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\(3.5\keV\) line claimed to come from bare sulfur nuclei

The ET radio signal at \(11\,{\rm GHz}\) was due to a Soviet satellite, LUX and others have found no dark matter directly, the LHC hasn't proven any deviation from the Standard Model whatsoever, and Tracy Slatyer now believes that the seemingly exciting Fermi bubbles arrive from some boring pulsars.

Signs of any progress in physics through the experiment are being carefully stopped by Mother Nature. She is telling everyone: Stop with these ludicrous experiments and start to work on string theory seriously. ;-) What other anomalies get killed these days?

In two 2014 articles

Signal of neutrino dark matter (February, by Adam Falkowski)

Controversy about the \(3.5\keV\) line (August),
you could have learned about some tentative astronomical observations of X-rays with energy \(3.5\keV\), sometimes attributed to a \(7\keV\) sterile neutrino dark matter or something else that was equally new.




Two weeks ago, a more conservative astro preprint (a murder attempt, if you wish) was posted and it was just published in the Astrophysical Journal:
Laboratory measurements compellingly support charge-exchange mechanism for the 'dark matter' \(\sim 3.5\keV\) X-ray line
Chintan Shah and 6 co-authors working in Germany and Benelux are experimenters and brought us a "prototype" of a process they claim to be responsible for the X-ray line. And because they don't assume any new particle, you may be pretty sure that according to their picture, the source of the line is not dark matter – but rather some very visible ordinary baryonic matter (which strongly interacts with the electromagnetic field).




In their experiment, they have fully ionized ions of sulfur, \({\rm S}^{16+}\) and some \({\rm S}^{15+}\) ions which have one electron. I think that only one type of the ions is enough and they seem to claim that it doesn't matter much which of them is used. Both of them may play a role in the actual origin of the line if they are right.

Now, these ions are interacting with some neutral molecules – it doesn't seem to matter much what molecules they are, some neutral gas. The speeds are low. And the sulfur ion simply captures one electron. They observe the \(3.47\keV\) line experimentally.

What's their theory? Their theory is that the electron is first captured to a highly excited state with \(n\geq 7\) – this quantum number is the same number you know from the hydrogen atom because the quantum mechanical problems are isomorphic – and the electron collapses to \(n=1\). The emitted line is simply close to the ionization energy of the ion.

As I said, it only differs from the hydrogen atom by the higher charge \(Z=+16\) of the nucleus. Because the energy levels go like \(Z^2\), I expect\[

-E_0\sim 16^2 \times 13.6\eV \sim 3.48\keV

\] Good enough and the lines starting with \(n\geq 7\) approach so close to the observed \(3.5\keV\) line that it's compatible with the observations within the error margin. Well, I don't really know why they talk about the intermediate bound state with a high \(n\). Can't the electron fall from the continuum directly to \(n=1\), thus producing the \(3.5\keV\) photon as well? The most natural initial state for the captured electron could very well be chosen to be a constant wave function (or plane wave with a very low momentum, relatively to the inverse typical size of the orbits in the sulfur atoms or ions). We want the energy slightly above \(3.5\keV\), anyway, don't we?

They say and it sounds plausible to me that these maximally ionized positive ions may be found between galaxies, along with the electrons in slow matter. What I don't understand is: Why sulfur? Is there something special about sulfur? Or can we observe all the X-ray and other electromagnetic emission lines from the non-sulfur elements as well? What about the sulfur's neighbors, phosphorus and chlorine? Have astronomers overlooked all the \(Z^2\times 13.6\eV\) X-ray lines?

See also Phys.org.

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