  We discuss a simple singular system in two dimension, two heavy particles
interacting with a light particle via an attractive contact interaction.
Although intuitively clear the actual application of the Born-Oppenheimer
approximation to this problem is quite subtle. Nevertheless, with due care we
show that this can be done, as a result we calculate the leading term of the
Born-Oppenheimer approximation and indicate how to get the higher order
corrections.
