We present observations of radio recombination lines ( RRL ) from the starburst galaxy Arp 220 at 8.1 GHz ( H92 \alpha ) and 1.4 GHz ( H167 \alpha and H165 \alpha ) and at 84 GHz ( H42 \alpha ) , 96 GHz ( H40 \alpha ) and 207 GHz ( H31 \alpha ) using the Very Large Array and the IRAM 30 m telescope , respectively .
RRLs were detected at all the frequencies except at 1.4 GHz where a sensitive upper limit was obtained .
We also present continuum flux measurements at these frequencies as well as at 327 MHz made with the VLA .
The continuum spectrum , which has a spectral index \alpha \sim - 0.6 ( S _ { \nu } \propto \nu ^ { \alpha } ) between 5 and 10 GHz , shows a break near 1.5 GHz , a prominent turnover below 500 MHz and a flatter spectral index above 50 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 3.2 \times 10 ^ { 7 } M _ { \odot } requiring 3 \times 10 ^ { 5 } O5 stars with a total Lyman continuum ( Lyc ) production rate N _ { \scriptstyle Lyc } \sim 1.3 \times 10 ^ { 55 } photons s ^ { -1 } .
The ratios of the expected to observed Br \alpha and Br \gamma fluxes implies a dust extinction A _ { V } \sim 45 magnitudes .
The derived Lyc photon production rate implies a continuous star formation rate ( SFR ) averaged over the life time of OB stars of \sim 240 M _ { \odot } yr ^ { -1 } .
The Lyc photon production rate of \sim 3 % associated with the high density HII regions implies similar SFR at recent epochs ( t < 10 ^ { 5 } yrs ) .
An alternative model of high density gas , which can not be excluded on the basis of the available data , predicts ten times higher SFR at recent epochs .
If confirmed , this model implies that star formation in Arp 220 consists of multiple starbursts of very high SFR ( few \times 10 ^ { 3 } M _ { \odot } yr ^ { -1 } ) and short durations ( \sim 10 ^ { 5 } yrs ) .

The similarity of IR-excess , L _ { IR } / L _ { Ly \alpha } \sim 24 , in Arp 220 to values observed in starburst galaxies shows that most of the high luminosity of Arp 220 is due to the on-going starburst , rather than produced by a hidden AGN .
A comparison of the IR-excesses in Arp 220 , the Galaxy and M33 indicates that the starburst in Arp 220 has an IMF which is similar to that in normal galaxies and has a duration longer than 10 ^ { 7 } yrs .
If there was no infall of gas during this period , then the star formation efficiency ( SFE ) in Arp 220 is \sim 50 % .
The high SFR and SFE in Arp 220 is consistent with their known dependences on mass and density of gas in star forming regions of normal galaxies .