Some atoms appear to be particularly stable because of the number of protons and neutrons
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A particular set of numbers has formed the backbone of nuclear research for decades, and now we finally know how it arises from the quantum mixing of nuclear particles and forces.
Almost 80 years ago, physicist Maria Goeppert Mayer showed that when the nucleus of an atom contains a certain number of protons and neutrons, say 50 or 82, it becomes exceptionally stable. In the years since, scientists have collected evidence for several such “magic numbers”, found in the most stable, and therefore most abundant, elements in our universe.
Goeppert Mayer and her contemporaries explained these numbers by proposing that protons and neutrons occupy discrete energy levels, or shells. This model, which is still used to interpret many nuclear experiments, treats each particle in the nucleus as independent, but our best quantum theories claim that particles in the nuclei actually interact strongly.
Jiangming Yao at Sun Yat-sen University in China and his colleagues have now resolved this contradiction and, in the process, elucidated how magic numbers emerge from these interactions.
Yao says the shell model relies on input from experiments and does not encode details of interactions between each particle. Instead, he and his team started their calculations from first principles, meaning they mathematically described how particles interact with each other, how they stick together and how much energy is needed to move them apart in more detail.
The two descriptions are analogous to images taken with low and high resolution respectively, says Yao. “Before, people modeled the system directly at low resolution, or they tried to understand nuclear structure at high resolution. We used modern methods to bridge these descriptions.”
He and his colleagues started with the high-resolution description, gradually blurring it at each step of the calculation and watching how the structure the particles formed changed.
Moving across their mathematical bridge, the researchers saw that the symmetry of the particle’s quantum states changed—drawing a graph based on the equations for those states would produce shapes with different symmetries at different resolutions. This change resulted in a nuclear structure such that the nucleus achieved the most stability when particles within it clustered in magic numbers.
Jean-Paul Ebran of the French Commission for Alternative and Atomic Energy says this work offers a theoretical probe – a kind of mathematical microscope – that mirrors how experiments work. “Nature looks different depending on the resolution you’re observing. This (study) really maps out what we’re doing experimentally.”
The change in symmetry that the researchers identified is related to effects described by Albert Einstein’s special theory of relativity, and thus paints an even fuller picture of how magic numbers connect different facets of nuclear theory, says Ebran.
So far, the researchers have tested their theoretical work on a type of tin that is doubly magical because its nuclei each contain 50 protons and 82 neutrons, as well as on several additional nuclei. Going forward, they want to extend the analysis to heavier atomic nuclei, which are usually unstable, and study processes where heavy nuclei are created in exploding stars or merging neutron stars, says Yao.
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