Evaluation of Phenomenological Characteristics of the Two-Proton Decay of the 45Fe Nucleus

In the extreme edge of the atomic world, where the forces holding a nucleus together are stretched to their breaking point, a rare and fleeting event occurs. Some atomic nuclei are so heavy with protons that they cannot hold them all; they are unstable and must shed the excess to find stability. While many unstable atoms simply eject a single proton, a very specific group of nuclei located beyond the "proton drip line" face a different challenge: they must eject two protons at once. This phenomenon, known as two-proton radioactivity, is a delicate dance of quantum mechanics where the timing and interaction of the escaping particles reveal the hidden structure of the nucleus itself. For decades, physicists have debated how this happens: do the two protons leave one after the other, pausing briefly in a real, intermediate state, or do they escape together in a single, coordinated burst through a virtual, fleeting configuration? Understanding this process is crucial because it acts as a probe into the fundamental forces that shape the atomic nucleus, offering a window into the behavior of matter under conditions that cannot be created anywhere else in the universe.

A team of researchers at Voronezh State University has developed a new mathematical framework to answer these questions, applying it to the iron-45 nucleus, a benchmark system for this type of decay. Iron-45 is a rare isotope that sits right on the edge of stability, and when it decays, it transforms into chromium-43 by ejecting two protons. The scientists created a sophisticated theory based on the concept of a "Green's function," which acts as a bridge connecting the initial nucleus to the final one through the intermediate stage. This approach allows them to treat the emission of the two protons as two consecutive steps, but with a crucial twist: the theory accounts for both scenarios where the intermediate nucleus exists as a real, temporary state and scenarios where it exists only as a virtual, mathematical possibility that never fully forms. By using this unified method, the researchers could calculate not just how fast the decay happens, but also the specific directions in which the protons fly apart.

The researchers applied their theory to iron-45 using a model that accounts for the superfluid nature of the nucleus, where protons pair up and move in a coordinated way, similar to how electrons move in a superconductor. They tested their calculations against real experimental data, specifically looking at the total speed of the decay and the angular distribution of the emitted protons. The results showed a striking sensitivity to the choice of the nuclear potential, which is the mathematical description of the force field inside the nucleus. The team found that only a very specific version of this potential, one that had been previously proposed in other studies, could simultaneously reproduce both the measured decay rate and the observed pattern of proton angles. Other potential models, while mathematically valid in other contexts, failed to match the experimental reality when applied to this specific decay.

One of the most significant findings is that the researchers were able to rule out the idea that the protons simply leave as independent particles without any correlation, or that they form a tight, pre-existing cluster called a "diproton" before escaping. Instead, the data supports a picture where the protons are emitted in a sequential manner, but the process is heavily influenced by the quantum mechanical "virtual" states of the intermediate nucleus. The study demonstrated that the angular distribution of the protons—the angles at which they fly apart—contains a hidden signature of the nuclear structure. When the researchers compared their theoretical predictions with the experimental histograms of proton angles, they found that the correct nuclear potential produced a curve that matched the data almost perfectly, capturing the subtle asymmetries that other models missed.

The paper concludes that this new Green-function approach provides a consistent and powerful tool for understanding two-proton radioactivity. It successfully bridges the gap between the theoretical description of real, sequential decays and the more elusive virtual decays, all within a single quantum mechanical framework. By showing that the correct choice of nuclear potential is essential to reproducing experimental results, the work highlights how sensitive these decay processes are to the microscopic details of the nucleus. The researchers emphasize that their method does not rely on arbitrary adjustments but emerges naturally from the underlying physics of proton pairing and shell structure. This suggests that the angular correlation of the emitted protons serves as a strict test for theoretical models, offering a way to distinguish between different descriptions of nuclear forces. Ultimately, the study confirms that the iron-45 nucleus decays through a mechanism that is best described by a sequential process involving virtual intermediate states, and that the specific shape of the nuclear force field is the key to unlocking the details of this rare cosmic event.