Disentangling the contributions of radiative and non-radiative localized plasmonic modes from the photonic density of states of metallic nanocavities between atomically-sharp tips and flat substrates remains an experimental challenge nowadays. Electroluminescence due to tunnelling through the tip-substrate gap allows discerning solely the excitation of radiative modes, but this information is inherently convolved with that of the electronic structure of the system. In this work we present a fully experimental procedure to eliminate the electronic-structure factors from the scanning tunnelling microscope luminescence spectra by confronting them with spectroscopic information extracted from elastic current measurements. Comparison against electromagnetic calculations demonstrates that this procedure allows characterizing the meV shifts experienced by the dipolar and quadrupolar plasmonic modes supported by the nanocavity under atomic-scale gap size changes. Our method, thus, gives us access to the frequency-dependent radiative Purcell enhancement that a microscopic light emitter would undergo when placed at the nanocavity.
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