  The pair-distribution function, which provides information about correlations
in a system of interacting particles, is one of the key objects of theoretical
soft matter physics. In particular, it allows for microscopic insights into the
phase behavior of active particles. While this function is by now well studied
for two-dimensional active matter systems, the more complex and more realistic
case of three-dimensional systems is not well understood by now. In this work,
we analyze the full pair-distribution function of spherical active Brownian
particles interacting via a Weeks-Chandler-Andersen potential in three spatial
dimensions using Brownian dynamics simulations. Besides extracting the
structure of the pair-distribution function from the simulations, we obtain an
analytical representation for this function, parametrized by activity and
concentration, which takes into account the symmetries of a homogeneous
stationary state. Our results are useful as input to quantitative models of
active Brownian particles and advance our understanding of the microstructure
in dense active fluids.
