Decay constants are not constants

Couplings between nuclei mean that their wave functions cannot be treated in isolation anymore. Here lies a tool for manipulating nuclear reaction rates, including nuclear fusion rates.

Our last article contrasted the simplistic “billiard ball” model of nuclear fusion with a more faithful physical approach of considering nuclear wave functions and transitions between them. Recall that nuclear wave functions represent the probability distributions of quantum particles. We hinted at the powerful implications of such a shifted perspective. Here we will talk a bit more about what is meant by that.

The time constants of different physical processes can have tremendously important practical implications. Such time constants includes the average time it takes for certain of atomic and molecular state transitions to occur — and also chemical reactions (which are a special case of atomic and molecular state transitions) as well as nuclear state transitions and nuclear reactions (which are a special case of nuclear state transitions). It can make a big difference whether a molecule, e.g. in a solar cell, loses energy from an energetically excited state within 1 picosecond or 100 picoseconds. And it can make a big difference whether a radioactive plutonium nucleus decays within 24,000 years or 24 seconds.

Average transition times are known as “decay constants” for nuclear state transitions and “relaxation times” for atomic and molecular state transitions. One would not typically call a molecular relaxation time a decay constant because it is well known that it can change as a function of its environment — so clearly it’s not a constant. That is the case because certain environments, for instance those that include couplings between molecules, affect the wave function of our molecule of interest. An impressive demonstration of this principle is the recent demonstration of accelerated chemical reactions.

That the same principle applies not just to atoms and molecules but also to atomic nuclei has been the main point in a remarkably underrated Physical Review Letter of 1965. In “Nuclear superradiance in solids“ two leading nuclear physicists of the time developed their argument as follows. This is important, so we will provide a longer quote:

“The solid, characterized by internal energy states of the nuclei, by the lattice vibrations, and by the electromagnetic field, is treated [in this paper for the first time] as an integrated quantized system rather than as a number of noninteracting nuclei. [..] In a solid composed of N identical two-level nuclei in a perfect crystal lattice at a uniform and low temperature, correlations in the internal motions of the radiators are more probable than in the case of a gas. Furthermore, the interactions among members of the solid system are much stronger than in the gas, because of the coupling between neighbors in the lattice. The usual assumption that each nucleus radiates independently of the states of other nuclei in the system is incompatible with the coupling of the nuclei through the common electromagnetic and phonon fields. Calculations of the spontaneous radiation rate for a solid system in which the nuclei are a priori assumed independent preclude the possibility of coherent spontaneous gamma emission by assumption. The present analysis is free from this inconsistency.”

What does this mean? In plain language, in a solid state environment, there are couplings between nuclei that don’t exist, for instance, in the plasma state. As a result, affected nuclei cannot be treated independently. They are not to be seen as simply a sum of isolated nuclear wave functions, but they have to be described by a single wave function that encompasses all coupled (or entangled) nuclei and the coupling mechanisms. When evaluating such comprehensive wave functions, one can find that the dynamics of nuclear state transitions is changed compared to those of nuclei in isolation. A beautiful experimental confirmation of this conjecture is a 2018 Nature Physics article that shows the acceleration of nuclear decay (by a factor of 15x) as a result of the entanglement of multiple nuclei.

These mechanisms open the door toward thinking about the systematic manipulation of nuclear transition and nuclear reaction parameters through the provision of suitable couplings and compositions of nuclei in a lattice. And that is exactly what nucleonics is all about. In many ways, Terhune & Baldwin 1965 is a paper that was seminal for nucleonics, even though it is clear that the authors then did not recognize to full scope of their argument. It wasn’t until the work of Hagelstein that a vision of precise control over nuclear states and nuclear reactions was articulated and systematically developed.