We present observations of radio recombination lines from the starburst galaxy Arp 220 at 1.4, 8.1, 84, 96 and 207 GHz (sensitive upper limit for the 1.4 GHz line and firm detections at the other frequencies), and the radio continuum spectrum between 330 MHz and 207 GHz. We show that a model with three components of ionized gas with different densities and area covering factors can consistently explain both RRL and continuum data. The total mass of ionized gas in the three components is 3 x 10^7 M_sun requiring 3 x 10^5 O5 stars with a total Lyman continuum production rate (NLyc) of 1.3 x 10^{55} photons /s. These values imply a dust extinction A_V ~ 45 magnitudes and an SFR of ~240 M_sun/yr. The NLyc of ~3% associated with the high density HII regions implies similar SFR at recent epochs. The data is also consistent with multiple starbursts of very high SFR and short durations. The derived value of 24 for the IR-excess favours a starburst rather than an AGN as the origin of the observed FIR luminosity. (the abstract has been abridged)
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