Using the Very Large Array (VLA) with an angular resolution of 3 '', w
e have detected the hydrogen recombination line H92 alpha from the gal
axies Arp 220, M83, and NGC 2146. The line emission arises from the nu
clear regions with a line-to-continuum ratio of 1% or less. In order t
o fit both the observed H92 alpha line and continuum data in the nucle
ar regions, we have considered two types of models. First, we utilize
a model with a collection of H rr regions. A large number of compact H
II regions are required in this model. With electron temperatures in
the range 5 x 10(3)-1 x 10(4) K and a range of electron densities, thi
s model can account for both the line intensity and the continuum spec
trum. In most cases, the H92 alpha line is dominated by internal stimu
lated emission due to free-free continuum arising within the H II regi
ons. In a low-density case (n(e) = 50 cm(-3)) for Arp 220, about half
the line emission comes from external stimulated emission due to the b
ackground nonthermal source. Typical rates of ionizing photons predict
ed from these models are similar to 5 x 10(52) S-1 for M83, similar to
4 x 10(53) S-1 for NGC 2146, and 5 x 10(54) S-1 for Arp 220. We infer
that 10(5) O5 stars are required in Arp 220, which is an order of mag
nitude greater than in NGC 2146 and 2 orders of magnitude greater than
in M83. Alternatively, several uniform slab models with T-e greater t
han or equal to 5 x 10(3) and n, in the range of 50-1 x 10(4) cm(-3) a
ppear to fit both the H92 alpha line and continuum data of Arp 220 and
M83. In the low-density models, stimulated emission by the background
nonthermal radiation appears to be dominant at low frequencies, and t
he lines at higher frequencies arise primarily from spontaneous emissi
on. The uniform slab model requires a higher ionizing photon rate than
the H n region model. No slab models with reasonable T-e can fit the
data observed in M83 and NGC 2146. Combining previous published data w
ith these new observations, a sample of 13 galaxies has been observed
for radio recombination lines (RRLs) with the VLA. Nine out of the 13
galaxies have been detected in the H92 alpha line. While the H92 alpha
line luminosity appears to be correlated with the Bra line luminosity
, we find that nearly all the RRL galaxies show a significant excess i
n H92 alpha line compared to the expected LTE value. The excess in the
H92 alpha line flux suggests that non-LTE effects are important for t
he H92 alpha line in these starburst nuclei. A strong correlation betw
een H92 alpha and the molecular lines of HCN/HCO+ is also found, indic
ating that the RRL emitters may be spatially associated with the dense
molecular cores. The inferred high electron density also suggests an
intimate relation between the RRLs and the dense molecular medium in t
hese galaxies.