  This paper describes a search for pairs of neutral, long-lived particles
decaying in the ATLAS calorimeter. Long-lived particles occur in many
extensions to the Standard Model and may elude searches for new promptly
decaying particles. The analysis considers neutral, long-lived scalars with
masses between 5 GeV and 400 GeV, produced from decays of heavy bosons with
masses between 125 GeV and 1000 GeV, where the long-lived scalars decay into
Standard Model fermions. The analysis uses either 10.8 fb$^{-1}$ or 33.0
fb$^{-1}$ of data (depending on the trigger) recorded in 2016 at the LHC with
the ATLAS detector in proton-proton collisions at a centre-of-mass energy of 13
TeV. No significant excess is observed, and limits are reported on the
production cross section times branching ratio as a function of the proper
decay length of the long-lived particles.
