Development of the {\gamma} strength function with the neutron number

Inside the heart of every atom, protons and neutrons cling together in a dense, chaotic crowd. When these atomic cores are excited, perhaps by a collision or a radioactive decay, they do not simply sit still; they shed their extra energy by emitting flashes of light, specifically gamma rays. Scientists have long studied how these nuclei absorb such light, a process dominated by a massive, collective vibration known as the giant dipole resonance, where the protons and neutrons sway back and forth against each other like two opposing fluids. However, the reverse process—how a nucleus releases energy as it cools down from a high-energy state—has remained a more elusive mystery. For decades, a prevailing idea suggested that the way a nucleus emits light should depend only on the energy of the light itself, regardless of how excited the nucleus was to begin with. This assumption, known as the Brink-Axel hypothesis, seemed to hold true until recent observations revealed a surprising twist: at very low energies, nuclei emit far more gamma radiation than anyone expected, a phenomenon that defied the old rules.

A team of researchers set out to understand this unexpected surge in low-energy light emission by building detailed computer models of atomic nuclei across a wide range of elements, including molybdenum, iron, tin, germanium, and gadolinium. They used two different theoretical frameworks to simulate the behavior of these nuclei: a traditional method that treats the nucleus as a sphere, and a newer, more complex approach that accounts for nuclei that are stretched into ellipses or triaxial shapes. By calculating the millions of possible transitions between energy states within these simulated nuclei, the team mapped out exactly how the strength of the emitted gamma rays changes as the energy of the light varies. Their work reveals that the behavior of this light emission is not random but follows a clear pattern dictated by the shape of the nucleus and the number of neutrons it contains.

The researchers found that in nuclei that are nearly spherical, the emission of gamma rays is dominated by a single, sharp spike of intensity at very low energies. They call this the Low Energy Magnetic Radiation, or LEMAR. It appears as a sudden burst of magnetic light that fades away exponentially as the energy increases. However, as the nuclei become more deformed—stretching out into football-like shapes—a second feature emerges alongside the low-energy spike. This new feature is a broad bump of intensity centered around three million electron volts, which corresponds to a well-known phenomenon called the scissors resonance. In this state, the protons and neutrons oscillate against one another in a way that resembles the opening and closing of a pair of scissors. The study shows that as the deformation of the nucleus increases, the single low-energy spike does not disappear; instead, it coexists with this scissors resonance, creating a bimodal profile with two distinct peaks of activity.

This transition from a single peak to a double peak is driven by the internal structure of the nucleus. In a spherical nucleus, the energy levels of the particles are grouped together in a way that allows for a simple, unified low-energy transition. But when the nucleus deforms, these energy groups split apart, much like a single beam of light breaking into a spectrum of colors when passing through a prism. This splitting creates a complex web of possible transitions. The low-energy spike arises from the chaotic mixing of these split states, while the scissors resonance bump comes from a specific type of collective motion that becomes possible only when the nucleus is deformed. The researchers observed that this pattern holds true across different elements: in the lighter iron and molybdenum isotopes, the shift from a single spike to a double peak correlates directly with the number of neutrons and the resulting shape of the nucleus.

The team also investigated how the chaotic nature of the nucleus influences these emissions. They discovered that the low-energy spike is characterized by a specific rate of decay that suggests the underlying states are highly complex and disordered, akin to a system where information is scrambled. This chaos is distinct from the overall temperature of the nucleus, which is a measure of how many energy states are available. In most of the nuclei they studied, the parameter describing the chaotic decay of the light emission was significantly lower than the thermodynamic temperature of the nucleus, indicating that the mechanism driving the low-energy light is a unique form of disorder that operates differently from the general thermal agitation of the particles.

One of the most significant findings concerns the relationship between the shape of the nucleus and the total amount of light it emits. The researchers found that the total strength of the magnetic radiation remains relatively constant as the nucleus changes shape, but the distribution of that strength shifts dramatically. In spherical nuclei, almost all the strength is concentrated in the low-energy spike. As the nucleus deforms, a portion of that strength migrates to the scissors resonance bump at higher energies, leaving the low-energy spike somewhat weaker but still present. This redistribution explains why some nuclei appear to have a "missing" amount of low-energy light compared to others; the light hasn't vanished, it has simply moved to a different energy range.

The study also touched upon the limits of these models. In nuclei where the number of protons and neutrons are nearly equal, the emission of low-energy light is strongly suppressed due to the conservation of a property called isospin, which acts as a sort of internal balance between the two types of particles. In these specific cases, the expected low-energy spike fails to appear, replaced by a flat, weak region. Furthermore, while the computer simulations successfully reproduced the general trends seen in experiments, they sometimes underestimated the total amount of light emitted, suggesting that the models, while powerful, still miss some subtle interactions between the particles.

Ultimately, this work provides a unified picture of how atomic nuclei shed their energy. It confirms that the emission of gamma rays is not a static process but one that evolves with the shape and composition of the nucleus. The transition from a simple, single-peak emission in spherical nuclei to a complex, two-peak structure in deformed nuclei is a robust feature of nuclear physics, driven by the splitting of energy levels and the chaotic mixing of particle states. By clarifying these mechanisms, the researchers have offered a clearer window into the quantum world, showing how the collective dance of protons and neutrons determines the very light that escapes from the atomic core.