New Ground State in ${}^{149}$La Removes Two-Neutron-Separation-Energy Anomaly in Lanthanum Isotopes

By identifying a previously overlooked ground state in ${}^{149}$La that is 221 keV/c² lighter than previously reported, this study resolves contradictory mass measurements and eliminates an anomalous prominence in lanthanum two-neutron separation energies, revealing a new kink structure attributed to a nuclear shape transition around $N=91$.

The Gist

Imagine the atomic nucleus as a tiny, bustling city made of protons and neutrons. For decades, physicists have tried to map out the "architecture" of these cities to understand how they hold together. A key tool in this mapping is measuring the mass of these nuclear cities. Just like weighing a building tells you about its foundation, weighing an atom tells you about the forces holding its core together.

Recently, scientists hit a roadblock while studying a specific neighborhood of atoms called Lanthanum isotopes (specifically, the heavy version known as Lanthanum-149).

The Great Mass Dispute

Think of two different surveyors trying to measure the weight of the same house.

• Surveyor A (The JYFL team) said, "This house is heavy! It weighs exactly 100 tons."
• Surveyor B (The CPT team) said, "No way, I measured it at 99 tons. You must have weighed the wrong house."

In the world of nuclear physics, a difference of just a tiny fraction of a ton (about 221 keV/c²) is massive. It changes the entire map of the neighborhood. Surveyor A's data suggested a strange "bump" in the stability of these atoms, while Surveyor B's data suggested a smooth, predictable slope. This contradiction was confusing everyone.

The Detective Work: Catching the "Ghost"

The authors of this new paper decided to solve the mystery by acting like detectives who don't just weigh the house, but also check its ID card and lifespan.

They used a high-tech machine called a Multi-Reflection Time-of-Flight Mass Spectrograph. Imagine a giant, ultra-precise racetrack where atoms are shot through. Lighter atoms finish the race faster; heavier ones take longer. By timing them perfectly, they can calculate the mass.

But here's the trick: they didn't just time the race. They also hooked up a beta-decay detector. This is like a motion sensor that only triggers if the atom is "alive" and radioactive.

• If the atom is the Ground State (the real, normal version of the house), it decays in a specific amount of time (about 0.9 seconds).
• If the atom is an Isomer (a weird, excited "ghost" version of the house), it might live longer or behave differently.

The Big Reveal

When the team ran their experiment, they found something surprising:

1. The atom they caught was lighter than what Surveyor A (JYFL) had reported.
2. It matched Surveyor B (CPT) perfectly.
3. Most importantly, the "motion sensor" confirmed that this lighter atom was the one decaying with the known half-life of Lanthanum-149.

The Conclusion: Surveyor A (JYFL) had accidentally weighed the "ghost" (a long-lived excited state), while Surveyor B and this new team weighed the "real house" (the ground state).

Why Does This Matter? The Shape-Shifting City

Once they corrected the weight, the map of the neighborhood changed dramatically.

• Before: The map showed a weird, sharp "bump" in stability that didn't make sense.
• After: The bump vanished. Instead, a new "kink" appeared, which looks exactly like the pattern seen in neighboring Cerium atoms.

This "kink" is a clue about the shape of the nucleus.

• Imagine the nucleus as a ball of clay. Sometimes it's a perfect sphere. Sometimes it's squashed like a football (quadrupole deformation). Sometimes it looks like a pear (octupole deformation).
• The data suggests that around a specific number of neutrons (N=91), the Lanthanum nucleus stops being "pear-shaped" and shifts into a different shape. It's like a dancer suddenly changing from a waltz to a tango.

The Takeaway

This paper is a victory for precision. By measuring both the mass and the lifespan of the atom simultaneously, the scientists cleared up a confusing contradiction. They proved that the "bump" in the data was an illusion caused by measuring the wrong version of the atom.

Now, the map of the atomic world is clearer, and we have a better understanding of how these tiny nuclear cities change their shapes as they grow larger. It's a reminder that in science, sometimes you have to look at the same object from two different angles (mass and time) to see the whole picture.

Technical Summary

1. Problem Statement

The study addresses a significant contradiction in nuclear physics regarding the atomic mass of the neutron-rich lanthanum isotope $^{149}\text{La}$ ($Z=57, N=92$).

• The Discrepancy: Two recent high-precision mass measurements yielded conflicting results:
  • JYFL (University of Jyväläskylä): Reported a mass that resulted in a distinct "prominence" (bump) in the two-neutron separation energy ($S_{2n}$) trend for lanthanum isotopes around $N=93$. This suggested a unique structural evolution different from neighboring cerium isotopes.
  • CPT (Canadian Penning Trap at CARIBU): Reported a mass approximately 221.6 keV/$c^2$ lighter than the JYFL result. If correct, this would eliminate the $S_{2n}$ prominence and align the lanthanum trend with cerium.
• The Hypothesis: The authors hypothesized that the discrepancy arises because the JYFL measurement inadvertently identified a long-lived isomeric state rather than the ground state, while the CPT measurement (using a different production method) may have accessed the ground state.
• Context: The region around $N \approx 90$ is critical for studying octupole deformation and shape transitions. Resolving the $^{149}\text{La}$ mass is essential for understanding nuclear shell evolution and the nature of the nuclear force in this region.

2. Methodology

The authors employed a simultaneous mass-lifetime measurement technique to unambiguously identify the nuclear state.

• Instrumentation:
  • MRTOF-MS: A Multi-Reflection Time-of-Flight Mass Spectrograph at RIKEN (Japan) for high-precision mass determination.
  • $\beta$-TOF Detector: A detector capable of measuring the time-of-flight of ions and correlating them with subsequent $\beta$-decay events.
• Production Methods:
  • Ions were produced via spontaneous fission using two different sources: $^{252}\text{Cf}$ and $^{248}\text{Cm}$.
  • Measurements were conducted for both singly charged ($q=1+$) and doubly charged ($q=2+$) ions to cross-check charge-state dependencies.
• Analysis Strategy:
  • Mass Determination: Used the single-reference method with $^{149}\text{Ce}$ as the mass reference. The mass excess ($ME$) was derived from the time-of-flight (TOF) ratio relative to the reference.
  • State Identification: The team correlated the TOF signal with $\beta$-decay events. By analyzing the decay curve of the TOF-correlated events, they determined the half-life of the specific ion species detected.
  • Logic: If the detected ion corresponds to the ground state, its half-life should match the established literature value for ground-state $^{149}\text{La}$ ($\sim 1.09$ s). If it were an isomer, the half-life would differ significantly.

3. Key Results

• Mass Measurement:
  • The measured mass excess of $^{149}\text{La}$ is $-60,209.7(50)$ keV.
  • This value is 221(6) keV/$c^2$ lighter than the JYFL result and in excellent agreement with the CPT result ($-60,209.9$ keV).
  • No secondary peak corresponding to the JYFL mass value was observed in any TOF spectrum.
• Half-Life Verification:
  • The $\beta$-decay spectrum of the detected ions yielded a half-life of 0.90(13) s.
  • This is consistent with the literature value for the ground state ($1.091(34)$ s) within $1.5\sigma$.
  • This confirms that the observed peak corresponds to the ground state of $^{149}\text{La}$.
• Resolution of the Anomaly:
  • The JYFL result likely measured a long-lived isomeric state (possibly the $7/2^-$ state suggested by previous $\gamma$-ray studies), while the current work and CPT measured the true ground state.
• Impact on $S_{2n}$ Trends:
  • The previously reported "prominence" in the $S_{2n}$ plot for lanthanum isotopes disappears.
  • A new "kink" structure appears at $N \approx 92$, making the $S_{2n}$ trend of lanthanum isotopes remarkably similar to that of neighboring cerium isotopes.

4. Theoretical Interpretation

• Shell Gap Analysis: The two-neutron shell gap ($\Delta_{2n}$) plot shows a valley-like shape reaching negative values at $N=91$, indicating a significant change in shell structure.
• Shape Transition:
  • Comparison with theoretical models (specifically FRDM12) suggests a nuclear shape transition occurs around $N=91$.
  • The transition is from octupole deformation (pear-shaped) to another type of deformation (likely quadrupole/prolate).
  • The FRDM12 model predicts the disappearance of the octupole component ($\beta_3$) and a slight enhancement of the quadrupole component ($\beta_2$) at this neutron number, consistent with the observed $S_{2n}$ kink.
• Spin-Parity Assignment: The results resolve a long-standing ambiguity in the level scheme of $^{149}\text{La}$. The ground state is confirmed to be lower in energy than the $7/2^-$ state (previously thought to be the ground state in some analyses), allowing for a consistent spin-parity assignment across all experimental data.

5. Significance

• Correction of Nuclear Data: The study definitively corrects the atomic mass of $^{149}\text{La}$, removing a major anomaly in the chart of nuclides that had confused theoretical interpretations of shell evolution.
• Insight into Nuclear Forces: The findings provide crucial experimental evidence for the evolution of octupole correlations in the rare-earth region. It demonstrates that the strong octupole correlations predicted near $N=90$ weaken as neutrons are added, leading to a shape transition.
• Methodological Advancement: The work highlights the power of simultaneous mass-lifetime measurements using MRTOF-MS and $\beta$-TOF detectors. This technique is proven to be essential for distinguishing between ground states and isomers in regions where production methods (e.g., spontaneous vs. induced fission) might populate different nuclear states.
• Theoretical Validation: The results validate the FRDM12 model's prediction of shape transitions in this region and constrain future theoretical models regarding the multipole components of the nuclear force.