Detection-time distribution for several quantum particles

We address the question of how to compute probability distribution time at which a detector clicks in situation $n$ nonrelativistic quantum particles volume $\mathrm{\ensuremath{\Omega}}\ensuremath{\subset}{\mathbb{R}}^{3}$ physical space and detectors placed along boundary $\ensuremath{\partial}\mathrm{\ensuremath{\Omega}}$ $\mathrm{\ensuremath{\Omega}}$. previously [Tumulka, Ann. Phys. (NY) 442, 168910 (2022)] argued favor rule for one-particle case that involves Schr\"odinger equation with an absorbing condition on introduced by Werner; we call this ``absorbing rule.'' Here, describe natural extension $n$-particle case. A key element is that, upon detection event, wave function gets collapsed inserting detected position, detection, into function, thus yielding $n\ensuremath{-}1$ particles. also moving detectors.