312) Another kind of beta decay?

Ludwik Kowalski; 10/28/2006
Department of Mathematical Sciences
Montclair State University, Upper Montclair, NJ, 07043

What follows is a message I posted on a restricted Internet list for CMNS researchers. It was prompted by a speculation, posted by another researcher, that half lives of radioactive nuclei can be reduced by keeping them at extremely low temperatures. My piece, ironically, is about speeding up the decay of some nuclei at extremely high temperatures.

Here is an idea that preoccupied me more than 25 years ago. It is recorded in a note from an old binder. I expected the half life, in beta-minus decay, to be reduced when atoms are ionized. Some bare radioactive nuclei (atoms without electrons) in very hot plasma, I speculated, would decay faster than nuclei in neutral atoms. This was based on what is known about beta-plus decay, where two decay paths are available (two ways of changing a proton into a neutron): (a) positrons are emitted or (b) orbital K electrons are absorbed by nuclei. The second path is known as EC (electron capture). The half life of a beta-plus decay would become longer if the second path could be prevented, somehow. By how much longer? It would depend on the fraction of nuclei decaying via the EC path. That fraction, by the way, is called branching ratio.

In the beta-minus decay (changing a neutron into a proton) we have only one path -- emission of an electron. The second conceivable path -- placing an electron into an atomic orbit of neutral atom -- is forbidden by Pauli principle. It is not possible to add an electron into an already-occupied orbit. The central idea was that a new path for the beta-minus decay is automatically open when bare nuclei are formed. By opening another decay path one would speed up the decay of some beta-minus radioactive nuclei.

Unfortunately, total ionization of atoms calls for temperatures that are probably too high for practical applications. Why did I not think about this when I first heard Roberto at ICCF11 ? He was talking about a "pyrolytic method" of destroying radioactivity. I do not know what kind of process it is and how high were his temperatures. My old binder shows that I was anticipating two hot plasma experiments. This was discussed with two plasma physicists in Princeton. The experiments never materialized. Here is a note composed on 1/5/1980. ". . . The second experiment in hot plasma has to do with "speeding up" the decay of beta-minus radioactive nuclei by a process that can be called orbit population, OP. In this process the transformation of a neutron into proton is associated with the emission of an antineutrino and with the appearance of an electron on an empty atomic orbital." Branching ratio formulas for the beta-plus decay can be found in many textbooks. Assuming the formulas are applicable not only to EC but also to OP (in fully ionized atoms), I was able to show that changes in half-lives can be very significant. I wrote that according to preliminary calculations, "the half-life of bare ¹⁰⁶Ru should be reduced by a factor of 23, as compared with neutral atoms. [That means about two weeks instead one year.] In most cases, however, the reduction factors are not that large." . . .
P.S.
(a) Temperatures T needed to produce nearly total ionization of atoms are high. The values of kT, where k is Boltzmann's constant, are usually expressed in keV (several keV, for light elements and up to about 100 keV for the elements at the end of the periodic chart).
(b) The OP process probably does take place in many stars. I would not be surprised to learn that it is taken under consideration by nuclear astrophysicists.

Appended on 12/10/06: For some reason, in speculating about the OP process nearly three decades ago, I was not aware that it was discussed by others. The paper of Gareev, presented in 2004 at ICCF11, discusses this topic much better. The title of the article was “Enhancement mechanisms of low-energy nuclear reactions” and the authors were: F.A. Gareev, I.E. Zhidkova and Yu.L. Ratis.