Shape coexisting intruder states in even Sn isotopes and their influence on the $B_{4/2}<1$ anomaly

Deep within the heart of every atom lies a nucleus, a dense cluster of protons and neutrons that behaves less like a static ball of clay and more like a droplet of liquid that can stretch, squash, and vibrate. For decades, physicists have studied these tiny cores to understand how they hold together and how they change shape. One of the most fascinating puzzles in this field involves atoms that seem to exist in two different shapes at the same time. Imagine a nucleus that can be perfectly round, like a billiard ball, and then suddenly stretch into a football shape without changing its number of particles. This phenomenon, known as shape coexistence, challenges our understanding of how matter organizes itself at the smallest scales. Scientists focus on a specific family of atoms called tin isotopes because they offer a long, stable chain of examples where these shape changes can be observed and measured. By studying how these atoms transition between their different shapes, researchers hope to uncover the fundamental rules that govern the structure of all matter.

In a recent study, a team of physicists turned their attention to a specific group of tin atoms, ranging from the lighter versions with mass numbers 114 to the heavier ones with mass number 122. They were particularly interested in a strange anomaly reported in some of these atoms: a measurement that suggested the nucleus was behaving in a way that defied standard expectations. Specifically, when these atoms jumped from one energy level to another, the probability of the jump did not follow the smooth pattern seen in other elements. Instead, the numbers dropped below a critical threshold, hinting that the internal structure of the atom was changing more drastically than anyone had predicted. To solve this mystery, the researchers built a mathematical model that treats the nucleus not as a collection of individual particles, but as a single object moving through a landscape of energy. They imagined this landscape as a valley with two distinct dips, or wells. One dip represents a round, spherical shape, while the other represents a stretched, deformed shape. The nucleus can settle in either dip, or it can exist in a state that is a mix of both.

The researchers used this double-well landscape to simulate the behavior of the tin atoms, adjusting the shape of the valley to see if they could reproduce the actual energy levels measured in laboratories. They found that by carefully tuning the depth and width of these two dips, their model could accurately match the experimental data for the different tin isotopes. The simulations revealed that the lighter and heavier atoms in the group, such as those with mass numbers 114 and 122, behave quite differently from the ones in the middle. In the lighter atoms, the nucleus starts in a nearly round shape but, as it gains energy and spins faster, it undergoes a sudden and dramatic shift to a highly stretched shape. This abrupt change in structure means that the wave describing the round state and the wave describing the stretched state do not overlap well. Because these two shapes are so different, the atom struggles to make the transition between them, resulting in the unusually low probability values that had puzzled scientists.

For the heavier atoms with mass numbers 120 and 122, the situation is slightly different but leads to a similar result. Here, the nucleus exists in a state where the round and stretched shapes are almost equally likely, creating a split personality where the atom is simultaneously in two very different configurations. This duality also disrupts the transition between energy levels, causing the probability to drop near the same low threshold. The atoms in the middle of the group, with mass numbers 116 and 118, show a more blended behavior where the two shapes merge more smoothly, avoiding the sharp drop in probability. The study also looked at how these shapes mix with one another. In some cases, the round and stretched configurations remain distinct and separate, a phenomenon known as shape coexistence without mixing. In other cases, they blend together. The researchers found that the specific way these shapes mix or stay apart is what determines the strength of the transitions between energy levels.

By successfully matching their model to the real-world data, the team provided a clear explanation for the anomalous measurements. They demonstrated that the strange drop in transition probability is not a random error or a sign of a broken theory, but a direct consequence of the nucleus changing its shape too quickly or existing in two conflicting shapes at once. The study confirms that the ground states of these tin atoms are nearly spherical, while their excited states are well-deformed. The key to the anomaly lies in the state where the atom has the highest spin in the main group, which acts as a bridge between the round and stretched worlds. When this bridge is built on a foundation of two very different shapes, the connection becomes weak, and the transition probability falls. This work offers a detailed map of how nuclear shapes evolve across a chain of elements, showing that the internal architecture of an atom can shift dramatically with just a few added particles, reshaping our understanding of the forces that hold the atomic nucleus together.