Monday, March 31, 2008

The geochemical quantification of double beta decay

In 1933, Enrico Fermi proposed a theory of beta decay using the neutrino particle suggested by Wolfgang Pauli three years earlier. During this time period, the promising young physicist Maria Goeppert married an American guy named Mayer and started 15 years of two body-related unemployment in the States (In contrast, the gap between the publication of her book, “Elementary Theory of Nuclear Shell Structure” and the awarding of the Nobel prize for that work was only 13 years).

During the great depression, Goeppert-Mayer decided to up the intellectual profile of housewives by suggesting, in 1935, the possibility of double beta decay. Where an intervening unstable isotope prevented sequential single beta decay, double beta decay would allow transformation to a lower energy Z-2 nucleus by simultaneous double electron-antineutrino emission. Most of the double decay candidates are neutron-rich R-process elements such as 96Zr, 100Mo, or 130Te. The predicted decay product of 130Te is 130Xe, a noble gas. In the late 40’s, an isotopic study of telluride minerals was performed, and a 130Xe excess in Xenon from telluride ores was reported by Inghram & Reynolds (1950).

Subsequent noble gas results verified the existence of 128Te – 128Xe and 82Se – 82Kr systems, all before the first direct detection of a double beta decay was established in Elliott et al. (1987)- almost 40 years after the initial geochemical result, and 15 years after Goeppert-Mayer's death.

Unfortunately, the ability of Tellurium and Selenium minerals to quantitatively retain noble gasses is poor, as these minerals have low closure temperatures, and are easily deformed. They are also difficult to date directly. But as every hard-up geochemist knows, if you’re desperate for a date and you don’t know where to turn, it never hurts to look for a zircon.

The dating of zircon using the uranium-lead decay scheme is arguably the most popular and rigorous geochronological method currently available. And as it just so happens, 96Zr is expected to decay into 96Mo. Since zircon usually doesn’t have much initial Mo, It should be possibly to detect a 96Mo excess, and use the U/Pb age from the same mineral to calculate a decay constant for 96Zr (Technically, this method determines the 238U/96Zr decay constant ratio).

This has been done a few times (e.g. here and here), but the process is complicated by the spontaneous fission of 238U. The fission products of this decay include most heavy isotopes of Mo, so the fissionogenic Mo excess and the double beta 96Mo excess have to be deconvolved. The result is that the precision on 96Zr double beta decay is fairly poor, with Wieser & De Laeter (2001) reporting a value of 9.4 ± 3.2 x 1018.

However, there is another promising double beta decay isotope. 100Mo decays into 100Ru. And molybdenite generally contains Re, so that the mineral can be dated using the Re/Os single beta decay scheme. And moly contains fuck-all uranium. It looks like the NSF thinks this is a promising technique as well, as they’ve awarded a $225,000 grant to a leading Re/Os lab for support for this and other experiments. And on the other side of the Pacific, Hidaka et al. 2004 have reported a result of 2.1 ± 0.3 x 1018.

In the meantime, the direct counting mob have continued to count decays. According to Barabash (2006), their current best determination of the 100Mo halflife is 7.1 ± 0.4 x 1018. It will be interesting to see if the Denver Re/Os crowd can do better, and if either group can explain why the direct counting gang have halflives that are approximately a factor of 2 higher than the geochemists (counters have 96Zr as 2.0±0.3x1019- also double the geochemical determination). Barabash 2006 does not address this discrepancy, or even reference the more recent geochemical results.

I’m also curious about the physicist’s budget. After all, I have a sneaking suspicion that the direct counting experiments cost a little bit more than a quarter million dollars.

Barabash (2006) (How is one supposed to reference arXiv entries?)
Elliott S R Hahn A A and Moe M K 1987 Phys. Rev. Lett. 59 2020
Goeppert-Mayer M 1935 Phys. Rev. 48 512
Hidaka H Ly C V Siziki K 2004. Physical Review C, 70, id. 025501
Inghram M G and Reynold J H 1950 Phys. Rev. 78 822
Wieser M E De Laeter J R 2001 Phys. Rev. C 64, 024308


Ed said...

How is 100MO obtained? My periodic table lists molybdenum as atomic weight of 95.96 +/- .02. (Atomic number of 42)

C W Magee said...

For multi-isotopic elements, the mean atomic weight listed on your table is the weighted mean of all the natural occurring isotopes.

Mo has 7 naturally occurring isotopes- 92, 94, 95, 96, 97, 98, and 100. To get the mean atomic weight, you multiply each by its relative abundance, and add the products:
Although if you want better than 1% accuracy, you need to use the exact mass, not the nominal mass (e.g. 99.907 amu for 100Mo instead of 100).

Because the half-life of 100Mo (and all other double beta decay isotopes) is millions of times longer than the age of the universe, the proportions of these isotopes have only changed a little bit from what they were when the solar system formed.

Molybdenum has 7 stable

Ed said...

Thanks for the explain. Chem is not my strong suit.
Yes I remember that things were pretty much of a mess back then (when the solor system formed)