The 21 centimeter hydrogen line originates from the hyperfine transition of neutral hydrogen. Are there any bigger wavelengths that originate from this method? Radio emissions from rotating stellar objects are not part of this category; clarifying in case this is brought up.
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$\begingroup$ Welcome to Astronomy SE. Are you asking about spectroscopic measurements only? $\endgroup$– Daddy KropotkinAug 19, 2021 at 20:14
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$\begingroup$ Yes. I’m asking about the spectroscopic measurement and the origin of that spectra emission. $\endgroup$– EvamentalityAug 19, 2021 at 20:20
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Any ion that captures an electron has the capability of forming a hydrogenic atom where you can have transitions between energy levels with very large principle quantum number. The conditions to make these transitions visible are a low density plasma to avoid collisional (de)excitation.
For example Peters et al. (2011) discuss "decametre" wavelength transitions, and some of these have been detected, mainly associated with carbon ions (e.g. the C631$\alpha$ radio recombination line at 26 MHz $=$ a wavelength of 11.5 m).
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$\begingroup$ Thank you for your response. Is there any mathematical framework or formulae that can be used to calculate this emission spectra? $\endgroup$ Aug 19, 2021 at 20:35
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$\begingroup$ currently unanswered in Physics SE: What is the lowest energy atomic transition ever detected and identified? and Can a nuclear electromagnetic transition rate be affected by the electron configuration (e.g. bare nucleus v neutral atom)? Any experimental examples? $\endgroup$– uhohAug 19, 2021 at 22:24
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$\begingroup$ Also see this answer: "Just by coincidence the most recent Physics Today reports on a paper about the detection of extra-galactic Rydberg atoms with 𝑛 as high as 508(!), which makes them roughly 250,000 times the size of the same atom in the ground state. That is larger than a micrometer." $\endgroup$– uhohAug 19, 2021 at 22:25
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$\begingroup$ @Evamentality There is no simple formula for the spectrum. You have to solve the equation for the level population up to very high quantum numbers, coupled with a calculation of the free electron spectrum (which determines both the production and loss rates for the levels). The spectral characteristics depend strongly on the plasma density. For sufficiently low frequencies (high quantum numbers) the lines become blended i.e. the spectrum continuous. I published a (very long) paper about this some years ago. $\endgroup$– ThomasAug 20, 2021 at 20:50