Atomic Nuclei Retain Surprising Order Despite Complex Internal Interactions

Scientists are investigating the surprising persistence of a quantum mechanical principle called ‘seniority’ within the complex environment of atomic nuclei. Chong Qi, from the School of Nuclear Science and Technology at Lanzhou University, and colleagues demonstrate that seniority, a method of classifying nuclear structures based on unpaired nucleons, is partially conserved in certain ‘semi-magic’ nuclei, despite expectations of symmetry breaking. This research, conducted in collaboration with the Institute of Modern Physics, Chinese Academy of Sciences, and the Key Laboratory of Nuclear Physics and Nuclear Chemistry of the Chinese Academy of Sciences, provides crucial insight into the behaviour of nuclear forces and the underlying symmetries governing nuclear structure. The discovery that specific nuclear configurations remain solvable even with residual interactions represents a significant advance, offering a new pathway to understanding and modelling the behaviour of many-body quantum systems and potentially refining our knowledge of nucleosynthesis processes.

Scientists have uncovered a surprising degree of order within the chaotic realm of nuclear physics, revealing that certain atomic nuclei retain a fundamental symmetry at unexpectedly high angular momenta. This discovery challenges existing theoretical predictions regarding the breakdown of seniority symmetry, a principle governing how nucleons (protons and neutrons) pair within the nucleus, and opens new avenues for understanding the structure of matter at its most fundamental level.

The research centres on the observation of partial seniority conservation in systems possessing an angular momentum of 9/2, a value previously thought to be too high for this symmetry to persist. This work demonstrates that, contrary to expectations, specific nuclear states maintain a discernible pattern of nucleon pairing even when subjected to complex interactions.

The implications extend beyond refining nuclear models, potentially influencing fields reliant on accurate simulations of many-body quantum systems, such as quantum computing and materials science. By identifying conditions under which this partial conservation occurs, researchers have established a new benchmark for exploring the limits of symmetry in complex quantum systems.

Detailed analysis reveals that two specific states with values of 4 and 6 remain unmixed, even under arbitrary interactions, a finding supported by both theoretical proofs and experimental data gathered from semi-magic nuclei. The study meticulously examines the theoretical underpinnings of the seniority scheme, tracing its connection to pairing interactions and the mathematical tools used to describe many-body systems.

Researchers employed advanced symbolic shell-model approaches to dissect the wave functions of these nuclei, revealing hidden symmetries and conserved quantum numbers. Evidence for this phenomenon has been found across five distinct regions of the nuclear chart, strengthening the validity of the findings. This partial conservation of seniority, observed at 9/2, provides a unique window into the interplay between single-particle behaviour and collective nuclear dynamics, promising a deeper understanding of nuclear structure and decay properties.

Symbolic calculations reveal structure in semi-magic nuclei

A detailed examination of nuclear energy levels relied heavily on the configuration interaction shell model with seniority symmetry as a guiding principle. This approach systematically constructs many-body wave functions by considering all possible combinations of single-particle configurations within a limited valence space.

Crucially, the study focused on semi-magic nuclei exhibiting 9/2 angular momentum orbitals, necessitating a computational framework capable of handling the associated complexities. To achieve this, researchers employed a symbolic shell-model program, a technique that represents operators and wave functions algebraically, enabling efficient manipulation and analysis of the many-body Schrödinger equation.

The symbolic approach proved essential for constructing and analysing wave functions, revealing hidden symmetries and conserved quantum numbers within the nuclear structure. This methodology allowed for the explicit calculation of coefficients of fractional parentage, which quantify the probability amplitudes for constructing collective states from single-particle configurations.

Furthermore, the program facilitated the computation of electromagnetic transition rates, specifically E2 transitions, providing a direct link between theoretical predictions and experimental observables. The choice of a symbolic approach, rather than purely numerical methods, was driven by the need to understand the underlying physics governing seniority conservation and to identify the conditions under which it persists despite residual interactions.

To validate the theoretical framework, the research incorporated a comprehensive analysis of experimental data from across five regions of the nuclear chart. Measured spectra and E2 transition properties of semi-magic nuclei were compared with theoretical predictions, providing stringent tests of the model’s accuracy.

Particular attention was given to the 2+ and 4+ energy levels, and their ratio, R4/2, serving as a sensitive probe of seniority-based behaviour. The study also investigated the B(E2) transition strengths, expecting suppressed values for transitions between states of differing seniority, a key signature of partial seniority conservation. This combination of advanced computational techniques and careful experimental comparison enabled a robust assessment of the seniority scheme in complex nuclear systems.

Analytic Solutions and Partial Seniority Conservation in Nuclei

Observations of semi-magic nuclei reveal partial seniority conservation at an angular momentum of 9/2, a finding that challenges expectations regarding the breakdown of seniority symmetry in higher orbital configurations. This research demonstrates that certain states within the (9/2)⁴ configuration remain analytically solvable despite the degeneracy typically associated with such systems.

Specifically, two distinct states exhibit this partial conservation, maintaining fixed wave functions irrespective of the interaction details. This unexpected solvability arises from hidden symmetries operating within the Hilbert space, representing a partial dynamical symmetry even when complete solvability is absent.

The study establishes that these states, defying conventional mixing under general two-body Hamiltonians, possess a unique characteristic: their energies are not determined through explicit diagonalization but retain analytic forms. This phenomenon is categorized as Type 2 solvability, distinct from simpler cases where solvability arises from angular momentum uniqueness or strict seniority conservation.

Further analysis reveals that states uniquely defined by total angular momentum and seniority also exhibit exact solvability, as exemplified by mid-shell systems like 213Pb with five neutrons in the 1g9/2 shell. Beyond these established cases, the work identifies additional partially solvable states, even within configurations like (11/2)⁶, where the v = 6, J = 0 and v = 4, J = 3 states remain solvable for any interaction.

These states, while not uniquely defined by seniority and angular momentum, maintain well-defined characteristics, extending the understanding of partial solvability beyond strict classifications. The discovery highlights a layered structure of symmetries in nuclear models, demonstrating that solvability is not simply an all-or-nothing concept but rather exists on a spectrum of conditions and behaviours.

The Bigger Picture

Scientists have long sought to understand the subtle symmetries governing the atomic nucleus, and a recent advance suggests our grasp of these symmetries is more nuanced than previously thought. For years, the expectation has been that certain organising principles within the nucleus, specifically, seniority, would inevitably break down as complexity increases.

However, new research demonstrates a surprising resilience in this symmetry, extending its reach to higher energy states than anticipated. This isn’t merely a refinement of existing models; it challenges fundamental assumptions about how nucleons interact and organise themselves. The difficulty lies in the sheer number of interacting particles within the nucleus.

While simplified models work well for lighter nuclei, the many-body problem becomes intractable as atomic number and neutron number increase. Traditional approaches struggle to account for the delicate balance between attractive and repulsive forces, leading to predictions that diverge from experimental observations.

This work offers a pathway to retaining analytical solvability in systems where it was previously thought impossible, providing a crucial benchmark for more complex calculations. The key finding, a specific angular momentum value where partial seniority conservation persists, is more than just a number.

It indicates that the nucleus exhibits a degree of order even in highly excited states, potentially opening doors to new methods for predicting nuclear properties and understanding the origins of elements. While the immediate applications may not be obvious, a deeper understanding of nuclear structure is vital for fields like astrophysics, where the creation of heavy elements in stellar environments depends on precise nuclear behaviour.

Limitations remain, of course. Extending these findings to even heavier nuclei will require significant computational resources and theoretical innovation. The observed partial conservation doesn’t imply complete symmetry, and the residual interactions that do cause deviations need further investigation. Nevertheless, this work represents a significant step forward, suggesting that the search for underlying order in the complex world of nuclear physics is far from over and may yet reveal unexpected connections between seemingly disparate phenomena.