Determining the Ground State for Superheavy Nuclei from the Deformed Relativistic Hartree–Bogoliubov Theory in Continuum
The deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc) has garnered significant attention for its ability to describe the properties of nuclei across the entire nuclear chart, from light to heavy nuclei, including both stable and exotic ones. As part of ongoing efforts to construct...
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2024-12-01
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| author | Sibo Wang Peng Guo Cong Pan |
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| description | The deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc) has garnered significant attention for its ability to describe the properties of nuclei across the entire nuclear chart, from light to heavy nuclei, including both stable and exotic ones. As part of ongoing efforts to construct a mass table using the DRHBc theory, determining the ground states of nuclei is a crucial task in the systematic studies of deformed nuclei. In this work, a strategy for identifying the ground state in the superheavy nuclei region is proposed and evaluated, by taking <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><mo>=</mo><mn>134</mn></mrow></semantics></math></inline-formula> and 135 isotopes as examples. First, we examine how the step size of the initial quadrupole deformation parameter, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>β</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>, affects the pattern of the potential energy curves (PECs) and the determination of the ground state. Our findings indicate that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>β</mi><mn>2</mn></msub><mo>=</mo><mn>0.05</mn></mrow></semantics></math></inline-formula> producing smooth and well-defined PECs while maintaining an acceptable numerical cost. Next, we explore the convergence of PECs with respect to the angular momentum cutoff, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>J</mi><mi>max</mi></msub></semantics></math></inline-formula>. Based on the results, we recommend using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mi>max</mi></msub><mo>=</mo><mn>31</mn><mo>/</mo><mn>2</mn><mo>ℏ</mo></mrow></semantics></math></inline-formula>, especially for nuclei with competing oblate and prolate minima. Finally, we conclude that the accurate identification of the ground state can be achieved by performing unconstrained calculations around the minima of the PECs. |
| format | Article |
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| spelling | doaj-art-607e8ef0316741a6907ddfd18d6cc2ef2025-08-20T02:57:17ZengMDPI AGParticles2571-712X2024-12-01741139114910.3390/particles7040070Determining the Ground State for Superheavy Nuclei from the Deformed Relativistic Hartree–Bogoliubov Theory in ContinuumSibo Wang0Peng Guo1Cong Pan2Chongqing Key Laboratory for Strongly Coupled Physics, Department of Physics, Chongqing University, Chongqing 401331, ChinaState Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, ChinaDepartment of Physics, Anhui Normal University, Wuhu 241000, ChinaThe deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc) has garnered significant attention for its ability to describe the properties of nuclei across the entire nuclear chart, from light to heavy nuclei, including both stable and exotic ones. As part of ongoing efforts to construct a mass table using the DRHBc theory, determining the ground states of nuclei is a crucial task in the systematic studies of deformed nuclei. In this work, a strategy for identifying the ground state in the superheavy nuclei region is proposed and evaluated, by taking <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><mo>=</mo><mn>134</mn></mrow></semantics></math></inline-formula> and 135 isotopes as examples. First, we examine how the step size of the initial quadrupole deformation parameter, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>β</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>, affects the pattern of the potential energy curves (PECs) and the determination of the ground state. Our findings indicate that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>β</mi><mn>2</mn></msub><mo>=</mo><mn>0.05</mn></mrow></semantics></math></inline-formula> producing smooth and well-defined PECs while maintaining an acceptable numerical cost. Next, we explore the convergence of PECs with respect to the angular momentum cutoff, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>J</mi><mi>max</mi></msub></semantics></math></inline-formula>. Based on the results, we recommend using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mi>max</mi></msub><mo>=</mo><mn>31</mn><mo>/</mo><mn>2</mn><mo>ℏ</mo></mrow></semantics></math></inline-formula>, especially for nuclei with competing oblate and prolate minima. Finally, we conclude that the accurate identification of the ground state can be achieved by performing unconstrained calculations around the minima of the PECs.https://www.mdpi.com/2571-712X/7/4/70superheavy nucleideformed relativistic Hartree–Bogoliubov theory in continuumpotential energy curvedeformation |
| spellingShingle | Sibo Wang Peng Guo Cong Pan Determining the Ground State for Superheavy Nuclei from the Deformed Relativistic Hartree–Bogoliubov Theory in Continuum Particles superheavy nuclei deformed relativistic Hartree–Bogoliubov theory in continuum potential energy curve deformation |
| title | Determining the Ground State for Superheavy Nuclei from the Deformed Relativistic Hartree–Bogoliubov Theory in Continuum |
| title_full | Determining the Ground State for Superheavy Nuclei from the Deformed Relativistic Hartree–Bogoliubov Theory in Continuum |
| title_fullStr | Determining the Ground State for Superheavy Nuclei from the Deformed Relativistic Hartree–Bogoliubov Theory in Continuum |
| title_full_unstemmed | Determining the Ground State for Superheavy Nuclei from the Deformed Relativistic Hartree–Bogoliubov Theory in Continuum |
| title_short | Determining the Ground State for Superheavy Nuclei from the Deformed Relativistic Hartree–Bogoliubov Theory in Continuum |
| title_sort | determining the ground state for superheavy nuclei from the deformed relativistic hartree bogoliubov theory in continuum |
| topic | superheavy nuclei deformed relativistic Hartree–Bogoliubov theory in continuum potential energy curve deformation |
| url | https://www.mdpi.com/2571-712X/7/4/70 |
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