Colloquium with Alumni Professor of Physics A. Ravi P. Rau.

Generally, a perturbation expansion with a non-zero first order term is
followed by smaller higher order terms. An unusual exception is forward
charge transfer between an ion and a neutral atom or molecule. At high
incident ion velocities, the second Born term dominates over the first
for that charge (electron) transfer from neutral to ion. Aspects of this
will be discussed, along with a peculiar connection to the most
efficient procedure for rescuing a person fallen overboard at sea.
Connections go back a hundred years to the early days of quantum
physics, even earlier in classical mechanics and to gravitational analogs.