The nickel-58 nucleus may contain elusive toroidal dipole excitations

Toroidal dipole modes are a singular set of excitations which can be predicted to occur in a wide range of physical systems, from atomic nuclei to metamaterials. What characterizes these excitations, or modes, is the toroidal distribution of currents, which leads to the formation of vortex structures.

A classic example is smoke rings, characteristic “rings” of smoke produced when clouds of smoke escape into the air through a narrow opening. Physical theories have also predicted the existence of toroidal dipole excitations in atomic nuclei, but observing these modes has up to now proven difficult.

Scientists from the Technische Universitat Darmstadt, the Joint Institute for Nuclear Research and other institutes have recently identified candidates for toroidal dipole excitations within the nucleus ⁵⁸Not for the primary time. Their paperpublished in Physical inspection lettersopens recent possibilities for experimental observations of those elusive modes in heavy nuclei.

“Toroidal flow appears in many different areas of physics, including solid-state physics, metamaterials, metaphotonics, heavy ion collisions, and more,” paper co-authors Peter von Neumann-Cosel and Valentin O. Nesterenko, co-authors of the paper, told Phys org . “This flow looks like a vortex ring produced by a current circulating on the surface of the torus. Toroidal motion occurs naturally as a result of turbulence in various classical fluids and gases.”

Vortex rings, which turn into visible when smoke passes through narrow passages or are blown out of the mouth, are literally invisible to humans, produced because the air is exhaled constantly. Smoke rings are only one example of how these rings can turn into visible.

“Based on this example, it is natural to expect toroidal flow in atomic nuclei as well,” said von Neumann-Cosel and Nesterenko. “Over the last 50 years, the toroidal mode has indeed been predicted in nuclei by various theoretical models. Additionally, preliminary signatures of the toroidal dipole resonance in inelastic scattering of a’ particles are discussed.

Experimental statement of those exotic modes during other nuclear reactions has up to now been difficult, primarily as a consequence of the dearth of reliable methods for searching and detecting them. Recent studies have attempted to guage low-energy dipole states in nuclei using precise photon, electron and proton scattering techniques.

“These studies have shown that some dipole states, which were previously thought to have the character of a magnetic dipole (M1), are in fact dipole-electric (E1), but have rather unusual properties resembling toroidal states,” explained von Neumann-Cosel and Nesterenko . “So we started wondering what the peculiar nature of these conditions might be.”

The study by von Neumann-Cosel, Nesterenko and their colleagues builds on recent research efforts on toroidal excitations in nuclei. Comparing scattering experiments with photons, electrons and photons within the nucleus ⁵⁸Ni, scientists have identified candidate excitations on this particular nucleus.

“All three types of experiments (i.e. photon, electron and proton scattering) are sensitive to dipole excitations and allow us to distinguish whether they are electrical or magnetic in nature,” von Neumann-Cosel and Nesterenko said. “The most important thing was that they all had high enough energy resolution to resolve the appropriate excitations in each experiment.”

The researchers compared theoretical predictions with electron scattering experiments. They found that scattering at a back-angle to the beam provides robust signatures of the toroidal mode.

“There are two well-known modes of collective electric dipole excitation in nuclei,” explain von Neumann-Cosel and Nesterenko. “One corresponds to the counter-oscillation of all protons relative to all neutrons, the opposite to the in-phase oscillation resulting in a change in density contained in the nucleus.

“The toroidal mode is the third class of electric dipole excitations. Like the other two, it is a general mode that should also appear in all nuclei and is therefore important for a general understanding of nuclear structure.”

A recent paper by von Neumann-Cosel, Nesterenko and their colleagues may have helpful implications for future research. In particular, it could help scientists higher understand the phenomenon observed in heavy nuclei, where the variety of neutrons will likely be greater than protons because proton binding is reduced as a consequence of the strong Coulombic repulsion between them.

“In these nuclei at low energies, a resonance-like structure of electric dipole strength can be found, the precise features of which influence the calculation of astrophysical reaction networks in an attempt to model the nucleosynthesis of heavy elements,” von Neumann-Cosel and Nesterenko said. “Our new results indicate that these may be toroidal excitations, as opposed to the currently favored model of oscillations of excess neutrons (which reside on the surface of the nuclei) relative to an inner core with approximately equal numbers of protons and neutrons.”

Recent work by this research team may contribute to a greater understanding of toroidal excitations in nuclei. Von Neumann-Cosel and Nesterenko are currently planning a brand new experiment for 2025, which shall be carried out on the S-DALINAC electron accelerator, situated on the Institute of Nuclear Physics of the Darmstadt University of Technology.

“Our work shows that electron scattering provides the clearest signature of toroidal excitations,” von Neumann-Cosel and Nesterenko added. “In our next experiment, we’ll study a heavy nucleus with an excess of neutrons to prove (or disprove) our claim that the low-energy structure mentioned above results from toroidal excitations of electrical dipoles and coincidentally measure the gamma decay to the bottom state.

“Theoretical work done for the purpose of interpretation ⁵⁸The Ni experiments in this paper indicate that these types of measurements provide additional unique signatures of toroidal excitations.”

© 2025 Science X Network