Wednesday, May 26, 2010

How magic is your work?

If you're Dr. Kate Jones of the University of Tennessee in Knoxville, the answer is very.

Inside of a nucleus, just like for the electrons in an atom, there are discrete energy levels into which the neutrons and protons can arrange themselves. In chemistry, this behavior - in electrons - leads to the periodic table: different elements behave in different ways chemically because of the number of electrons they have. More precisely, what matters is the number of electrons outside of a closed shell. I'll explain what this means.

One can (albeit simply) view the electrons of an atom as orbiting the nucleus, and the energy of the electrons are determined by the orbital in which they reside. Electrons can change orbitals, if the precise amount of energy necessary to "jump" from one orbital to another is put into the system (or carried out of the system). And because of the intrinsic nature of electrons (and all nucleons), only so many of them can be in a given orbital at once. As soon as the orbital, or "shell," is full, it's referred to as a "closed shell." The electrons in the last shell (which is typically not full) are known as valence electrons.

Interestingly, the nucleons (protons and neutrons) inside the nucleus of an atom behave in a similar way. They also pack into shells, with discrete energy differences in between. The study of this behavior has elucidated many variations on the simple theme, but one thing which continues to be of interest is the location of the "shell closures" - these locations being indicated by magic numbers. Once a magic number of nucleons (a magic number of protons, or neutrons, or both) is attained, like in the ultra-stable nucleus 208Pb, the nucleus behaves in a different way. It's like the "noble gases" in chemistry - helium, neon, argon, etc - which are much more stable and inert than other elements, because they have closed electron shells (in other words, magic numbers of electrons).

So the search was on for other nuclei that might be just like lead-208 because of their "magicity" (that's a great term, isn't it?). In essence, nuclear physicists wanted to find other nuclei that behave as almost perfectly magic due to their internal structure. It just so happens that tin-132, an isotope of tin with 50 protons and 82 neutrons (both magic numbers, making 132Sn "doubly magic"), is one such nucleus. And Dr. Jones and her collaborators proved it (the Editor's Summary can be read for free on the Nature webpage here).

By looking one nucleon away from the doubly-magic tin isotope, at tin-133, the collaboration was able to show that the tin-133 behaved essentially like a single particle - in other words, the single nucleon outside of the closed shell of tin-132 completely dictated the behavior of the entire nucleus. That means the tin-132 "core" was as inert as it could be, precisely what you expect from a doubly-magic nucleus.

Dr. Jones and her collaborators performed the ground-breaking work at the Holifield Radioactive Ion Beam Facility (HRIBF) at Oak Ridge National Laboratory (ORNL) in Tennessee. And it couldn't have been done anywhere else. I know, because I was there. "Magical" results like this (if you'll excuse the pun) don't come easily; it takes years of work. But the reward - finding another nucleus which demonstrates so clearly the successes of the nuclear shell model - was well worth the wait.

Jones, K., Adekola, A., Bardayan, D., Blackmon, J., Chae, K., Chipps, K., Cizewski, J., Erikson, L., Harlin, C., Hatarik, R., Kapler, R., Kozub, R., Liang, J., Livesay, R., Ma, Z., Moazen, B., Nesaraja, C., Nunes, F., Pain, S., Patterson, N., Shapira, D., Shriner, J., Smith, M., Swan, T., & Thomas, J. (2010). The magic nature of 132Sn explored through the single-particle states of 133Sn Nature, 465 (7297), 454-457 DOI: 10.1038/nature09048


  1. Hi, Miss Atomic!

    How intriguing. It sounds as though the neutrons and protons have independent magic settings, unlike the electrons, of which there is only one type and one setting. Does that mean that some kind of spatial segregation exists between them, where a magic number of protons hang out in one part of the nucleus and a gang of neutrons on the other side of the playground? One might imagine that the neutrons are in the center, but there I am, thinking electostatically!

    Perhaps more seriously, do the neutrons and protons affect each other's shell satisfactions at all? I'm guessing they have wave functions that just don't interact? Clearly, I have no idea what I'm talking about.

  2. Burk - in a way, yes, the neutrons and protons are independent, since the protons are subject to Coulomb (eletrostatic) repulsion in addition to the strong force, whereas the neutrons are not. However, they are also dependent, as their wavefunctions do interact, but not enough such that a magic number of total protons+neutrons (say, 23 and 27, giving a magic number of 50) behaves magically. The protons and neutrons occupy completely separate shells, but their overall presence can alter the behavior of those shells.
    In spatial terms, it all gets fuzzy (quite literally) thanks to quantum mechanics. We can't say that the protons exist on one side and the neutrons on the other. Their wavefunctions expand to fill the whole space available to them.

  3. Burk - if I may give an example to illustrate Miss Atomic Bomb's statement of how the overall presence of protons and neutrons affects their shell structures:

    One of these magic numbers for protons and neutrons is 8. It is due to this number that there is a significant amount of oxygen in the universe, as most oxygen has 8 protons and 8 neutrons. It is a doubly magic nucleus, so ehibits a huge shell gap for both protons and neutrons. However, if one starts 'removing' protons, by looking at nuclei with fewer protons but the same number of neutrons, one finds the neutron shell gap changes. By the time one gets to the exotic nucleus beryllium-12 (4 protons, 8 neutrons) one finds the shell gap has disappeared entirely! This is why the recent paper on tin-132 is so important - we know that this change in shell structure does occur, but finding where it becomes significant, especially in heavy nuclei, is a major challenge.

    In fact, that nuclei exhibit shell structure at all is quite amazing. Unlike electrons, which have wavefunctions in an external potential (the Coulomb potential of the nucleus) - the proton and neutron wavefunctions are in a self-generated potential, due mostly to a force that has a range of about the size of the nucleons themselves. That the protons and neutrons are so closely packed, yet can still move independently, is a fascinating example of how quantum mechanics defies our intuition.

  4. I was delighted to see that our Nature manuscript was accompanied by an Editor's Summary as well as a "News & Views" piece, "Doubly magic tin," by Dr. Paul Cottle of Florida State University. However, I was a bit surprised to find that Dr. Cottle's list of stable, doubly-magic isotopes included "lead-28 (28Pb...)"! If 28Pb did, in fact, exist at all, it would hardly be stable. I think they mean lead-208. Well done, Nature Publishing Group. It's not every day that a typo is so funny.


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