  We investigate a detector scheme designed to measure the arrival of a
particle at $x=0$ during a finite time interval. The detector consists of a two
state system which undergoes a transition from one state to the other when the
particle crosses $x=0$, and possesses the realistic feature that it is
effectively irreversible as a result of being coupled to a large environment.
The probabilities for crossing or not crossing $x=0$ thereby derived coincide
with earlier phenomenologically proposed expressions involving a complex
potential. The probabilities are compared with similar previously proposed
expressions involving sums over paths, and a connection with time operator
approaches is also indicated.
