Lead-208’s doubly magic nucleus defies expectations with surprising shape properties

In a surprising turn of events, an international team of scientists has found that lead-208 (²⁰⁸Pb), the heaviest known “doubly magic” nucleus, exhibits unexpected shape characteristics that current nuclear models fail to predict accurately.

Doubly magic refers to nuclei that have complete shells of both protons (82) and neutrons (126), a configuration that should theoretically favor a perfectly spherical shape.

The research published in Physical Review Letters focuses on the deformation and collective behavior of lead-208, especially the spectroscopic quadrupole moments of two excited states.

The spectroscopic quadrupole moment measures how much a nucleus deviates from a perfect sphere, quantifying the distribution of charge within the nucleus.

Phys.org spoke to the first author of the study, Dr. Jack Henderson from the University of Surrey. “We fired beams of germanium, tellurium, neodymium, and erbium at a lead foil,” explains Dr. Henderson.

“When these particles scatter off the foil, they can give energy to the lead nuclei, potentially leaving them in an excited state. The probability that this excitation occurs depends on the shape of the nuclei, so by carefully measuring it, we were able to deduce the deformation of lead-208.”

Magic numbers and nuclei shapes

Similar to how noble gases represent stable electronic configurations, magic and doubly magic nuclei result in stable nuclei. These “magic numbers” are 2, 8, 20, 28, 50, 82, and 126.

For magic nuclei, the number of neutrons or protons is equal to the magic number, whereas for doubly magic nuclei, both are magic numbers.

This means the nuclear shells are filled, resulting in a more stable nucleus, doubly so in the case of doubly magic nuclei. The protons and neutrons are paired and symmetrically arranged, resulting in a more spherical nucleus.

Lead-208, with 82 protons and 126 neutrons, sits at the intersection of two magic numbers, making it doubly magic and theoretically predisposed to maintain a spherical shape.

Dr. Henderson explained the importance of magic numbers, saying, “Magic numbers are incredibly important for understanding nuclear physics, as well as related properties, because they give nuclei in their vicinity more binding energy.”

“This distorts the nuclear landscape, and, for example, is the cause of the peaks in abundances in heavy-element nucleosynthesis in the so-called rapid neutron capture process (the r-process).”

Coulomb excitation

While the study of doubly magic nuclei is not new, researchers used state-of-the-art experimental equipment to provide more conclusive measurements, especially regarding the sign and magnitude of the deformation.

The researchers used Coulomb excitation, a method where atomic nuclei are excited through electromagnetic interactions without involving the nuclear strong force.

“Coulomb excitation is exceptionally sensitive for determining deformation because it depends only on the electromagnetic force, which we have understood since the late 1800s,” Henderson explained.

The experimental setup consisted of four different beams (germanium, tellurium, neodymium, and erbium) directed at a lead-208 foil.

Researchers used the GRETINA array of high-purity germanium detectors to measure gamma rays emitted when the excited nuclei return to their ground state, while simultaneously tracking scattered particles with the CHICO2 detector array.

In particular, the researchers focused on two excited states to study the deformation, the first quadrupole excitation and the first octupole excitation.

The data were analyzed using the GOSIA semiclassical Coulomb-excitation code.

Challenging models, impact, and future work

The researchers conclusively demonstrated that both excited states they studied exhibit large, negative spectroscopic quadrupole moments, indicating the nucleus prefers an elongated (prolate) rather than flattened shape.

When compared to predictions from three different theoretical approaches—the nuclear shell model, density functional theory, and Hartree-Fock calculations—none could reproduce the sign and magnitude of the observed deformation.

Dr. Henderson addressed the discrepancy, saying, “The models seem to fail to reproduce our observables, and the reason isn’t entirely clear. One possibility is that the nuclear interactions used require refining or a degree of freedom we hadn’t recognized as being important is missing.”

As mentioned, lead-208 plays a crucial role in understanding how heavy elements are formed in cosmic events like neutron star mergers, i.e., the r-process. Therefore, the impact extends from nuclear studies to stellar evolution.

The researchers plan on addressing these challenges, with Dr. Henderson, hinting at future work, said, “One possibility is that neighboring nuclei, such as lighter and heavier isotopes of lead, could help better understand the missing ingredient in the theoretical interpretation.”

“Another potential route forward is to improve our understanding of how the nuclear shape vibrates by looking for key signature states, which have thus far eluded conclusive identification.”

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