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Physical Sciences

Atom vs anti-atom?

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#1 of 3 Posted Nov-2 8:24 PM

From Jon Woolf - Sysop Posts 1621 Last 6:46 AM
To All [Msg # 129401.1 ]

Hypothetical scenario: Suppose you have a carbon-12 nucleus -- just the nucleus, no electron cloud, confined in a volume that is otherwise completely empty. Six protons and six neutrons.

Next, add to that volume a nucleus of "anti-carbon" -- that is, a carbon nucleus made of 6 antiprotons and 6 antineutrons.

Now let them collide. What happens? Matter-antimatter annihilation, of course, but exactly how does that occur? Do the two carbon nuclei react as two units and mutually annihilate completely? Or do the protons, neutrons, antiprotons, and antineutrons react as individual particles, producing annihilation only between the first (say) proton that contacts an antiproton, while the remainder of the two nuclei get scattered like shrapnel from the explosion? Or does it work some other way?

Does it matter what velocity the two nuclei are moving at when they collide? What about the angle at which they meet?

-- JSW

#2 of 3 Posted Nov-3 1:06 AM

From bbbeard755113176 Posts 121 Last Nov-22
To Jon Woolf - Sysop [Msg # 129401.2 129401.1 ]

Well, it is... complicated.

First, do you understand how to compute the reaction cross section for, say, electron-positron annihilation? It's not really that trivial, but it's not too terribly hard, either -- at least to first order in perturbation theory. It's the kind of calculation that second-year physics grad students are expected to master. It's got something to do with gamma matrices. Just for fun, I've attached an old 8.810 problem set where I do some analogous manipulations for polarized muon decay. Annihilations are similar in spirit; you just have to set up the boundary conditions, write down the spinor algebra, and turn the crank. [Anecdotal aside: this was the actual problem set where I learned the hard way that, yes, Virginia, you have to include the normalization factors if you're going to get the angular dependence correct...]

The short answer is that a C12 + anti-C12 annihilation "actually" proceeds via fundamental processes, e.g. quark-antiquark annihilation. Because there are so many actors floating around, however, a complete perturbation theory calculation is probably not feasible, I would think. You'd probably have to resort to a cruder model, something in the spirit of one-boson exchange potentials like the nu-ku-lar physicists use.

BBB

Attachments
	Name: 810PS4_2.pdf	Size: 44 K

#3 of 3 Posted Nov-3 9:33 AM

From Jon Woolf - Sysop Posts 1621 Last 6:46 AM
To bbbeard755113176 [Msg # 129401.3 129401.2 ]

Bernard,

>> First, do you understand how to compute the reaction cross section for, say, electron-positron annihilation? <<

Not a clue. My understanding of subatomic physics is hopelessly inadequate. I still think of particles as tiny solid objects. I think I understand the general concepts of electron clouds and QM and normalization and such things, but the mathematics of it are totally beyond me. Even the paper you attached is at the ragged edge of what I can follow -- give me a while to stare at it and I might figure it out, but I can't rattle it off the way you can.

-- JSW

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Physical Sciences

Atom vs anti-atom?

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