Magic Number <i>N</i> = 350 Predicted by the Deformed Relativistic Hartree-Bogoliubov Theory in Continuum: <i>Z</i> = 136 Isotopes as an Example

Magic Number <i>N</i> = 350 Predicted by the Deformed Relativistic Hartree-Bogoliubov Theory in Continuum: <i>Z</i> = 136 Isotopes as an Example

The investigation of magic numbers for nuclei in the hyperheavy region <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>Z</mi><mo>></mo><mn>120<...

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Bibliographic Details
Main Authors:	Wei-Jian Liu, Chen-Jun Lv, Peng Guo, Cong Pan, Sibo Wang, Xin-Hui Wu
Format:	Article
Language:	English
Published:	MDPI AG 2024-11-01
Series:	Particles
Subjects:	relativistic density functional theory deformed relativistic Hartree-Bogoliubov theory in continuum magic number hyperheavy nuclei
Online Access:	https://www.mdpi.com/2571-712X/7/4/65
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Summary:	The investigation of magic numbers for nuclei in the hyperheavy region <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>Z</mi><mo>></mo><mn>120</mn><mo>)</mo></mrow></semantics></math></inline-formula> is an interesting topic. The neutron magic number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>350</mn></mrow></semantics></math></inline-formula> is carefully validated by the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), via analysing even-even nuclei around <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>350</mn></mrow></semantics></math></inline-formula> of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><mo>=</mo><mn>136</mn></mrow></semantics></math></inline-formula> isotopes in detail. Nuclei with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><mo>=</mo><mn>136</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>340</mn><mo>≤</mo><mi>N</mi><mo>≤</mo><mn>360</mn></mrow></semantics></math></inline-formula> are all found to be spherical in their ground states. A big drop of the two-neutron separation energy <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mrow><mn>2</mn><mi>n</mi></mrow></msub></semantics></math></inline-formula> is observed from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>350</mn></mrow></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>352</mn></mrow></semantics></math></inline-formula> in the isotopic chain of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Z</mi><mo>=</mo><mn>136</mn></mrow></semantics></math></inline-formula>, and a peak of the two-neutron gap <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>δ</mi><mrow><mn>2</mn><mi>n</mi></mrow></msub></semantics></math></inline-formula> appears at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>350</mn></mrow></semantics></math></inline-formula>. There exists a big shell gap above <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>350</mn></mrow></semantics></math></inline-formula> around the spherical regions of single-neutron levels for nucleus with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>Z</mi><mo>=</mo><mn>136</mn><mo>,</mo><mi>N</mi><mo>=</mo><mn>350</mn><mo>)</mo></mrow></semantics></math></inline-formula>. These evidences from the DRHBc theory support <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>350</mn></mrow></semantics></math></inline-formula> to be a neutron magic number in the hyperheavy region.
ISSN:	2571-712X