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Re: [Phys-L] collisions



John Denker wrote:

1) Start with identical hydrogen atoms. Cool them off to a
few thousandths of a degree above absolute zero. Using a
seriously powerful magnet, align all the electron spins and
the nuclear spins.

In this regime, the atoms are not like baseballs. They are
not hard little spheres that bounce off each other. Rather,
they are big fluffy clouds that diffract through each other.
If you go by the thermal de Broglie length, the atoms are
the size of bacteria.

In this regime, you cannot distinguish between the two
cases of right-angle scattering. The add-before-you-square
law applies. You see interference between the two cases.
This effectively doubles the 90-degree scattering amplitude.

2) Interestingly enough, at higher temperatures you /can/
distinguish the two cases. The thermal de Broglie length is
small compared to the Bohr radius, so the atoms act like little
baseballs. The two possible trajectories are offset from one
another by about one atomic diameter, and if you look closely
enough you can distinguish the two cases on this basis. Even
though the particles are nominally identical, the trajectories
are distinguishable, and that's all the quantum mechanical laws
care about. In this situation the square-before-you-add law
gives the right answer. You can quantify all this in terms
of wavefunction phase angles et cetera.

Perfect, just what I'm after. Two comments:

1. Did this work get published? If so, can you send me some references?

2. Let's expand a bit on the oven ideas. I assume one starts with a little oven (or fridge) full of a large number of hydrogen atoms. So the temperature of the gas is well defined. Then I assume the launchers consist of drilling small holes in the oven (opening into a vacuum chamber).

Question A: Does it matter if one uses two separate ovens versus one oven with two holes? (Are there any special correlations in the latter case? The answer may be temperature dependent.)

Continuing, I can compute lambda1 = h/p where p is a momentum of a single atom. I can also compute lambda2 = h/sqrt(2*pi*m*k*T) while an atom is in the oven, where T is well defined.

Question B: How are lambda1 and lambda2 related? Does lambda2 still make sense once we're talking about a single atom flying in empty space outside the oven? For that matter, suppose the atom didn't come from an oven: I just got it going in empty space using some other device - what would you need to know about the "launcher" to figure out lambda2 (ie. an effective value of T) for that atom?

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Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
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