rather common, forbidden transitions account for a significant percentage of the photons emitted by the ultra-low density gas in space. Forbidden transitions in highly charged ions resulting in the emission of visible, vacuum-ultraviolet, soft x-ray and x-ray photons are routinely observed in certain laboratory devices such as electron beam ion traps and ion storage rings, where in both cases residual gas densities are sufficiently low for forbidden line emission to occur before atoms are collisionally de-excited. Using laser spectroscopy techniques, forbidden transitions are used to stabilize atomic clocks and quantum clocks that have the highest accuracies currently available. Forbidden lines of nitrogen ([N II] at 654.8 and 658.4 nm), sulfur ([S II] at 671.6 and 673.1 nm), and oxygen ([O II] at 372.7 nm, and [O III] at 495.9 and 500.7 nm) are commonly observed in astrophysical plasmas. These lines are important to the energy balance of planetary nebulae and H II regions. The forbidden 21-cm hydrogen line is particularly important for radio astronomy as it allows very cold neutral hydrogen gas to be seen. Also, the presence of [O I] and [S II] forbidden lines in the spectra of T-tauri stars implies low gas density. Notation Forbidden line transitions are noted by placing square brackets around the atomic or molecular species in question, e.g. [O III] or [S II]. References Further reading Osterbrock, D.E., Astrophysics of gaseous nebulae and active galactic nuclei, University Science Books, 1989, . Heinrich Beyer, Heinrich F. Beyer, H.-Jürgen Kluge, H.-J. Kluge, Viatcheslav Petrovich Shevelʹko, X-Ray Radiation of Highly Charged Ions, Springer Science & Business Media, 1997, . Gillaspy, John, editor, Trapping Highly Charged Ions: Fundamentals and Applications, Edited by John Gillaspy. Published by Nova Science Publishers, Inc., Huntington, NY, 1999, . Wolfgang Quint, Manuel Vogel, editors, Fundamental Physics in Particle Traps, Springer Tracts in Modern Physics, Volume 256 2014, . Astronomical spectroscopy Quantum chemistry Spectroscopy Nuclear physics