and torques acting on two closely separated
spherical squirmers -- accurate to second order in the ratio of cell-cell
spacing to squirmer radius -- in order to calculate their scattering dynamics.
Attention is limited to squirmers whose orientation vectors lie in the same
plane. We characterise the outgoing angles of pairs of bottom-heavy squirmers
in terms of their incoming angles, the squirmer parameter $\beta$, and the
strength of the external gravitational field, discovering transient scattering,
stationary bound states, pairwise swimming motion, and circular orbits. These
results compare well with full numerical solutions obtained using boundary
element methods, highlighting the utility of lubrication theory. We expect
these results will be useful for the foundations of mesoscale continuum models
for suspensions of spherical microorganisms.
