  Quantum mechanical scattering resonances for colliding particles occur when a
continuum scattering state couples to a discrete bound state between them. The
coupling also causes the bound state to interact with itself via the continuum
and leads to a shift in the bound state energy, but, lacking knowledge of the
bare bound state energy, measuring this self-energy via the resonance position
has remained elusive. Here, we report on the direct observation of
self-interaction by using a nano-eV atom collider to track the position of a
magnetically-tunable Feshbach resonance through a parameter space spanned by
energy and magnetic field. Our system of potassium and rubidium atoms displays
a strongly non-monotonic resonance trajectory with an exceptionally large
self-interaction energy arising from an interplay between the Feshbach bound
state and a different, virtual bound state at a fixed energy near threshold.
