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Structure of even-even Zr isotopes with 52 $\leq$ N $\leq$ 58 neutrons

This study investigates the structure of even-even Zr isotopes with 52 $\leq$ N $\leq$ 58 neutrons through new experimental data on excited levels and half-lives, combined with Large Scale Shell Model calculations, to elucidate the evolution of collectivity, phase transitions, and the role of the $\nu$ 9/2 $^+$ [404] extruder orbital in the region.

Original authors: W. Urban, A. Abramuk, T. Rz\caca-Urban, M. Jentschel, P. Mutti, U. Köster, G. de France, C. A. Ur

Published 2026-07-14

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CC BY 4.0

Original authors: W. Urban, A. Abramuk, T. Rz\caca-Urban, M. Jentschel, P. Mutti, U. Köster, G. de France, C. A. Ur

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

Imagine the atomic nucleus not as a boring, solid marble, but as a squishy, magical jelly that can change its shape, spin, and dance to different tunes. Scientists have been trying to figure out the secret choreography of a specific family of these jellies: the Zirconium (Zr) isotopes. These are the "teenagers" of the nuclear world, sitting in a tricky zone where they can't decide if they want to be round and spherical or long and football-shaped.

In this study, a team of researchers acted like cosmic detectives, using a giant, super-sensitive camera array called EXILL (located in Grenoble, France) to take snapshots of these nuclei. They didn't just look; they listened to the "music" the nuclei made when they were hit by neutrons or when they decayed. Here is what they found, what they crossed off their list, and what they are still guessing about.

The Big Discovery: A New Map and a New Clock

The main goal was to map out the "excited levels" of Zirconium-92, Zirconium-94, and Zirconium-98. Think of these levels as the different floors of a building where the nucleus can live. Before this, the map was full of holes and wrong addresses.

The team found 54 new floors (energy levels) and 180 new ways the nucleus can jump between them (gamma transitions). They also fixed the addresses (spin and parity) for 70 of these levels.

One of their coolest tools was a new "stopwatch" they invented. Usually, measuring how long a nucleus stays on a floor before jumping down is hard if it happens in a blink of an eye (picoseconds). The team realized that when a nucleus jumps while still flying through space (like a firework), the light it emits gets stretched out, or "broadened," due to the Doppler effect. By measuring how blurry the light is, they could calculate the time. Using this trick, they estimated the lifetimes of 61 different states and measured how fast they jumped.

What They Ruled Out: The "Strongly Deformed" Ghost

For a long time, scientists thought there was a specific "ghost" in Zirconium-98. They believed that at a certain energy level (1436.1 keV), there was a strongly deformed band of states—a long, stretched-out chain of energy levels that looked like a rigid, spinning football.

The paper does not confirm this ghost.
The authors looked for the "smoking gun" of this shape: a specific jump (a gamma ray) between two levels that must exist if the band were real. They didn't find it. In fact, the limit they set says that if this jump exists, it's so weak it's basically invisible. Previous studies had also failed to confirm this band.

The Verdict: The idea of a "strongly deformed" band on top of that specific level is not confirmed by this data. The nucleus isn't doing that specific dance there (or at least, the evidence for it is missing). Instead, they found a different, more "moderately deformed" band on top of a lower level (854.0 keV), which behaves more like a regular, spinning top.

The "Extruder" and the Shape-Shifter

The paper suggests a fascinating story about why these nuclei change shape. It involves a special neutron orbital called $\nu9/2^+[404]$ . Imagine this orbital as a "catalyst" or a "matchmaker."

As the nucleus adds more neutrons (going from 52 to 58), this special neutron acts like a catalyst that helps the nucleus suddenly switch from being round to being squashed (prolate). It's like a magic switch that flips the whole structure.

But there's a twist! The paper also talks about a different kind of shape: oblate (like a pancake). They suggest that some of the mysterious "extra" levels (the $0^+_3$ states) are formed when a pair of neutrons jumps from that "extruder" orbital to a different, high-energy orbital called $\nu11/2^-[505]$ . This creates a "pancake" shape that is very stable. This idea helps explain why some energy levels are lower than expected and why certain transfer reactions (where scientists swap neutrons between nuclei) happen so fast or so slow.

The "Proto-Gamma" Dance

The researchers also spotted something called "gamma collectivity." Imagine the nucleus isn't just spinning; it's wobbling like a jelly. They found evidence of "proto-gamma" bands in Zirconium-92, 94, 96, and 98. These are like practice runs for a wobbling dance that gets mixed up with the regular spinning. It's a complex mix of "single-particle" moves (one dancer moving) and "collective" moves (the whole group wobbling).

Specifics You Can Trust

Precision: They measured the neutron binding energy of Zirconium-92 with incredible precision: 8634.81(2) keV. That's a very exact number.
Isomers: They found that the level at 3894.1 keV in Zirconium-98 is likely a "few ns isomer." This means it hangs around for a few nanoseconds before jumping down, which is a long time in nuclear physics!
Gamow-Teller: In Zirconium-94, they proposed a specific type of transition (Gamow-Teller) to a level at 4670.3 keV.
Negative Parity: They confirmed a level at 3894.1 keV in Zirconium-98 has a spin of 9 and negative parity, fitting a specific pattern of neutron coupling.

What's Still a Mystery?

The paper is careful not to claim everything is solved.

They suggest that the "proto-gamma" bands are mixed with other structures, but the exact details of this mixing are complex and still being figured out.
They propose that the oblate configurations (the pancake shapes) explain the strange behavior of certain energy levels, but they note that the proton structure of some levels in Zirconium-100 is still not determined.
They suggest that the "extruder" orbital is the key to the shape change, but they acknowledge that other models exist and that more measurements (like transfer reactions) are needed to fully verify their theory.

The Bottom Line

This paper is a massive cleanup of the nuclear map for Zirconium. They found new rooms in the building, fixed the addresses, and built a new stopwatch to time the jumps. They could not confirm the existence of a "strongly deformed" ghost in Zirconium-98, suggesting instead a more complex, mixed-up reality involving wobbling dances and special neutron catalysts. While they haven't solved every mystery, they've provided a much clearer picture of how these nuclei decide to be round, football-shaped, or pancake-shaped.

Technical Summary: Structure of Even-Even Zr Isotopes with 52 ≤ N ≤ 58 Neutrons

Problem and Motivation
The mechanism governing the creation of excited $0^+_2$ states, their internal structure, and their relationship to deformation changes in the $A \approx 100$ region remains a subject of intensive study. Previous systematics of $0^+_2$ states in Ru and Sr isotopes revealed distinct behaviors: Ru isotopes exhibit an avoided crossing of $0^+_1$ and $0^+_2$ structures, while transitional Sr isotopes show no such interaction, with $2^+_1$ excitations dominated by single-particle (s.p.) configurations rather than phonon nature. The trend in Zr transitional isotopes appeared chaotic, lacking clear correlation between $0^+$ and $2^+$ levels. This study aims to resolve these ambiguities by searching for new levels, particularly $0^+$ excitations, and improving spin-parity assignments in $^{92,94,98}$ Zr to understand the evolution of collectivity and the role of single-particle excitations in phase transitions and shape coexistence in this region.

Methodology
The investigation utilized high-statistics $\gamma$ -coincidence data obtained at the Institut Laue-Langevin (ILL) in Grenoble using the EXILL Ge array (16 large germanium detectors, including eight Clovers).

$^{92}$ Zr: Studied via cold-neutron capture on enriched $^{91}$ Zr targets ( $^{91}$ Zr(n, $\gamma$ ) $^{92}$ Zr) and complemented by $\beta^-$ decay measurements of $^{92}$ Y produced in $^{235}$ U fission.
$^{94}$ Zr and $^{98}$ Zr: Studied using prompt $\gamma$ decays following neutron-induced fission of $^{235}$ U, with data complemented by $\beta^-$ decay of yttrium isotopes.
Analysis Techniques:
- Spectroscopy: Triple- $\gamma$ coincidences and $gS_2$ (sum-energy) histograms were used to build excitation schemes and identify primary transitions, significantly reducing Compton background.
- Spin-Parity Determination: Angular correlations and directional-linear polarization measurements were performed using EXOGAM Clover detectors as Compton polarimeters.
- Half-Life Estimation: A new technique, Doppler-Broadening Estimate (DBE), was developed to estimate picosecond-range half-lives ( $T_{dbe}$ ) for levels populated in fission fragments. This method correlates the ratio of peak height to area ( $R=H/A$ ) with half-lives, calibrated against known values in Sr, Zr, and Mo nuclei.
- Systematics: New phenomenological systematics for $2^+$ and $0^+$ excitations were developed, supported by Large Scale Shell Model (LSSM) calculations, to classify excitations in Zn-Zr even-even nuclei ( $50 \le N \le 60$ ).

Key Results
The study reports the following experimental findings:

New Levels and Transitions: A total of 54 new levels, 180 new $\gamma$ transitions, and 70 new or improved spin-parity assignments were determined across $^{92,94,98}$ Zr.
$^{92}$ Zr:
- A precise neutron binding energy of $S_n = 8634.81(2)$ keV was determined.
- No candidate for a $0^+$ excitation around 1.9 MeV (previously suggested) was found.
- New cascades were identified on top of the $2^+_2$ (1847.37 keV) and $2^+_3$ (2066.74 keV) levels.
- Spin-parity assignments were revised for several levels, including the $3^-$ assignment for the 3039.83 keV level and the proposal of a $2^-$ assignment for the 3407.94 keV level.
$^{94}$ Zr:
- A Gamow-Teller transition was proposed to the 4670.3 keV level.
- The 2507.9 keV level is proposed to belong to a collective structure associated with emerging $\gamma$ instability.
$^{98}$ Zr:
- The $(9^-)$ , 3894.1 keV level is identified as a likely few-nanosecond isomer.
- The decay pattern of the 17 $^-$ , 6607.0 keV isomer was clarified, distinguishing between E1 and E2 decay branches.
- A new E3 decay was found from the $3^-$ , 1806.20 keV level.
- A $\gamma$ -structure was identified on top of the 1590.80 keV level.
- The previously proposed strongly deformed band on top of the $0^+_3$ (1436.1 keV) level was not confirmed; the upper limit for the unobserved 154.7 keV transition is $4 \times 10^{-4}$ relative intensity.
Half-Lives and Transition Rates: The DBE technique provided 61 half-life estimates and 60 $B(\pi, \lambda)$ rate limits for transitions in $^{96,98}$ Zr and $^{94,96}$ Sr.
Systematics and Interpretation:
- $2^+$ Excitations: Experimental $2^+$ levels in Zn-Zr nuclei follow "parabolic" trends linked to specific proton-neutron configurations (e.g., $\nu d_{5/2}\pi p_{1/2}$ , $\nu g_{7/2}\pi g_{9/2}$ ), reproduced well by LSSM calculations.
- $0^+$ Excitations: A new classification links $0^+$ levels via "parabolas." The evolution of collectivity is explained by the role of the $\nu 9/2^+[404]$ extruder orbital as a catalyst for prolate deformation and the creation of $0^+$ excitations.
- Oblate Configurations: A special configuration involving a pair of neutrons excited from the $\nu 9/2^+[404]$ extruder to the oblate $\nu 11/2^- [505]$ intruder orbital is proposed for $0^+_3$ levels in $^{94,96}$ Sr, $^{96,98}$ Zr, and $0^+_2$ levels in $^{98}$ Sr, $^{100,102}$ Zr.
- $\gamma$ Collectivity: Structures with characteristic $3^+$ excitations, related to $\gamma$ collectivity (or "proto- $\gamma$ " bands), were identified in $^{92,94,96,98}$ Zr. These are strongly mixed with collective structures based on $0^+_2$ levels and built around the $\pi(g_{9/2})^2$ multiplet.
- Deformation Change: The rapid variation in two-neutron separation energies ( $\Delta S_{2n}$ ) around $N=59$ is explained by the weak binding of the $\nu 9/2^+[404]$ extruder pair in the prolate potential and the subsequent population of oblate-driving orbitals.

Significance
The paper claims that the new phenomenological systematics, backed by LSSM calculations, successfully explain the evolution of collectivity in zirconium isotopes. Specifically, it highlights the role of the $\nu 9/2^+[404]$ extruder orbital in driving the phase transition and deformation changes in the region. The work provides a coherent explanation for the rapidly varying cross-sections of transfer reactions (e.g., $(t,p)$ , $(^6\text{Li}, ^8\text{B})$ ) to $0^+$ states and the variations in $S_{2n}$ energies. By identifying "proto- $\gamma$ " bands and clarifying the nature of $0^+$ and $2^+$ excitations, the study offers a refined understanding of shape coexistence and the interplay between single-particle and collective modes in transitional nuclei near stability. The authors emphasize that high-resolution measurements using large Ge arrays are crucial for discovering these subtle effects, which complement transfer reaction studies in probing wave function contents.