  Previous radio recombination line (RRL) observations of dust clumps
identified in the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL)
have led to the detection of a large number of RRLs in the 3mm range. Here, we
aim to study their excitation with shorter wavelength (sub)millimeter radio
recombination line (submm-RRL) observations. We made observations of submm-RRLs
with low principal quantum numbers ($n$ $\leq$ 30) using the APEX 12 m
telescope, toward 104 HII regions associated with massive dust clumps from
ATLASGAL. The observations covered the H25$\alpha$, H28$\alpha$, and H35$\beta$
transitions. Toward a small subsample the H26$\alpha$, H27$\alpha$,
H29$\alpha$, and H30$\alpha$ lines were observed to avoid contamination by
molecular lines at adjacent frequencies. We have detected submm-RRLs
(signal-to-noise $\geq$ 3 $\sigma$) from compact HII regions embedded within 93
clumps. The submm-RRLs are approximately a factor of two brighter than the
mm-RRLs and consistent with optically thin emission in local thermodynamic
equilibrium (LTE). The average ratio (0.31) of the measured
H35$\beta$/H28$\alpha$ fluxes is close to the LTE value of 0.28. No indication
of RRL maser emission has been found. The Lyman photon flux, bolometric, and
submm-RRL luminosities toward the submm-RRL detected sources present
significant correlations. The trends of dust temperature and the ratio of
bolometric luminosity to clump mass, $L_{\rm bol}/M_{\rm clump}$, indicate that
the HII regions are related to the most massive and luminous clumps. By
estimating the production rate of ionizing photons, $Q$, from the submm-RRL
flux, we find that the $Q$(H28$\alpha$) measurements provide estimates of the
Lyman continuum photon flux consistent with those determined from 5 GHz radio
continuum emission.
