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Evidence of the Excited X(5)-like Critical-Point Symmetry Structures in 152Sm

This study utilizes high-statistics gamma-ray spectroscopy of $^{152}$ Sm to identify new excited collective bands and transition strengths that provide evidence for X(5)-like critical-point symmetry structures extending beyond the well-known low-lying spectrum, thereby offering new constraints on shape-phase transitions in the N=90 region.

Original authors: S. Basaka, S. Rajbanshi, T. Bhattacharjee, D. Kumar, A. Pal, S. S. Alam, A. Saha, A. K. Sikdar, J. Nandi, Ananya Das, Shabir Dar, S. Samanta, S. Chatterjee, R. Raut, S. S. Ghugre, A. Adhikari, Y. Sapk

Published 2026-06-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: S. Basaka, S. Rajbanshi, T. Bhattacharjee, D. Kumar, A. Pal, S. S. Alam, A. Saha, A. K. Sikdar, J. Nandi, Ananya Das, Shabir Dar, S. Samanta, S. Chatterjee, R. Raut, S. S. Ghugre, A. Adhikari, Y. Sapkota, R. Rahaman, A. Gupta, A. Bisoi, S. Sharma, S. Das, P. Das, U. Datta, I. Ray, G. Duchêne

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 solid marble, but as a squishy, dancing drop of liquid. Sometimes this drop is perfectly round, like a ball. Other times, it stretches out into a football shape. The scientists in this paper are studying a specific nucleus, Samarium-152 ( $^{152}\text{Sm}$ ), to see exactly how it dances as it changes shape.

Here is the story of their discovery, broken down into simple concepts:

The Big Idea: A "Critical Point" Dance

In physics, there's a concept called a phase transition. Think of water turning into ice. At the exact moment it freezes, it's neither fully liquid nor fully solid; it's in a "critical" state where everything is changing rapidly.

Scientists have a mathematical model called X(5) that predicts how an atomic nucleus behaves right at this "critical point" between being a round ball (spherical) and a stretched football (deformed). It's like a perfect recipe for a specific type of dance move that nuclei should do when they are in this transition zone.

For a long time, scientists knew that Samarium-152 was a great example of this dance, but they had only watched the first few steps (the lowest energy levels). They wanted to see if the nucleus kept doing this specific dance all the way up to higher, more energetic steps.

The Experiment: Shaking the Nucleus

To see these higher steps, the researchers at the Variable Energy Cyclotron Centre in India had to "excite" the nucleus. They did this by firing a beam of helium nuclei (alpha particles) at a target of Neodymium-150.

Think of this like hitting a bell with a hammer. The collision creates a new, heavier nucleus (Samarium-152) that is "vibrating" with extra energy. As this excited nucleus settles down, it releases that energy by shooting out tiny particles of light called gamma rays.

The team used a giant array of 12 super-sensitive detectors (like a high-tech camera array) to catch these gamma rays. By measuring the energy of the rays and the direction they came from, they could reconstruct the "dance steps" the nucleus took as it cooled down.

The Discovery: New Steps in the Dance

The researchers found several new "levels" or steps in the nucleus's energy ladder. They identified five distinct "bands" of energy states.

The Known Steps: They confirmed the first two bands (the ground state and the first excited state) behave exactly as the X(5) recipe predicts.
The New Steps: They found two new bands built on top of excited "zero-spin" states (states where the nucleus isn't spinning yet).

The Analogy: Imagine a staircase. The X(5) model predicts that every step up the stairs should be a specific height, and the distance between steps should follow a perfect pattern.

The scientists found that the first few steps (the ground state and the first excited band) fit the pattern perfectly.
They also found that the third and fourth bands (the new discoveries) generally follow the same pattern. It's as if the nucleus is continuing the same dance routine even when it gets very energetic.

The Twist: The Dance Isn't Perfectly Perfect

While the new bands look very much like the X(5) prediction, they aren't a 100% match.

The Height Issue: The higher steps were a bit lower than the perfect recipe predicted.
The Strength Issue: The "strength" of the transitions (how easily the nucleus jumps between steps) was weaker than the ideal model suggested.

Why? The "Finite Size" Problem.
The X(5) model is like a theoretical recipe for a nucleus that is infinitely large. But real nuclei, like Samarium-152, are small and finite.

The Metaphor: Imagine a perfect, rigid square box (the ideal model). Now, imagine a real, slightly squishy box (the real nucleus). When you bounce a ball inside the perfect box, it follows a perfect path. When you bounce it in the squishy box, the walls give a little, and the path changes slightly.
The paper explains that because the nucleus is a "finite" system (it has a limited number of particles), it can't perfectly achieve the "infinite" critical point. It's close, but the "squishiness" (finite-size effects) and the mixing of different internal configurations cause the deviations.

The Conclusion

The paper concludes that Samarium-152 is indeed a champion of the X(5) critical-point symmetry. It proves that this specific type of "shape-shifting" behavior isn't just a fluke for the lowest energy levels; it extends to higher, more complex excited states as well.

However, the nucleus isn't a perfect mathematical ideal. It is a real, physical object with finite size, and those real-world limitations cause small but noticeable differences from the theoretical "perfect" dance. This helps scientists understand that while the X(5) model is a powerful tool, real nuclei are a bit more complex and "squishy" than the simplest equations suggest.

Technical Summary: Evidence of the Excited X(5)-like Critical-Point Symmetry Structures in 152Sm

Problem Statement
The study of quantum shape-phase transitions in atomic nuclei seeks to understand the structural evolution between spherical (U(5)) and axially deformed (SU(3)) limits. The Interacting Boson Approximation (IBA) describes these limits, while critical-point symmetries (CPS), specifically X(5), provide analytic solutions for nuclei at the first-order phase transition point. While the nucleus $^{152}$ Sm is widely recognized as a benchmark for X(5) behavior in its low-lying spectrum (specifically the ground-state band and the first excited $0^+$ band, corresponding to $s=1$ and $s=2$ ), significant discrepancies exist between experimental data and ideal X(5) predictions, particularly regarding interband transition strengths. Furthermore, the spectroscopic properties of higher-lying collective excitations ( $s \geq 3$ ) in $^{152}$ Sm remain largely unexplored, limiting the understanding of how finite-size effects and configuration mixing influence the realization of critical-point symmetry in real nuclei.

Methodology
The authors investigated the positive-parity structure of $^{152}$ Sm using high-statistics $\gamma$ -ray spectroscopy. The experiment utilized the $^{150}$ Nd( $\alpha$ , 2n) $^{152}$ Sm reaction at a laboratory energy ( $E_{lab}$ ) of 26 MeV with a 10 mg/cm $^2$ enriched target.

Detection: An array of twelve Compton-suppressed HPGe clover detectors was employed, positioned at 40 $^\circ$ , 90 $^\circ$ , and 125 $^\circ$ relative to the beam axis.
Analysis: Data were sorted into $\gamma$ - $\gamma$ matrices and $\gamma$ - $\gamma$ - $\gamma$ cubes. Spin and parity assignments were determined through Directional Correlation from Oriented states (DCO) ratios ( $R_{DCO}$ ) and linear polarization ( $P$ ) measurements.
Transition Strengths: Electromagnetic transition strengths, specifically $B(E2)$ values, were deduced by combining measured branching ratios with previously reported level lifetimes.

Key Contributions and Results

Extension of the Level Scheme: The study successfully extended the level scheme of $^{152}$ Sm to include higher-lying collective bands built on excited $0^+$ states. Specifically, the authors identified and characterized band structures (labeled QB4 and QB5) built on the $0^+_3$ (1082.9 keV) and $0^+_4$ (1755.3 keV) states, respectively.
Spin-Parity Assignments: New spin-parity assignments were established for several levels, including the $2^+_5$ (1893 keV) and $4^+_5$ (2113 keV) states, utilizing DCO and polarization data. Parity-changing transitions connecting these positive-parity bands to negative-parity octupole bands were also observed.
X(5) Systematics:
- Energy Ratios: The measured excitation energy ratios $R_{4/2} = E(4^+_1)/E(2^+_1) = 3.01$ and $E(0^+_2)/E(2^+_1) = 5.62$ align closely with X(5) predictions (2.91 and 5.67, respectively).
- Higher Bands: The bands built on $0^+_3$ and $0^+_4$ were identified as the $s=3$ and $s=4$ families of the X(5) solution. The ratio of interband transition strengths, such as $B(E2: 0^+_3 \to 2^+_2) / B(E2: 0^+_3 \to 2^+_1)$ , showed satisfactory agreement with X(5) predictions (104(5) vs. 124).
- Exclusion of QB5: The band QB5 (built on the $0^+_4$ state at 1659.7 keV in some contexts, though the text identifies the $0^+_4$ bandhead at 1755.3 keV for the X(5) sequence) was excluded from the strict X(5) sequence due to the absence of expected intra-band E2 transitions and a lack of the predicted strong decay to the $s=3$ band.
Deviations from Ideal Symmetry: While the overall systematics support an X(5)-like interpretation, systematic deviations were observed for higher-lying excitations:
- Excitation energies of higher $0^+$ states were overestimated by the ideal X(5) model by approximately 300–400 keV.
- Interband $B(E2)$ transition strengths were systematically weaker than predicted (differing by a factor of roughly three in some cases).

Significance and Claims
The paper claims that the observed systematics provide evidence for excited collective structures in $^{152}$ Sm that exhibit X(5)-like characteristics, extending the known critical-point symmetry sequence beyond the well-established $s=1$ and $s=2$ families to include the $s=3$ family.

However, the authors maintain a modest stance regarding the exact nature of this symmetry. They conclude that $^{152}$ Sm should not be regarded as an exact realization of the X(5) critical-point symmetry. Instead, the observed deviations—specifically the compression of excited $0^+$ structures and reduced interband transition strengths—are attributed to:

Finite-size effects: The broadening of the phase transition due to finite boson numbers.
Configuration mixing: The mixing of competing collective degrees of freedom.
Potential shape: The influence of a softer $\beta$ potential compared to the infinite square-well potential assumed in the original X(5) formulation.

Ultimately, the results offer new experimental constraints on the manifestation of critical-point behavior in finite nuclei, suggesting that while $^{152}$ Sm lies in the immediate vicinity of the U(5)–SU(3) critical point, it resides within a transitional region where idealized symmetries are modified by nuclear structure complexities.

The Big Idea: A "Critical Point" Dance

The Experiment: Shaking the Nucleus

The Discovery: New Steps in the Dance

The Twist: The Dance Isn't Perfectly Perfect

The Conclusion

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