The GBT Diffuse Ionized Gas Survey (GDIGS): Survey Overview and First
  Data Release
  The Green Bank Telescope (GBT) Diffuse Ionized Gas Survey (GDIGS) traces
ionized gas in the Galactic midplane by measuring $4-8$GHz radio recombination
line (RRL) emission. The nominal survey zone is $32.3^{\circ}> l >-5^{\circ}$,
$|b|<0.5^{\circ}$, but coverage extends above and below the plane in select
fields, and additionally includes the areas around W47 ($l \simeq
37.5^{\circ}$) and W49 ($l \simeq 43^{\circ}$). GDIGS simultaneously observes
22 Hn$\alpha$ (15 usable), 25 Hn$\beta$ (18 usable), and 8 Hn$\gamma$ RRLs (all
usable), as well as multiple molecular line transitions (including of
H$_2^{13}$CO, H$_2$CO, and CH$_3$OH). Here, we describe the GDIGS survey
parameters and characterize the RRL data, focusing primarily on the Hn$\alpha$
data. We produce sensitive data cubes by averaging the usable RRLs, after first
smoothing to a common spectral resolution of 0.5km/s and a spatial resolution
of 2.65' for Hn$\alpha$, 2.62' for Hn$\beta$, and 2.09' for Hn$\gamma$. The
average spectral noise per spaxel in the \hna\ data cubes is $\sim\!10$mK
($\sim\!5$mJy/beam). This sensitivity allows GDIGS to detect RRLs from plasma
throughout the inner Galaxy. The GDIGS Hn$\alpha$ data are sensitive to
emission measures $EM \gtrsim 1100$cm$^{-6}$pc, which corresponds to a mean
electron density $\langle n_e \rangle \gtrsim 30$cm$^{-3}$ for a 1pc path
length or $\langle n_e \rangle \gtrsim 1$cm$^{-3}$ for a 1kpc path length.
