One of the most convenient methods to obtain information about the energydistribution function of electrons in conducting materials is the measurementof the energy resolved current $j(\omega)$ in field emission (FE) experiments.Its high energy tail $j_>(\omega)$ (above the Fermi edge) contains invaluableinformation about the nature of the electron--electron interactions inside theemitter. Thus far, $j_>(\omega)$ has been calculated to second order in thetunnelling probability, and it turns out to be divergent toward the Fermi edgefor a wide variety of emitters. The extraction of the correlation propertiesfrom real experiments can potentially be obscured by the eventually moredivergent contributions of higher orders as well as by thermal smearing around$E_F$. We present an analysis of both factors and make predictions for theenergy window where only the second order tunnelling events dominate thebehaviour of $j_>(\omega)$. We apply our results to the FE from Luttingerliquids and single-wall carbon nanotubes.
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