Einblick - Nuclear Physics - # Low-lying states of deformed 21Ne nucleus

Quantum-number projected generator coordinate method for the low-lying states of deformed 21Ne nucleus with a chiral two-nucleon-plus-three-nucleon interaction

Q: How would the results change if the three-nucleon interaction is included up to higher-order terms beyond the normal-ordering approximation used in this work?

Including higher-order terms of the three-nucleon interaction (3N) beyond the normal-ordering approximation could significantly alter the results of the quantum-number projected generator coordinate method (PGCM) calculations for the low-lying states of (^{21})Ne. The normal-ordering approximation simplifies the treatment of interactions by focusing on the most significant contributions while neglecting higher-order correlations that can arise from the 3N interaction. If these higher-order terms were included, one might expect a more accurate representation of the nuclear forces, leading to refined energy spectra and transition rates. Higher-order contributions could enhance the effective Hamiltonian's ability to capture complex correlations among nucleons, particularly in the context of odd-mass nuclei where the interplay between single-particle and collective motions is crucial. This could result in a better description of the excitation energies and the structure of low-lying states, potentially revealing new collective phenomena or modifying existing ones. Furthermore, the inclusion of these terms might help mitigate some of the limitations associated with the effective Hamiltonians derived from simpler models, leading to a more robust framework for ab initio calculations in nuclear physics.

Q: What are the potential limitations of the PGCM approach in describing the low-lying states of odd-mass nuclei, and how could these be addressed in future developments?

The PGCM approach, while powerful, has several limitations when applied to odd-mass nuclei. One significant limitation is the reliance on a single-reference state, which may not adequately capture the complex correlations present in odd-mass systems. This can lead to inaccuracies in the predicted energy spectra and transition rates, particularly in cases where the nuclear structure is highly deformed or exhibits significant collective behavior. Another limitation is the treatment of the generator coordinates, which may not fully encompass the relevant degrees of freedom necessary for a complete description of the nuclear states. The choice of collective coordinates, such as quadrupole deformation, may not capture all the essential dynamics, especially in nuclei with rich structure. To address these limitations, future developments could focus on incorporating multi-reference configurations into the PGCM framework, allowing for a more comprehensive treatment of correlations. Additionally, expanding the set of generator coordinates to include other collective modes, such as octupole or hexadecapole deformations, could enhance the model's flexibility and accuracy. Integrating PGCM with advanced computational techniques, such as the in-medium generator coordinate method (IM-GCM) or machine learning approaches, could also provide new insights and improve the predictive power of the model.

Q: What insights can the low-lying states of 21Ne provide into the nuclear structure and the interplay between single-particle and collective motions in deformed odd-mass nuclei?

The low-lying states of (^{21})Ne serve as a valuable probe into the nuclear structure, particularly in understanding the interplay between single-particle and collective motions in deformed odd-mass nuclei. The presence of odd nucleons introduces unique configurations that can significantly influence the overall nuclear behavior. The PGCM calculations reveal how these configurations interact with collective modes, such as quadrupole deformation, leading to a rich spectrum of low-lying states. The energy spectra obtained from the PGCM approach highlight the importance of both single-particle excitations and collective correlations. For instance, the lifting of Kramers's degeneracy in the HFB states indicates that the odd nucleon experiences a different potential landscape due to the collective motion of the even-even core. This interplay can lead to phenomena such as band structures, where states with similar angular momentum exhibit systematic energy patterns, reflecting the underlying collective dynamics. Moreover, the study of low-lying states in (^{21})Ne can provide insights into the role of three-nucleon interactions in enhancing quadrupole collectivity, as evidenced by the differences observed when comparing Hamiltonians with and without 3N interactions. Understanding these interactions is crucial for developing a comprehensive picture of nuclear structure, particularly in the context of nuclear reactions and the synthesis of heavier elements. Overall, the low-lying states of (^{21})Ne exemplify the complex and fascinating nature of nuclear interactions, offering a window into the fundamental principles governing nuclear structure and dynamics.

Kernkonzepte

The low-lying states of the deformed 21Ne nucleus are studied using the quantum-number projected generator coordinate method (PGCM) with a chiral two-nucleon-plus-three-nucleon (NN+3N) interaction.

Zusammenfassung

The authors report a study of the low-lying states of the deformed 21Ne nucleus within the framework of the quantum-number projected generator coordinate method (PGCM), starting from a chiral two-nucleon-plus-three-nucleon (NN+3N) interaction.

The nuclear wave functions are constructed as a linear combination of a set of axially-deformed Hartree-Fock-Bogliubov (HFB) wave functions with different quadrupole deformations. These HFB wave functions are projected onto different angular momenta and the correct neutron and proton numbers for 21Ne.

The results of calculations based on the effective Hamiltonians derived by normal-ordering the 3N interaction with respect to three different reference states, including the quantum-number projected HFB wave functions for 20Ne, 22Ne, and an ensemble of them with equal weights, are compared.

The inclusion of the three-nucleon interaction is found to significantly impact the low-lying states of 21Ne. Without the three-nucleon interaction, the energy spectrum becomes more stretched, and the quadrupole collectivity is notably reduced. The energy spectra from the Hamiltonians normal-ordered with respect to 20Ne and 22Ne are very close to each other.

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Statistiken

The contribution of the three-nucleon interaction to the energy is 80.338 MeV.
The term depending solely on the one-body density provides the predominant contribution to the energies.

Zitate

"The inclusion of the three-nucleon interaction significantly impacts the low-lying states. Without it, the energy spectrum becomes stretched, and the quadrupole collectivity is notably reduced."
"The energy spectra from the Hamiltonians normal-ordered with respect to 20Ne and 22Ne are very close to each other."

Wichtige Erkenntnisse aus

Quantum-number projected generator coordinate method for $^{21}$Ne with a chiral two-nucleon-plus-three-nucleon interaction

by W. Lin, E. F... um arxiv.org 10-02-2024

https://arxiv.org/pdf/2403.01177.pdf

$Quantum-number projected generator coordinate method for $^{21}$Ne with a chiral two-nucleon-plus-three-nucleon interaction$

Tiefere Fragen

How would the results change if the three-nucleon interaction is included up to higher-order terms beyond the normal-ordering approximation used in this work?

Including higher-order terms of the three-nucleon interaction (3N) beyond the normal-ordering approximation could significantly alter the results of the quantum-number projected generator coordinate method (PGCM) calculations for the low-lying states of (^{21})Ne. The normal-ordering approximation simplifies the treatment of interactions by focusing on the most significant contributions while neglecting higher-order correlations that can arise from the 3N interaction. If these higher-order terms were included, one might expect a more accurate representation of the nuclear forces, leading to refined energy spectra and transition rates.
Higher-order contributions could enhance the effective Hamiltonian's ability to capture complex correlations among nucleons, particularly in the context of odd-mass nuclei where the interplay between single-particle and collective motions is crucial. This could result in a better description of the excitation energies and the structure of low-lying states, potentially revealing new collective phenomena or modifying existing ones. Furthermore, the inclusion of these terms might help mitigate some of the limitations associated with the effective Hamiltonians derived from simpler models, leading to a more robust framework for ab initio calculations in nuclear physics.

What are the potential limitations of the PGCM approach in describing the low-lying states of odd-mass nuclei, and how could these be addressed in future developments?

The PGCM approach, while powerful, has several limitations when applied to odd-mass nuclei. One significant limitation is the reliance on a single-reference state, which may not adequately capture the complex correlations present in odd-mass systems. This can lead to inaccuracies in the predicted energy spectra and transition rates, particularly in cases where the nuclear structure is highly deformed or exhibits significant collective behavior.
Another limitation is the treatment of the generator coordinates, which may not fully encompass the relevant degrees of freedom necessary for a complete description of the nuclear states. The choice of collective coordinates, such as quadrupole deformation, may not capture all the essential dynamics, especially in nuclei with rich structure.
To address these limitations, future developments could focus on incorporating multi-reference configurations into the PGCM framework, allowing for a more comprehensive treatment of correlations. Additionally, expanding the set of generator coordinates to include other collective modes, such as octupole or hexadecapole deformations, could enhance the model's flexibility and accuracy. Integrating PGCM with advanced computational techniques, such as the in-medium generator coordinate method (IM-GCM) or machine learning approaches, could also provide new insights and improve the predictive power of the model.

What insights can the low-lying states of 21Ne provide into the nuclear structure and the interplay between single-particle and collective motions in deformed odd-mass nuclei?

The low-lying states of (^{21})Ne serve as a valuable probe into the nuclear structure, particularly in understanding the interplay between single-particle and collective motions in deformed odd-mass nuclei. The presence of odd nucleons introduces unique configurations that can significantly influence the overall nuclear behavior. The PGCM calculations reveal how these configurations interact with collective modes, such as quadrupole deformation, leading to a rich spectrum of low-lying states.
The energy spectra obtained from the PGCM approach highlight the importance of both single-particle excitations and collective correlations. For instance, the lifting of Kramers's degeneracy in the HFB states indicates that the odd nucleon experiences a different potential landscape due to the collective motion of the even-even core. This interplay can lead to phenomena such as band structures, where states with similar angular momentum exhibit systematic energy patterns, reflecting the underlying collective dynamics.
Moreover, the study of low-lying states in (^{21})Ne can provide insights into the role of three-nucleon interactions in enhancing quadrupole collectivity, as evidenced by the differences observed when comparing Hamiltonians with and without 3N interactions. Understanding these interactions is crucial for developing a comprehensive picture of nuclear structure, particularly in the context of nuclear reactions and the synthesis of heavier elements. Overall, the low-lying states of (^{21})Ne exemplify the complex and fascinating nature of nuclear interactions, offering a window into the fundamental principles governing nuclear structure and dynamics.