Low-energy collective structure of $^{92,94}$Zr and $^{94}$Mo from ($e,e^{\prime}$) and ($p,p^{\prime}$) scattering I. Experimental results

Inside the heart of every atom, protons and neutrons do not simply sit still; they move in a complex, collective rhythm. While we often picture these particles as individual dots, in many atomic nuclei they behave more like a fluid, swaying together in specific patterns. Physicists have long understood that these swaying motions come in two main flavors. In the most common type, the protons and neutrons move in perfect unison, like a single, unified crowd marching in step. This is known as a fully symmetric state. However, there is a more subtle, elusive pattern where the protons and neutrons move against each other, like two groups in a tug-of-war that are still part of the same team. This is called a mixed-symmetry state. Finding and confirming these mixed-symmetry states is crucial because they reveal the specific nature of the force that binds the atomic nucleus together, acting as a sensitive test for our theories of how matter is constructed at its most fundamental level.

To catch a glimpse of these hidden patterns, a team of researchers turned their attention to a specific group of atomic nuclei: zirconium-92, zirconium-94, molybdenum-94, molybdenum-96, and zinc-70. These are not random choices; they are nuclei that sit just outside the stable "closed shells" where protons and neutrons usually pack themselves neatly, making them ideal laboratories for studying these collective movements. The scientists did not look at these nuclei with a single tool. Instead, they fired two different types of projectiles at them: high-speed electrons and high-speed protons. The electrons, being light and electrically charged, interact with the nucleus primarily through the electric force, giving a clear picture of how the protons move. The protons, being heavier and interacting through the strong nuclear force, provide a different view that includes how the neutrons move. By comparing the results from these two very different experiments, the researchers could separate the motion of the protons from the motion of the neutrons, effectively listening to the two sides of the nucleus speak in different voices.

The experiments took place at specialized facilities in Germany and South Africa. The team bombarded thin metal foils of the target nuclei with beams of electrons and protons, carefully measuring the angles at which the particles scattered after hitting the nucleus. When a particle bounces off, the angle of its bounce depends on the shape and nature of the vibration inside the nucleus. The researchers collected vast amounts of data, mapping out how often particles scattered at different angles for dozens of excited states within these nuclei. They then compared these real-world scattering patterns against theoretical calculations that predicted how a nucleus would behave if it were vibrating in a specific way. This comparison allowed them to assign a "spin" and "parity" to each excited state, which are essentially labels describing the type of rotation and symmetry of the vibration.

The results provided a detailed map of the low-energy structure of these nuclei. The team successfully identified many states that were already known, confirming their nature as fully symmetric vibrations where protons and neutrons move together. More importantly, they identified possible candidates for the elusive mixed-symmetry states and provided the necessary experimental data for their confirmation. For instance, in the nucleus of zirconium-94, they identified a specific excited state that is a candidate for a mixed-symmetry state, noting that it shows a distinct difference in how the protons and neutrons contribute to the vibration. Similarly, in molybdenum-94, they pinpointed a state that had been suspected of being a mixed-symmetry state, and their new data on how it scatters protons and electrons supports that identification. The study also looked at higher-energy vibrations, such as those involving octupole shapes, which are more complex than simple squashing and stretching, and found evidence for both symmetric and potentially mixed-symmetry versions of these as well.

What makes this work particularly significant is the method used to gather data for confirming these states. Rather than relying solely on how the nucleus decays or emits light, which can sometimes be ambiguous, the researchers used the direct comparison of electron and proton scattering to look at the transition densities. This is a measure of how the distribution of protons and neutrons changes during the vibration. In a fully symmetric state, the protons and neutrons change their distribution in the same way. In a mixed-symmetry state, they change in opposite ways. By showing that the experimental data fits the predictions for these opposite movements, the team established the foundation for a new and robust signature for identifying these states. This approach helps resolve long-standing debates about the existence of certain types of vibrations in these nuclei, particularly those with higher spins that were difficult to classify before, with the full analysis and final identification presented in a companion paper.

The study did not just confirm what was already known; it also clarified uncertainties. In some cases, where previous experiments had suggested a state might be a mix of different types, the new data allowed for a clearer assignment. For example, in zinc-70, the team examined a doublet of states near 3044 keV; while other experiments had identified a 5- state, the new angular distribution data was best described by assuming a doublet of a 2+ and a 5- state, though definitive spin assignments for the individual components remained challenging in some overlapping regions. They also found that in some heavier nuclei like molybdenum-96, the energy levels are so crowded that individual states are harder to distinguish, yet they were still able to extract meaningful information about the collective behavior of the protons and neutrons. The work serves as a foundational step, providing the experimental data necessary for more complex theoretical models to be tested. By establishing a clear picture of how these nuclei vibrate, the research deepens our understanding of the nuclear force and the intricate dance of protons and neutrons that holds the universe's matter together.