Friday, May 20, 2011

Why carbon-14 is like an old woman

Everyone knows that there exist in nature "old women." These "grans," as they are technically referred to, live nearly forever, relentlessly refusing to give up the ghost, stretching their lifetimes out indefinitely. Carbon-14 is one of these, too. As nuclei go, it may be pretty famous, but it's famous because it's anomalous... it lives too long. And a new paper in Physical Review Letters finally explains why (publicly available version here).
To get to the crux of it, the issue is the approximations we always use in science to get "first order" solutions to otherwise almost impossibly difficult problems. Some equations are just so convoluted and complicated that they can't be solved analytically (ie, in an exact mathematical way), so they have to be approximated. This is typically done by taking the equation and breaking it down into small chunks, called a series, and determining how many of the "orders" of the series are necessary to get a reasonable answer. The first piece of the series is zeroeth order, then first order, then second order, third order, and so on. Generally, at a certain point, adding more orders to the series will result in smaller and smaller changes to the solution, so you can then reliably pick a cutoff and can solve the equation "to first order." A lot of good and interesting physics has come out of these bulk approximations - we can model a nucleus like one particle outside of a larger particle instead of as dozens of individual ones, for instance - but sometimes the approximation just isn't good enough. Carbon-14 is one of those cases.
The authors, including a friend of mine, have taken into account numerous things in order to get past the approximation and get to the basic principles of how a carbon-14 nucleus is formed and behaves. This includes building it up particle-by-particle and accounting for not just nucleon-nucleon forces, but also three-body forces as well, and sticking all of this information into the Schroedinger equation of quantum mechanics. By examining both carbon-14 and nitrogen-14, which 14C decays into, the authors could determine any systematic uncertainties in their approach.
Now, I mentioned that we use the approximations in order to make the math "doable," and that's still true. By starting from basic principles and not using approximations, the authors made their lives very difficult. But fortunately, they didn't have to solve these equations by hand - enter Jaguar, the ORNL supercomputer. It is only with this level of computing power that such a study becomes feasible.
In the end, the authors found that a sort of "cancellation" was occurring in certain components of the physics governing the nucleus of 14C, which was allowing for the anomalously long half life. But a lot of work went into discovering this. Sometimes the most interesting things exist just under our noses.

P. Maris, J. P. Vary, P. Navrátil, W. E. Ormand, H. Nam, & D. J. Dean (2011). Origin of the Anomalous Long Lifetime of 14C Physical Review Letters, 106 (20) : 10.1103/PhysRevLett.106.202502

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