Q: Muon-substituted molecular H2
Uncle Al
Suppose one took an ordinary hydrogen molecule (ortho or para, make it
hard on yourself) and substituted two muons for its two electrons.
1) Would the new bond length scale inversely as the new reduced
masses? Chemists assume stationary nuclei, which is a much worse
approximation for muons vs electrons. The muon-catalyzed fusion folk
ought to have a handle on this - but I need protium, not deuterium or
tritium.
2) Would the liquid and solid densities of mu2-H2 scale as the bond
length? A scientific wild ass guess will do here. The solid is more
interesting. Remember molecular polarizability, Mandelung forces...
"8^>) Solid hydrogen is such an odd bird anyway.
3) Then, there is the color of the stuff. Thoughts on energies of
molecular optical transitions are welcome. (Hell, will H-H stretch jump
into the Raman UV anti-Stokes shift plus microwave Stokes?) I'm curious
about breakdown of approximations used to model molecular spectra. Why
shouldn't science fiction be available in decorator colors?
(The muon's short half-life is not a problem. That is a job for Dr.
Schund and his neutrino squeegee!)
If things get slow and you must look busy, it's heeeere! (If too many
students in the class still have passing grades - one homework
assignment, no problem!) I assure you that Dr. Schund has all sorts of
outrageous and undesirable uses planned for *really* heavy hydrogen -
molecular, solid, and metallic.
Credit will be given where due unless requested otherwise.
--
Uncle Al Schwartz
Uncl...@ix.netcom.com ("zero" before @)
http://pw2.netcom.com/~uncleal0/uncleal.htm
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James Logajan
Uncle Al (Uncl...@ix.netcom.com) wrote:
: Suppose one took an ordinary hydrogen molecule (ortho or para, make it
: hard on yourself) and substituted two muons for its two electrons.
: 1) Would the new bond length scale inversely as the new reduced
: masses? Chemists assume stationary nuclei, which is a much worse
: approximation for muons vs electrons. The muon-catalyzed fusion folk
: ought to have a handle on this - but I need protium, not deuterium or
: tritium.
Several QM texts cover muonic atoms; the simplest exposition I found easily
at hand is example 4-9 on page 106 of "Quantum Physics of Atoms, Molecules,
Solids, Nuclei, and Particles, " 2nd edition by Robert Eisberg and Robert
Resnick. It should give you a leg up - of course, a muonic H molecule would
be a tad more involved.
: 2) Would the liquid and solid densities of mu2-H2 scale as the bond
: length? A scientific wild ass guess will do here. The solid is more
: interesting. Remember molecular polarizability, Mandelung forces...
: "8^>) Solid hydrogen is such an odd bird anyway.
: 3) Then, there is the color of the stuff. Thoughts on energies of
: molecular optical transitions are welcome. (Hell, will H-H stretch jump
: into the Raman UV anti-Stokes shift plus microwave Stokes?) I'm curious
: about breakdown of approximations used to model molecular spectra. Why
: shouldn't science fiction be available in decorator colors?
The example quoted above for the muonic atom gives the wavelength for the
first line in the Lyman series as ~ 6.5 Angstrom; soft X-rays. Not
surprising, since the binding energy is 2530 eV.
Another text that might help is Quantum Mechanics by Claude Cohen-Tannoudji,
Bernard Diu, and Franck Laloe.
Not sure if any of this is new information, but no warranties are given
on information posted. And no refunds allowed.
James Logajan
Uncle Al (Uncl...@ix.netcom.com) wrote:
: Suppose one took an ordinary hydrogen molecule (ortho or para, make it
: hard on yourself) and substituted two muons for its two electrons.
See also problem 7.17, p. 273, Introduction to Quantum Mechanics,
David J. Griffiths:
"The classic paper on muon-catalyzed fusion is J. D. Jackson, Phys. Rev. 106,
330 (1957) ..."
Benjamin P. Carter
Uncle Al <Uncl...@ix.netcom.com> writes:
>Suppose one took an ordinary hydrogen molecule (ortho or para, make it
>hard on yourself) and substituted two muons for its two electrons.
This makes a nice Gedankenexperiment. I don't see how it could be
accomplished in a real laboratory.
> 1) Would the new bond length scale inversely as the new reduced
>masses? Chemists assume stationary nuclei, which is a much worse
>approximation for muons vs electrons. The muon-catalyzed fusion folk
>ought to have a handle on this - but I need protium, not deuterium or
>tritium.
The new bond length would be roughly 200 times smaller than the old, just
as it is for a muonic molecular ion (involving only a single muon). A
calculation would be required to determine the bond length more precisely.
It might be hard to find someone willing to do the calculation in the
absence of a plausible suggestion for an experiment to measure the bond
length.
> 2) Would the liquid and solid densities of mu2-H2 scale as the bond
>length? A scientific wild ass guess will do here. The solid is more
>interesting. Remember molecular polarizability, Mandelung forces...
>"8^>) Solid hydrogen is such an odd bird anyway.
There is no chance of producing enough mu2-H2 molecules to form a macroscopic
sample; so it makes no sense to consider the solid or liquid states
except as a Gedankenexperiment. Even if you could produce Avogadro's
number of muons (give or take several powers of ten), you wouldn't want
to get very close to them.
> 3) Then, there is the color of the stuff. Thoughts on energies of
>molecular optical transitions are welcome. (Hell, will H-H stretch jump
>into the Raman UV anti-Stokes shift plus microwave Stokes?) I'm curious
>about breakdown of approximations used to model molecular spectra. Why
>shouldn't science fiction be available in decorator colors?
The energy levels of muonic hydrogen are about 200 times those of ordinary
hydrogen. Transitions that change the principal quantum number would involve
energy shifts of hundreds of eV. Vibrational, rotational, and hyperfine
states don't scale in such a simple way, but they probably scale about the
same way for the neutral molecule as they do for the molecular ion.
>(The muon's short half-life is not a problem. That is a job for Dr.
>Schund and his neutrino squeegee!)
Huh? How is the short half-life not a problem? Who is Dr. Shund?
What is a neutrino squeegee? Is my lower extremity under tension?
--
Ben Carter
Uncle Al
It is for a science fiction short story. Look up "Schund" in a German
dictionary.
Your lower extrremity is less under tension than your willing disbelief
suspended.
(See what happens when I try to be subtle?)
--
Uncle Al Schwartz
Uncl...@ix.netcom.com ("zero" before @)
http://pw2.netcom.com/~uncleal0/uncleal.htm
http://www.ultra.net.au/~wisby/uncleal.htm
http://www.guyy.demon.co.uk/uncleal/uncleal.htm
(Toxic URLs! Unsafe for children, Democrats, and most mammals)
"Quis custodiet ipsos custodes?" The Net!
Uncle Al
James Logajan wrote:
>
> Uncle Al (Uncl...@ix.netcom.com) wrote:
> : Suppose one took an ordinary hydrogen molecule (ortho or para, make it
> : hard on yourself) and substituted two muons for its two electrons.
[snip]
> Several QM texts cover muonic atoms; the simplest exposition I found easily
> at hand is example 4-9 on page 106 of "Quantum Physics of Atoms, Molecules,
> Solids, Nuclei, and Particles, " 2nd edition by Robert Eisberg and Robert
> Resnick. It should give you a leg up - of course, a muonic H molecule would
> be a tad more involved.
[snip]
Thanks for the references! The mu2-H2 molecule will be a "tad more
involved," oh yes, hence my post. I can work the Bohr radius easily
enough, and scale everything thereafter trivially, but, is it
justified? The molecular case is more than a little hairy, likewise
condensed phase. And metallic mu2-H2 could be a thing of (transient)
beauty.
I'd hate to claim the universe ends in a deasil swirl if it really goes
down withershins.
KVA...@my-dejanews.com
In article <355861...@ix.netcom.com>,
Uncl...@ix.netcom.com wrote:
>
> It is for a science fiction short story. Look up "Schund" in a German
> dictionary.
> Your lower extrremity is less under tension than your willing disbelief
> suspended.
>
> (See what happens when I try to be subtle?)
>
That was truly offal...
cheers,
kvah
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