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Independent Validation of Octupole Collectivity in radium-224 through lifetime measurements of low-lying negative-parity states

This study independently validates the octupole collectivity and confirms a strongly quenched intrinsic electric-dipole moment in $^{224}$ Ra by precisely measuring the lifetimes of its low-lying negative-parity states via $\beta$ -decay, thereby providing a critical benchmark for nuclear models used in searches for electric dipole moments.

Original authors: D. White, D. O'Donnell, A. Avaa, J. R. Murias, S. Murillo Morales, R. Umashankar, V. Vedia, C. Andreoiu, D. W. Annen, A. D. Ayangeakaa, G. C. Ball, V. Bildstein, M. Bowry, I. Dillmann, E. G. Fuakye, L

Published 2026-09-09

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CC BY 4.0

Original authors: D. White, D. O'Donnell, A. Avaa, J. R. Murias, S. Murillo Morales, R. Umashankar, V. Vedia, C. Andreoiu, D. W. Annen, A. D. Ayangeakaa, G. C. Ball, V. Bildstein, M. Bowry, I. Dillmann, E. G. Fuakye, L. P. Gaffney, A. B. Garnsworthy, P. E. Garret, E. D. Geerlof, S. Georges, A. L. Grimes, G. F. Grinyer, G. Hackman, P. M. Jones, J. Liu, B. Olaizola, S. D. Olorunfunmi, F. Rowntree, N. K. Syeda, D. Shah, P. Spagnoletti, C. E. Svensson, F. Wu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

At the heart of matter lies the atomic nucleus, a dense cluster of protons and neutrons that usually holds a perfectly round or slightly flattened shape. However, some heavy nuclei are different; they do not just bulge or flatten, but stretch into a shape that lacks a mirror plane, resembling a pear. This unusual form, known as octupole deformation, arises when the internal building blocks of the nucleus align in a specific way that breaks the usual symmetry. Scientists are deeply interested in these pear-shaped nuclei because they act as powerful amplifiers for rare physical effects. If the fundamental laws of nature treat time and mirror symmetry differently, these distorted nuclei would reveal those violations more clearly than any other object. To understand this, researchers must first map the nucleus with extreme precision, measuring how it vibrates and how its internal charges are distributed, to separate the expected behavior from the subtle signals of new physics.

In a recent study, a team of physicists turned their attention to radium-224, a nucleus that has long been considered a prime example of this pear-shaped behavior. Previous experiments had already shown that radium-224 possesses a strong octupole deformation, confirming that it indeed holds this asymmetric shape. However, a lingering question remained about the nucleus's internal electric properties. Theory predicted that while the nucleus is pear-shaped, its internal electric dipole moment—a measure of how its positive and negative charges are separated—should be surprisingly weak. This weakness was expected because two large, opposing forces inside the nucleus were thought to cancel each other out almost perfectly. To test this, the researchers needed to measure how long specific excited states of the nucleus exist before they decay, a process that reveals the strength of the electric transitions between energy levels.

The experiment took place at TRIUMF, Canada's particle accelerator center, where a beam of radioactive francium-224 was created and directed into a specialized detection array called GRIFFIN. As the unstable francium atoms decayed, they transformed into radium-224, populating specific excited states within the new nucleus. The researchers focused on two low-lying states with negative parity, which are directly linked to the pear-shaped vibration of the nucleus. Using a set of highly sensitive detectors made of lanthanum bromide crystals, the team measured the time it took for these states to emit gamma rays and drop to lower energy levels. This technique, known as fast-timing, allowed them to determine the mean lifetimes of these states with remarkable precision. They found that the first negative-parity state lived for 444 picoseconds, while the second lived for 460 picoseconds. These numbers are incredibly small, representing trillionths of a second, yet they provided the key to unlocking the nucleus's electromagnetic secrets.

With these precise lifetimes in hand, the team calculated the reduced transition probabilities, which describe how easily the nucleus can change its shape and emit energy. The results matched the values inferred from earlier, more complex experiments involving the scattering of heavy ions, but with significantly better accuracy. This independent confirmation was crucial because it validated the electromagnetic matrix elements that describe the nucleus's structure. More importantly, the data confirmed the theoretical prediction that the intrinsic electric dipole moment of radium-224 is strongly suppressed. The calculated value for this moment was approximately 0.032 electron-femtometers, a number that is tiny compared to what one might expect for such a distorted nucleus. This small value arises because the macroscopic shape of the nucleus and the microscopic arrangement of its protons and neutrons work against each other, nearly canceling out the electric separation that usually accompanies a pear shape.

The findings serve as a rigorous benchmark for the models scientists use to describe nuclear structure. While some theoretical calculations could reproduce the general shape and energy levels of radium-224, they failed to predict the extreme weakness of the electric dipole moment, often overestimating its strength by large factors. The new measurements show that reproducing the energy levels alone is not enough; a successful model must also account for the delicate cancellation between different internal contributions. This level of detail is essential for future searches for permanent electric dipole moments, which could reveal new physics beyond the standard model. By proving that the electric dipole moment in radium-224 is indeed quenched, the study ensures that future experiments looking for violations of time-reversal symmetry are built on a solid, experimentally verified foundation. The work demonstrates that even in a field where unique facilities and rare isotopes are required, independent verification remains the gold standard for establishing the reliability of scientific knowledge.

Technical Summary: Independent Validation of Octupole Collectivity in $^{224}$ Ra Through Lifetime Measurements

Problem and Motivation
The nucleus $^{224}$ Ra serves as a critical benchmark for understanding stable octupole deformation and the theoretical descriptions of enhanced Schiff moments in reflection-asymmetric nuclei. While previous Coulomb-excitation experiments (specifically Gaffney et al.) established strong octupole collectivity in $^{224}$ Ra, theoretical models predict a subtle and counter-intuitive phenomenon: the intrinsic electric-dipole moment ( $D_0$ ) should be strongly quenched due to a near-cancellation between macroscopic and microscopic contributions. Despite the importance of these findings for fundamental symmetry tests and searches for permanent electric dipole moments (EDMs), relatively few independent measurements have verified the electromagnetic matrix elements extracted from the initial Coulomb-excitation analysis. Independent verification is essential in nuclear physics to establish the reliability of benchmark results, particularly given the scarcity of unique radioactive-beam facilities and the high demand for experimental time.

Methodology
This study performed direct fast-timing measurements of the mean lifetimes of the low-lying $J^\pi = 1^-$ and $3^-$ states in $^{224}$ Ra. The experiment was conducted at TRIUMF-ISAC using the GRIFFIN array.

Production: A 520 MeV proton beam from the cyclotron impinged on a uranium carbide ( $UC_x$ ) target with a rhenium surface-ion source. The Isotope Separation On-Line (ISOL) technique extracted $^{224}$ Fr ions, which were implanted into a moving Mylar tape collector at the center of the array.
Decay and Detection: The implanted $^{224}$ Fr nuclei $\beta$ -decayed to populate states in $^{224}$ Ra. The GRIFFIN array utilized fifteen high-purity germanium (HPGe) clover detectors and eight cerium-doped lanthanum bromide (LaBr $_3$ (Ce)) detectors. The HPGe detectors were used to gate on specific transitions to isolate decay paths and minimize background, while the LaBr $_3$ (Ce) detectors provided the fast timing required for lifetime measurements.
Analysis: Mean lifetimes were determined using the delayed and anti-delayed coincidence method. Time-to-Amplitude Converters (TACs) measured the time difference between feeding ( $E_f$ ) and decaying ( $E_d$ ) transitions. The resulting TAC histograms were fitted with a function consisting of a Gaussian convoluted with an exponential decay to extract the mean lifetime ( $\tau = 1/\lambda$ ).

Key Results
The experiment yielded the following mean lifetimes with significantly improved precision compared to previous inferences:

$1^-_1$ State: $\tau = 444(6)$ ps (measured via two independent gate combinations yielding consistent results).
$3^-_1$ State: $\tau = 460(18)$ ps.
$2^+_1$ State (Validation): $\tau = 1.02(4)$ ns, consistent with literature values within systematic uncertainties.

From these lifetimes, the reduced electric-dipole transition probabilities, $B(E1)$ , were extracted. The results show:

The $B(E1)$ values are in excellent agreement with those inferred from the Coulomb-excitation experiment by Gaffney et al., but with substantially higher precision.
The three measured $B(E1)$ values correspond to a common, strongly-quenched intrinsic dipole moment of $D_0 \simeq 0.032$ efm.
The ratio $B(E1; 1^-_1 \to 2^+_1) / B(E1; 1^-_1 \to 0^+_1)$ is $2.11(13)$ , consistent with a simple $K=0$ rotational model (expected ratio of 2).
However, the ratio $B(E1; 3^-_1 \to 2^+_1) / B(E1; 1^-_1 \to 0^+_1)$ is $1.03(6)$ , which is significantly lower than the rigid-rotator expectation of $\approx 1.29$ , suggesting the assumption of a spin-independent E1 matrix element may not hold for all members of the $K^\pi = 0^-$ band.

Significance and Claims
The paper asserts that these measurements provide an independent validation of the electromagnetic matrix elements associated with octupole collectivity in $^{224}$ Ra. The primary significance lies in confirming that $^{224}$ Ra possesses strong octupole correlations while simultaneously exhibiting an anomalously small intrinsic electric-dipole moment.

The authors claim that reproducing both the large octupole collectivity and the suppressed intrinsic dipole moment provides a stringent experimental benchmark for nuclear-structure models used to estimate Schiff moments. The data reveals that theoretical models (including mapped IBM and macroscopic-microscopic approaches) must not only reproduce excitation energies and collective octupole strength but also accurately account for the delicate proton-neutron cancellations responsible for the observed dipole-moment quenching. This level of theoretical accuracy is deemed crucial for the interpretation of Schiff moments and future searches for non-zero electric dipole moments.

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