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I am aware that outer shell electrons in rubidium atoms in an optical lattice can be excited to Rydberg levels, in which the electrons orbit well beyond the atoms to which they are bound. Is this something that can happen within the bulk of a metal as well?

If this is not something that has been experimentally examined, assume there are one or more straightforward mechanisms that could provide the requisite excitation—naturally occurring alpha or beta emitters, for example.

If Rydberg levels within the bulk of a metal are not possible, why is this the case? If they are possible, how would the electron charge density be affected? In the non-Rydberg case, I understand the d-electron density will be quite low in the interstitial regions. Would this change in the Rydberg case? How long would the excited state last? How would the blockade effect factor in? Can you recommend a suitable approach for modeling the charge density?

(It seems a 1996 paper did some calculations that are relevant here, which I will take a look at. I am still interested in any information that people can provide.)

Eric Walker
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  • I can't say for sure but I find this very unlikely. The lifetimes of Rydberg states should be very short. Also, normal metals are very hot compared to the ultra-cold experiment you mention. Thermal behavior should further reduce the lifetime of the excited states. – Kevin Driscoll Aug 20 '13 at 07:46
  • @KevinDriscoll: Interesting thought. My off-the-cuff ideas -- (1) kinetic energy of the metal atoms is << eV, while the electronic structure requires energy on the order of eV to perturb. (2) Higher temperatures should increase rather than decrease the likelihood of perturbation. – Eric Walker Aug 20 '13 at 13:40
  • related: http://physics.stackexchange.com/questions/36064/is-ultradense-deuterium-real –  Aug 20 '13 at 18:48
  • @KevinDriscoll some Rydberg states have a lifetime of almost 1 ms, which is quite long considering the relevant time scales. This is exactly why they are used in research for e.g. quantum computers – Funzies Aug 20 '13 at 19:03
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    @Erik: I assume the lifetime of 1 ms is for free atoms. In condensed matter, such states would be almost instantly disrupted by collisions. –  Aug 20 '13 at 19:13
  • @BenCrowell yes, you are probably right, excuse my mistake! – Funzies Aug 20 '13 at 20:36
  • a related question about pseudoscience with claims linking it to Rydberg states in condensed matter: http://physics.stackexchange.com/questions/43960/is-there-any-reproducible-tested-evidence-for-ni-h-cold-fusion –  Aug 22 '13 at 15:28
  • @BenCrowell: you're not outing anyone -- I freely acknowledge that this is related to cold fusion. All of my questions are related to cold fusion. But I think you're missing the interesting physics of it, outside of that context, which is what is relevant to this site. (Interesting, at least, to amateurs who are still learning about this stuff.) – Eric Walker Aug 22 '13 at 16:05
  • @BenCrowell: As an assistance to anyone who might be confused on that point, I am adding a note to my profile to this effect. Feel free to point people to it. – Eric Walker Aug 22 '13 at 16:26
  • There is such (fat) thing in a insulating solid as a Frenkel exciton, which is an electron-hole analog of a Rydberg atom. But this hardly applies to metals... – Slaviks Sep 19 '13 at 19:34
  • Oops, the other guy - Wannie-Mott exciton - which is like Rydberg. Sorry for the mix up on my above comment. – Slaviks Sep 19 '13 at 19:38

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Some quick thoughts, but hopefully useful:

The direct analogue of Rydberg states would just be exciting an electron to a very high energy band. I don't believe this does anything terribly interesting, other than decay quickly. There are just too many decay channels. Note, the electrons are delocalized in a metal, so there is no sense in which one gets a "big atom" from such a high energy electrons. I think the opposite, such an electron would look essentially free, and very "small" because of its short wavelength.

A better analogue of a Rydberg state, (and perhaps this is what you have in mind),might be a donor site in the gap of a semiconductor. This would be a positively charged impurity in the lattice. If the material is right this hosts hydrogen-like states (if I recall correctly you need a small effective mass). These states lie in the gap, so there is no delocalization like in the electronic bands. In the naivest approximation (which is all that I know) you get precisely the Rydberg series, but with a different mass and dielectric constant, so that your orbits are very big and your "Rydberg" is very small.

Largely eqivalent is a Wannier exciton, which is a bound state of electron and hole in the same fashion.

Haven't really seen anything about highly excited states of these things, but that could be ignorance on my part. Again hard to imagine that the lifetimes would be long, but excitons themselves can have surprisingly long lifetimes, up to a millisecond.

BebopButUnsteady
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  • I was thinking of the donor site in the semiconductor case, which is interesting. About the delocalization of the electrons -- I believe this only holds for the most loosely bound electrons. Unless I am mistaken, a majority of the electrons are still quite localized around the lattice sites. – Eric Walker Aug 21 '13 at 04:21
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I assume the question traces back somehow to Leif Holmlid's claims to have discovered "Rydberg matter" and "ultradense deuterium" in the lab.

Can Rydberg states exist within the bulk of a metal?

The answer is no, for straightforward reasons. For example, Rydberg states in monoatomic hydrogen can only exist at low densities. This is simply because the radius of state $n$ goes like $n^2$. There isn't enough room for arbitrarily high $n$ states to exist, and they would be disrupted by collisions, whose cross-section goes like $n^4$. In the sun's absorption spectrum, for example, there is a cutoff in the $n$ values that are observed, because the density of the gas is fairly high. This is why there's no way we're going to see them in condensed matter.

Holmlid is a kook who is very persistent about pushing his claims. For example, he tried to promote himself in a Wikipedia article, "Rydberg matter," writing the article himself and citing his own papers extensively. Although he has managed to get his articles published in journals, a literature search showed that out of 2154 references to his papers (presumably not all on Rydberg matter), 1863 were self-citations. What little recognition his work has received from others seems to have been mainly from cold-fusion kooks, such as Hora and Miley, with whom he has co-authored papers.

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    No intentional connection to Holmlid's work -- my reference is primarily the series of experiments with rubidium atoms along the lines of the phys.org article. But your comments are helpful. – Eric Walker Aug 20 '13 at 19:30