Transition frequency -> Rydberg oxygen atoms

[Shivani_Ram]

TL;DR

Atomic physics, Rydberg atoms

Hi all,
My exposure to atomic physics is limited and hence could use some expert opinion on a basic question. From my knowledge, Rydberg atoms are assumed to be hydrogen-like and hence the Rydberg formula to calculate the transition frequency is generally used. But not all atoms are the same. Especially for heavier elements, for lower l states the quantum defect dominates and this changes their energy significantly. Can the Rydberg formula with the Rydberg constant assuming infinite nuclear mass be used for the calculation of atomic transition frequencies in Oxygen?


Views along with references to some literature theoretical calculations or experimental measurements will be appreciated.
Thank you!

 

[Vanadium 50]

A Rydberg oxygen ion would have charge 7+. Is that what you are working with?

 

[Shivani_Ram]

I am working with Rydberg Oxygen atoms. The atoms I am working with are produced by sputtering due to alpha recoil from radioactive decay of 210Pb and are created with mean energies fo 12 eV.

 

[Vanadium 50]

12 eV is not enough to strip 7 electrons from oxygen.

 

[Shivani_Ram]

They are ionized by the thermal black body radiation at room temperature of T ≈ 300 K

 

[Vanadium 50]

Not to a state of 7+ they aren't. That would take ~20 million degrees.

 

[Cthugha]

I am working with Rydberg Oxygen atoms. The atoms I am working with are produced by sputtering due to alpha recoil from radioactive decay of 210Pb and are created with mean energies fo 12 eV.

That sounds like you are working on the KATRIN measurement for precisely measuring Neutrino masses via tritium beta decay. I am a semiconductor (Rydberg) physics guy, but one person from our astroparticle physics department who has ties to people working at KATRIN once asked me about Rydberg stuff as Rydberg atoms seem to be the source of the most dominant background in the spectrometer there. If you are not working on KATRIN, their experience may help you:
https://www.sciencedirect.com/science/article/pii/S0927650522000020

If I remember correctly, KATRIN has lead decaying to Polonium and in the process there is a chance to release oxygen atoms from the steel, out of which the chamber is built. Is this your problem as well?

There is the standard reference for all stuff related to excited states in atomic oxygen which also includes some quantum defects:
https://pubs.aip.org/aip/jpr/articl...zation-Cross-Sections?redirectedFrom=fulltext

However, in practice, I am afraid the exact transition energies of the highly excited states will depend strongly on its surroundings. The polarizability of Rydberg atoms is huge. Besides that, the general answer to your question is: It depends. Taking the modified hydrogen model with the quantum defect may or may not be a good approximation for your purpose. What do you want to do exactly?

 

[Shivani_Ram]

Hi,
Thank you for the detailed reply and the reference for atomic oxygen this will be useful. You got it right!:) I do work for the KATRIN experiment on a background reduction technique using sub-THz radiation to induce transitions in Rydberg atoms to de-excite them. Yes, 210-Pb --> 210 Po and subsequent alpha decay to 206 Pb. The alpha recoils sputter off Rydberg atoms from the stainless steel surface.

A narrow band THz source is used tunable to KHz precision. I wanted to calculate the transition frequency for states of Oxygen and Hydrogen Rydberg with at least MHz precision. For hydrogen, I use the R_h Rydberg constant assuming the reduced mass of the hydrogen atom. I wanted to ask whether for Oxygen atom transition energy using the R_inf is an accurate approximation.

 

[Vanadium 50]

Now at least its clear what you have.

If I had Lithium with one electron in a very high state, say n = 5 or 10, it cab be treated as a Rydberg-like atom with a core of rghe nucleus and the 1S electrons, and the outer electron far away. How good is this approximation? Depends on how big n is.

For oxygen uts worse, since you have a bigger "pseudo nucleus", one with p electrons as well as s electrons. And of course the electron wavefunctions need to be antisymmetrized under all 28 possible exchanges. As this is a many body problem, there is no exact solution. Your best bet is to find someone who has measured them.

 

[Shivani_Ram]

Thanks for that explanation. The transitions I am interested to target are (n=35 → n’=34) (n=32 → n’=31) (n=29 → n’=29). I would try to look for measurements for those transitions. Probably there are numerical simulations to calculate this? Would be interested if you know of such work.

 

[Vanadium 50]

I don't know how good the calculations are (or how good they need to be).

n = 29 would have a radius of ~841a₀ and the core a radius of ~6a₀. So that means nuclear size effects are 1/140 or so, which is the same size as your fine structure. Further, the "pseudo-nucleus" has an atomic-sized magnetic moment, not a nuclear-sized one. That makes your hyperfine, fine, and nuclear-size perturbations all about the same size. Not good for calculating.

Also, this is a 9 body problem. Maybe the 1S electrons can be ignored, but that still leaves 7. That's still 21 degrees of freedom with 23 symmetry constraints.