The presented results are concerned with the shapes of the Balmer-α line emitted by a low-pressure rf 13.56-MHz discharge in hydrogen. Optical emission analysis has been done using a monochromator with a high spectral resolution (0.04 Å). Essentially, the lines present a central nearly Gaussian-shape peak with a FWHM of about 0.3 Å emerging from a wide pedestal constituted by two plateaus with widths equal to 0.9 and 1.5 Å, respectively, and by large wings whose intensity quasilinearly decreases on both sides of the central wavelength. We explain these profiles by the Doppler broadening due to fast H atoms produced by the dissociative excitation and the dissociative ionization of the H2 molecules by electron impact generally followed by the excitation of the resulting atoms towards emitting states.
We address the problem of the definition of the finite-volume correlation length. First, we study the large-N limit of the N -vector model, and we show the existence of several constraints on the definition if regularity of the finite-size scaling functions and correct anomalous behaviour above the upper critical dimension are required. Then, we study in detail a model in which the zero mode in prohibited. Such a model is a generalization of the fixed-magnetization Ising model which is equivalent to the lattice gas. Also in this case, we find that the finite-volume correlation length must satisfy appropriate constraints in order to obtain regular finite-size scaling functions, and, above the upper critical dimension, an anomalous scaling behaviour. The large-N results are confirmed by a one-loop calculation in the lattice φ 4 theory.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.