  We present results of the impurity local density of states of the interacting
resonant level model at zero temperature. We concentrate on low-energy
properties and predominantly use the numerical renormalisation group technique.
As interaction is increased, we find that the resonance peak at zero energy
disappears, while two new peaks at finite energy emerge. This is in the absence
of any field breaking the resonance. We further show that the height of the
spectral function does not scale in the same way as the width, and in fact
defines a second distinct exponent. We back up our results with analytic
strong-coupling calculations as well as an analytic diagrammatic
renormalisation group calculation that rather surprisingly gets the second
exponent exactly, even for strong interactions.
