The discovery of the first naturally occurring high gain hydrogen recombination line (HRL) maser, in the millimeter and submillimeter spectrum of the emission line star MWC349, requires an expansion of current paradigms about HRLs. In this paper we re-examine in general the physics of non-LTE populations in recombining hydrogen and specify the conditions necessary for high-gain masing and lasing in HRLs. To do so we use the extensive new results on hydrogen level populations produced by Storey and Hummer (1995), and our calculations for the net (that is, line plus continuum) absorption coefficient for the hydrogen, and we present results for the α-and β-lines whose principal quantum numbers n are between 5 and 100, for gas whose electron number density 3 ≤ log N e (cm −3 ) ≤ 11, at two electron temperatures, T e = 5, 000 and 10,000 K. We show that the unsaturated maser gain in an HRL is a sharp function of N e , and thus to achieve high-gain masing each line requires a sufficiently extended region over which the density is rather closely specified.Saturation of masing recombination lines is a critical consideration. We derive a simple equation for estimating the degree of saturation from the observed flux density and the interferometric and/or model information about the amplification path length, avoiding the vague issue of the solid angle of masing. We also present a qualitative way to approach the effects of saturation on adjacent emission lines, although the detailed modeling is highly case-specific.We draw attention to another non-LTE phenomenon active in hydrogen: the overcooling of populations. This occurs for HRLs with n > ∼ 20, in gas where N e < ∼ 10 5 cm −3 . Observationally the HRL overcooling might manifest itself as an anomalously weak emission recombination line, or as a "dasar," that is, an anomalously strong absorption line. In the simplest case of a homogeneous HII region the absorption can be observed on the proper free-free continuum of the region, if some conditions for the line or/and continuum optical depths are satisfied.We briefly discuss the prospects of detecting hydrogen masers, lasers and dasars in several classes of galactic and extragalactic objects, including compact HII regions, Be or Wolf-Rayet stars, and AGNs.

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The conditions of masing and lasing in the hydrogen recombination lines (HLR) in the disk and outflow of MWC349 are studied. Comparison of the complete set of the observed α-lines, from H2α through H92α, with simple models of optically thin spontaneous emission shows that observable HRL masing in this source is limited to the interval of the principal quantum numbers n ≈ 10 -36.We use our analytical and numerical results for the conditions of optimum masing (Strelnitski et al. 1995b; "Paper 2"), and the morphological parameters of a photoevaporized circumstellar disk modelled by Hollenbach et al. (1994), to obtain analytical approximations and quantitative estimates for the expected unsaturated maser gain and the degree of saturation in HRL masers in the disk of MWC349. It is shown that the unsaturated maser gains of the IR and optical HRL lasers should be very high but in fact all of these transitions are strongly saturated. Due to saturation, their relative intensity with respect to the spontaneous emission should steeply drop toward smaller n's which explains why optical and near infrared HRL lasers are not seen in MWC349. This result is quite general and makes the prognosis for observable high-frequency lasers in other sources pessimistic as well. An exception might arise due to special geometry, if lasing were confined to very small solid angles.We show that weak masing from the outflow of MWC349 is only possible in low n α-lines (n < ∼ 20-30), and then only if the outflow begins much closer to the central star than the Hollenbach et al. model predicts (≈ 3 • 10 15 cm). We therefore conclude that maser emission from the disk, rather than from the outflow, is responsible for the observed weak amplification of the "pedestal" spectral components in the α-lines with n < ∼ 40. The fluxes in the lower frequency α-lines are well explained by spontaneous emission from the outflow, with proper corrections for free-free absorption.We review the current state (and prospects) of observations of masing and lasing hydrogen β-lines in MWC349. We argue in favor of "close in n," rather than "close in frequency" α/β pairs for intensity analysis, when maser amplification is present.

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