Shape Resonance

  • Thread starter Thermodave
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Greetings. I've been reading papers on plasma kinetics and have come across the term "shape resonance" a few times when describing peaks in electron impact cross section (function of energy). I have seen calculations attempting to explain these for atoms like helium but I'm not sure how close they are to experimental data. However, I am mostly intrested in air, good old oxygen and nitrogen. This term comes up with describing ground state nitrogen (N2(X) + e- -> N2(X,v) +e-) and I've found a few papers that discuss this a bit. My crude understanding of this phenomenon is essentially that some kind of metastable ion forms. However, if this is the case than why is this part of the excitation cross section and not the ionization cross section?

On a related note, why do these resonances never show up for electronic excitations? Shouldn't there be similar peaks for the electronic states, N2(A), N2(B), etc.?
 

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  • #2
DrDu
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Could you be more specific about in which papers you saw shape resonances being discussed?
In my understanding, shape resonances are due to the potential energy surface of some excited state of a molecule having a local (non-global minimum) so that the vibrational states in that minimum decay by tunneling through the barrier (that is, the molecule dissociates).
That's why I don't understand how this terms comes up in the discussion of ground state nitrogen electron scattering from nitrogen molecules. Or do they describe the dynamics of the scattered electron in some inverted Born-Oppenheimer type approximation so that a potential energy surface can be ascribed to the electron?
 
  • #3
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Thank you for the response. An example of what I'm speaking of can be found in Phys. Rev A v56 n.2 (1997) by Sweeney & Shyn. If you don't have access to this journal just message me your email and I can send you a copy. To summarize, the authors are discussing a known shape resonance of the ground state N2 by electron impact. I'm curious to know how this comes about and why excited electronic states do not exhibit this feature at certain electron energies and vibrational levels.
 
  • #4
DrDu
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I had a look at the article you cited, but I still don't understand your question too well.
The basic process is that of the formation of a metastable negative molecular ion, [tex] \mathrm{N_2}+e^- \rightarrow \mathrm{N_2^- }\rightarrow \mathrm{N_2}+e^- [/tex].
Obviously this appears in the excitation spectrum and not in the ionization spectrum as the N_2 is only temporarily ionized. Ionization means that something like [tex] \mathrm{N_2}+e^- \rightarrow \mathrm{N_2^+}+2e^- [/tex] takes place.

Similar effects may be possible for excited states N2(A), N2(B) in principle, but to detect them, you would have to start from excited Nitrogen, wouldn't you?
Maybe this article is helpfull:
http://dx.doi.org/10.1103/RevModPhys.45.378
 
  • #5
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Yes, I guess it's very logical that this would fall into the excitation spectrum now that you mention it. I'll take a look at the Schulz article you linked and maybe I'll get a better understanding of this. Before posting this I was assuming that such a region (resonance) in the spectrum only occurred for the ground state since the excited states didn't seem to have similar erratic patterns at certain energy levels, hence me asking why that is true. Perhaps a similar process occurs but it's just far less noticeable. Does the negative ion of an excited state exist? N2(A)-? My guess would be that if this could happen than it would be for the lowest excited state, which is metastable.

N2 + e- -> N2(A)- -> N2(A)+e-
 

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