ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- IV. Radio Recombination Lines and evolution of star formation efficiencies

We report detection of radio recombination line (RRL) H$_{40\alpha}$ toward 75 sources, with data obtained from ACA observations in the ATOMS survey of 146 active Galactic star forming regions. We calculated ionized gas mass and star formation rate with H40U line emission. The mass of ionized gas is significantly smaller than molecular gas mass, indicating that ionized gas is negligible in the star forming clumps of the ATOMS sample. The star formation rate (SFR$_{{\rm H}_{40\alpha}}$) estimated with RRL H$_{40\alpha}$ agrees well with that (SFR$_{\rm L_{bol}}$) calculated with the total bolometric luminosity (L$_{\rm bol}$) when SFR $\gtrsim 5 {\rm M_\odot My}r^{-1}$, suggesting that millimeter RRLs could well sample the upper part of the initial mass function (IMF) and thus be good tracers for SFR. We also study the relationships between L$_{\rm bol}$ and the molecular line luminosities (L0mol) of CS J=2-1 and HC$_3$N J=11-10 for all the 146 ATOMS sources. The Lbol-L0mol correlations of both the CS J=2-1 and HC3N J=11-10 lines appear approximately linear and these transitions have success in predicting L$_{\rm bol}$ similar to that of more commonly used transitions. The L$_{\rm bol}$-to-L$_{\rm mol}$ ratios or SFR-to-mass ratios (star formation efficiency; SFE) do not change with galactocentric distances (R$_{\rm GC}$). Sources with H$_{40\alpha}$ emission (or H$_{\rm II}$ regions) show higher L$_{\rm bol}$-to-L$_{\rm mol}$ than those without H$_{40\alpha}$ emission, which may be an evolutionary effect.