Core Concepts

The alpha-decay half-lives of heavy, neutron-rich isotopes are correlated with the symmetry energy of nuclear matter, with softer symmetry energy leading to longer half-lives.

Abstract

**Bibliographic Information:**Choi, Y.-B., Gil, H., Hyun, C. H., & Lee, C.-H. (2024). Correlation between alpha-decay half-lives and symmetry energy. arXiv preprint arXiv:2407.19647v2.**Research Objective:**This study investigates the correlation between alpha-decay half-lives and the stiffness of symmetry energy in heavy, neutron-rich nuclei using the Korea-IBS-Daegu-SKKU (KIDS) nuclear models.**Methodology:**The researchers calculated alpha-decay half-lives for even-even isotopes with atomic numbers 84 ≤ Z ≤ 92 using the semiclassical WKB approximation. They employed the density-dependent cluster model with density distributions obtained from four different KIDS models (A-D), each representing varying stiffness of the symmetry energy. The models were validated against experimental binding energies and quadrupole deformation data.**Key Findings:**- The calculated half-lives were generally consistent with experimental data.
- A clear correlation was observed between the predicted half-lives and the stiffness of the symmetry energy. Nuclei modeled with softer symmetry energy (KIDS-D) exhibited longer half-lives compared to those with stiffer symmetry energy (KIDS-A).
- This correlation is attributed to the influence of symmetry energy on neutron distribution within the nucleus. Softer symmetry energy leads to a higher concentration of neutrons in the core, affecting the tunneling barrier and increasing the half-life.
- An interesting finding was the reduced model dependence of half-lives in nuclei with a neutron number of N=142, suggesting a unique characteristic of this neutron number in heavy nuclei.

**Main Conclusions:**The study demonstrates a significant correlation between alpha-decay half-lives and the symmetry energy of nuclear matter, particularly in neutron-rich heavy isotopes. This correlation arises from the impact of symmetry energy on the distribution of neutrons within the nucleus, influencing the alpha-decay process.**Significance:**This research provides valuable insights into the role of symmetry energy in nuclear structure and alpha decay. It suggests that alpha-decay studies, alongside neutron skin thickness measurements, can offer complementary constraints on the density dependence of symmetry energy, a crucial factor in understanding nuclear matter properties and neutron star characteristics.**Limitations and Future Research:**The study primarily focused on even-even nuclei. Further research could explore the impact of symmetry energy on alpha decay in odd-A nuclei. Additionally, investigating the specific behavior of N=142 nuclei and its implications for nuclear structure could provide valuable insights.

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The ratio of half-lives calculated with the KIDS-D model (soft symmetry energy) to those with the KIDS-A model (stiff symmetry energy) ranged from 1.2 to 1.5 for most isotopes.
The neutron skin thickness of 208Pb calculated with KIDS-A was 0.235 fm, while for KIDS-D it was 0.168 fm, indicating a significant sensitivity to symmetry energy.

Quotes

Key Insights Distilled From

by Yong-Beom Ch... at **arxiv.org** 10-15-2024

Deeper Inquiries

This correlation could significantly impact our understanding of nucleosynthesis, particularly in neutron-rich environments like supernovae and neutron star mergers. Here's how:
r-process Calculations: The r-process (rapid neutron capture process) is responsible for the production of roughly half of the elements heavier than iron. The accuracy of r-process calculations relies heavily on precise nuclear physics inputs, including alpha-decay half-lives. Since the symmetry energy significantly influences these half-lives, especially in neutron-rich nuclei, incorporating this correlation into r-process models could lead to more accurate predictions of elemental abundances.
Neutron Star Mergers: The recent observation of gravitational waves and electromagnetic counterparts from neutron star mergers has provided a wealth of information about these events. The correlation between alpha-decay half-lives and symmetry energy could help us better understand the nuclear reactions occurring during these mergers, leading to insights about the formation of heavy elements and the properties of matter at extreme densities.
Nuclear Equation of State: The symmetry energy is a crucial component of the nuclear equation of state, which describes the properties of nuclear matter. By studying alpha-decay half-lives, we gain an indirect probe of the symmetry energy at densities relevant to neutron stars. This can help constrain the equation of state and improve our understanding of neutron star structure and evolution.
Overall, this correlation provides a valuable link between nuclear physics experiments and astrophysical observations, potentially leading to a more complete picture of nucleosynthesis and the nature of dense matter.

Yes, several other nuclear properties can be used to further validate the KIDS models, especially in the context of alpha decay:
Charge Radii and Neutron Skin Thickness: The distribution of protons and neutrons within a nucleus directly impacts alpha decay. Comparing the model predictions for charge radii and neutron skin thickness (the difference between neutron and proton radii) with experimental data, particularly for heavy, neutron-rich nuclei, can provide a stringent test of the models' accuracy.
Alpha-decay Spectroscopy: Beyond half-lives, the energy and angular distribution of emitted alpha particles (alpha-decay spectroscopy) offer valuable information about the structure of the parent and daughter nuclei. Comparing theoretical predictions of these spectroscopic properties with experimental data can further validate the models.
Cluster Emission Probabilities: The preformation factor, which represents the probability of finding a preformed alpha particle within the parent nucleus, is a crucial input for alpha-decay calculations. The KIDS models could be used to calculate cluster emission probabilities for other light nuclei (like deuterons or tritons), and these predictions could be compared with experimental data to assess the models' accuracy.
Giant Resonances: Giant resonances are collective excitations of the nucleus that depend on the nuclear matter distribution and the effective nucleon-nucleon interaction. Studying the properties of giant resonances, such as their energies and widths, can provide insights into the nuclear equation of state and further validate the KIDS models.
By examining these additional nuclear properties, we can gain a more comprehensive understanding of the strengths and limitations of the KIDS models, particularly in their application to alpha decay and related phenomena.

The influence of neutron distribution on alpha-decay half-lives highlights a broader theme in quantum mechanics: the spatial arrangement of particles within a system can significantly impact its properties and behavior. Here are some other quantum phenomena influenced by particle arrangement:
Superconductivity: In conventional superconductors, electrons form Cooper pairs, which can move through the material with zero resistance. The spatial arrangement of atoms in the crystal lattice and the resulting electron-phonon interactions play a crucial role in the formation of Cooper pairs and the emergence of superconductivity.
Quantum Hall Effect: The quantum Hall effect occurs in two-dimensional electron systems subjected to strong magnetic fields. The quantized values of Hall resistance are directly related to the spatial arrangement of electrons into Landau levels, demonstrating the profound influence of particle arrangement on electrical conductivity.
Bose-Einstein Condensation: Bose-Einstein condensation (BEC) is a state of matter where a large fraction of bosons occupy the lowest quantum state. The spatial confinement of the bosons plays a crucial role in achieving the low temperatures and high densities required for BEC.
Molecular Properties: In chemistry, the spatial arrangement of atoms within a molecule (its molecular geometry) dictates its polarity, reactivity, and other chemical properties. This arrangement determines the overlap of electron orbitals, influencing bond strength and molecular behavior.
Nuclear Reactions: Beyond alpha decay, the spatial arrangement of protons and neutrons within the nucleus influences other nuclear reactions, such as fission and fusion. The probability of these reactions occurring depends on the overlap of nuclear wave functions, which is sensitive to the spatial distribution of nucleons.
These examples demonstrate that the spatial arrangement of particles, whether electrons in a solid, atoms in a molecule, or nucleons in a nucleus, can have profound and often unexpected consequences for the behavior of quantum systems. This underscores the importance of considering spatial distribution when studying quantum phenomena across various fields.

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