  We address the question of how to compute the probability distribution of the
time at which a detector clicks, in the situation of $n$ non-relativistic
quantum particles in a volume $\Omega\subset \mathbb{R}^3$ in physical space
and detectors placed along the boundary $\partial \Omega$ of $\Omega$. We have
previously [arXiv:1601.03715] argued in favor of a rule for the 1-particle case
that involves a Schr\"odinger equation with an absorbing boundary condition on
$\partial \Omega$ introduced by Werner; we call this rule the "absorbing
boundary rule." Here, we describe the natural extension of the absorbing
boundary rule to the $n$-particle case. A key element of this extension is
that, upon a detection event, the wave function gets collapsed by inserting the
detected position, at the time of detection, into the wave function, thus
yielding a wave function of $n-1$ particles. We also describe an extension of
the absorbing boundary rule to the case of moving detectors.
