Tetrahedral Ground State and Lambda Impurity Effects in $^{80}$Zr and $^{81}_{\Lambda}$Zr Using the Multidimensionally Constrained Relativistic Hartree-Bogoliubov Model

Core Concepts

Theoretical calculations using the multidimensionally constrained relativistic Hartree-Bogoliubov model predict a tetrahedral ground state for $^{80}$Zr, coexisting with prolate and axial-octupole shape isomers, and explore how the binding of a Lambda hyperon affects the structure of $^{81}_{\Lambda}$Zr.

Abstract

• Bibliographic Information: Yang, D., & Rong, Y. (2024). Tetrahedral shape and Lambda impurity effect in 80Zr with a multidimensionally constrained relativistic Hartree-Bogoliubov model. arXiv preprint arXiv:2411.02946v1.

• Research Objective: This study investigates the presence of a tetrahedral ground state in the nucleus $^{80}$Zr and explores the impact of adding a Lambda hyperon on the structure of the resulting hypernucleus, $^{81}_{\Lambda}$Zr, using the multidimensionally constrained relativistic Hartree-Bogoliubov (MDC-RHB) model.

• Methodology: The authors employ the MDC-RHB model with various density-dependent effective interactions to calculate the potential energy surfaces (PESs) of $^{80}$Zr and $^{81}_{\Lambda}$Zr. By analyzing the minima and saddle points on these PESs, they determine the favored shapes of these nuclei. Additionally, they calculate the Lambda separation energy (SΛ) and the overlap integral (Ioverlap) between the Lambda and nucleon densities to understand the binding strength of the Lambda hyperon.

• Key Findings: The calculations consistently predict a tetrahedral ground state for $^{80}$Zr, regardless of the chosen effective interaction, alongside prolate and axial-octupole shape isomers. The addition of a Lambda hyperon does not significantly alter the overall shape of the nucleus, and $^{81}_{\Lambda}$Zr also exhibits a tetrahedral ground state. The binding strength of the Lambda hyperon is found to be dependent on the specific orbital it occupies and the chosen effective interaction. Notably, the tetrahedral shape exhibits the strongest binding for the Lambda hyperon in the 1/2−[101] orbital.

• Main Conclusions: The study provides strong theoretical evidence for a tetrahedral ground state in $^{80}$Zr and demonstrates the persistence of this shape in the hypernucleus $^{81}_{\Lambda}$Zr. The findings highlight the importance of considering both axial and reflection asymmetry in nuclear structure calculations and provide valuable insights into the role of Lambda hyperons in modifying nuclear properties.

• Significance: This research contributes to the understanding of exotic nuclear shapes and the behavior of hypernuclei. The confirmation of a tetrahedral ground state in $^{80}$Zr has significant implications for nuclear structure theory and provides a benchmark for refining theoretical models. The study of Lambda impurity effects in tetrahedral nuclei opens new avenues for exploring the interplay between hyperons and nuclear structure.

• Limitations and Future Research: The study is limited to the MDC-RHB model and a specific set of effective interactions. Further investigations using different theoretical approaches and a wider range of interactions would be beneficial to confirm the robustness of the findings. Additionally, experimental studies aimed at confirming the predicted tetrahedral ground state in $^{80}$Zr and exploring the properties of $^{81}_{\Lambda}$Zr would be highly valuable.

Stats

The ground state of 80Zr exhibits a tetrahedral shape with β20 = 0.000 and β32 = 0.192 when calculated using the PK1 effective interaction.
The binding energy of the Λ particle in the 1/2+[000] state is approximately 22 MeV.
The difference in charge radii (∆rc) between 81ΛZr and 80Zr ranges from -0.04 fm to 0.01 fm when the Λ particle occupies the s1/2 orbit.

Quotes

"Among nuclei predicted to exhibit a tetrahedral shape, 80Zr serves as a prime example."
"Therefore, this work investigates the shape of 80Zr and the Λ hyperon impurity with tetrahedral shapes."
"Our calculations also show the presence of other possible shapes (spherical, oblate, and triaxial) at slightly higher energies on the PES, suggesting a potential coexistence of shapes."
"This consistency reinforces the conclusion that 80Zr exhibits a tetrahedral ground state, independent of the specific effective interaction employed."

Key Insights Distilled From

Tetrahedral shape and Lambda impurity effect in $^{80}$Zr with a multidimensionally constrained relativistic Hartree-Bogoliubov model

by Dan Yang, Yu... at arxiv.org 11-06-2024

https://arxiv.org/pdf/2411.02946.pdf

Deeper Inquiries

What experimental techniques could be used to confirm the predicted tetrahedral ground state of $^{80}$Zr and study the properties of $^{81}_{\Lambda}$Zr?

Confirming the tetrahedral ground state of $^{80}$Zr and studying $^{81}_{\Lambda}$Zr experimentally poses significant challenges due to their exotic nature and short lifetimes. However, some potential experimental techniques include:
For $^{80}$Zr:

High-precision mass measurements: As highlighted in the paper, recent mass measurements revealed $^{80}$Zr to be more strongly bound than anticipated. Further refined mass measurements with increased precision could provide stronger evidence for or against the tetrahedral shape by comparing them to theoretical predictions for different nuclear shapes.
Coulomb excitation and lifetime measurements: By colliding a beam of $^{80}$Zr ions with a heavy target at specific energies, one can excite the nucleus to higher energy levels. Measuring the de-excitation gamma rays, particularly their energies and lifetimes, can reveal information about the nuclear shape. Tetrahedral nuclei are expected to exhibit specific rotational bands and transition probabilities distinct from other shapes.
Laser spectroscopy: This technique can provide precise measurements of nuclear charge radii and electric quadrupole moments, which are sensitive to nuclear deformation. Comparing experimental values with theoretical predictions for different shapes can offer insights into the ground state configuration.
For $^{81}_{\Lambda}$Zr:

Heavy-ion induced reactions with strangeness production: Producing $^{81}_{\Lambda}$Zr requires reactions involving the creation of a Λ hyperon. This can be achieved by colliding heavy ions at high energies. For example, a beam of $^{82}$Kr could be collided with a beryllium target. The challenge lies in achieving sufficient production yields and efficiently separating the hypernucleus from other reaction products.
Gamma-ray spectroscopy of hypernuclear decay: Once produced, $^{81}_{\Lambda}$Zr will eventually decay, emitting gamma rays. Measuring the energies and angular correlations of these gamma rays can provide information about the energy levels and structure of the hypernucleus, shedding light on the influence of the Λ hyperon on the tetrahedral shape.
These experiments require cutting-edge facilities with high beam intensities, efficient detection systems, and advanced analysis techniques.

Could the presence of other hyperons, such as the Sigma or Xi hyperons, further influence the shape and stability of 80Zr?

Yes, the presence of other hyperons like Sigma (Σ) or Xi (Ξ) hyperons could significantly influence the shape and stability of $^{80}$Zr. Here's why:

Different interactions: Σ and Ξ hyperons interact with nucleons differently than Λ hyperons. They experience different spin-orbit interactions and have different coupling strengths to various meson fields. These differences can lead to distinct modifications of the nuclear potential energy surface, potentially favoring different shapes compared to the Λ hyperon.
Additional degrees of freedom: Introducing Σ or Ξ hyperons adds additional degrees of freedom to the nuclear system. This can lead to more complex interplay between the hyperon and the core nucleons, potentially resulting in exotic shapes not observed in conventional nuclei or even Λ hypernuclei.
Influence on shell structure: Hyperons can modify the underlying single-particle energy levels (shell structure) of the nucleus. This is because they introduce new attractive or repulsive forces that can shift the energy levels and alter their ordering. These changes in shell structure can impact the stability and deformation of the nucleus.
For example, theoretical studies suggest that Σ hyperons can induce significant shape polarization in some nuclei, leading to highly deformed configurations. Similarly, Ξ hyperons, being heavier and experiencing weaker Pauli blocking, can penetrate deeper into the nuclear core, potentially influencing the nuclear shape more strongly than Λ hyperons.
Exploring these effects requires sophisticated theoretical models that accurately describe the interactions of different hyperons with nucleons. Experimentally, studying such systems presents even greater challenges due to the difficulty in producing and characterizing hypernuclei containing Σ or Ξ hyperons.

How does the understanding of tetrahedral nuclei impact our understanding of neutron star structure and the formation of heavy elements in astrophysical environments?

While tetrahedral nuclei like the predicted $^{80}$Zr are not directly involved in neutron star structure or heavy element formation, understanding their properties and the underlying physics can have indirect implications for these astrophysical phenomena:
Neutron Star Structure:

Nuclear matter properties: Studying exotic nuclear shapes, including tetrahedral configurations, provides valuable insights into the behavior of nuclear matter under extreme conditions of density and isospin asymmetry. These insights can inform and constrain theoretical models of nuclear matter, which are crucial for understanding the composition and properties of neutron star cores.
Nuclear pasta phases: Theoretical calculations suggest that at the crust-core boundary of neutron stars, nuclear matter can exhibit complex shapes dubbed "nuclear pasta phases" due to their resemblance to various pasta types. These phases arise from the competition between nuclear attraction and Coulomb repulsion. Understanding the factors governing the formation and stability of exotic shapes in finite nuclei can contribute to a better understanding of these pasta phases and their impact on neutron star properties.
Heavy Element Formation:

Nuclear structure far from stability: Exploring exotic nuclei, including those with tetrahedral shapes, expands our knowledge of nuclear structure far from stability. This knowledge is essential for understanding the rapid neutron capture process (r-process), a key mechanism for synthesizing heavy elements in explosive astrophysical environments like supernovae and neutron star mergers.
Nuclear reactions and reaction rates: The properties of nuclei, including their shapes and stability, influence the rates of nuclear reactions involved in the r-process. While tetrahedral nuclei themselves might not be directly involved, understanding the factors governing nuclear deformation and stability can improve our understanding of reaction networks and nucleosynthesis pathways in astrophysical environments.
In summary, while not directly observed in neutron stars or heavy element formation processes, studying tetrahedral nuclei and other exotic nuclear structures contributes to a more comprehensive understanding of nuclear physics under extreme conditions. This knowledge, in turn, can refine our models of neutron star structure and heavy element synthesis, ultimately leading to a deeper understanding of these fascinating astrophysical phenomena.