玻色子-费米子系统形状相变的代数簇模型计算

IF 1.5 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Modern Physics Letters A Pub Date : 2024-04-08 DOI:10.1142/s0217732324500214
M. Ghapanvari, N. Amiri, M. A. Jafarizadeh, M. Seidi
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We schemed a solvable extended transitional Hamiltonian based on affine <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">SU</mtext></mstyle><mo stretchy=\"false\">(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math></span><span></span> Lie algebra within the framework for two-, three- and four-body algebraic cluster models that explains both regions <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>O</mi><mo stretchy=\"false\">(</mo><mn>4</mn><mo stretchy=\"false\">)</mo><mo>↔</mo><mi>U</mi><mo stretchy=\"false\">(</mo><mn>3</mn><mo stretchy=\"false\">)</mo></math></span><span></span>, <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>O</mi><mo stretchy=\"false\">(</mo><mn>7</mn><mo stretchy=\"false\">)</mo><mo>↔</mo><mi>U</mi><mo stretchy=\"false\">(</mo><mn>6</mn><mo stretchy=\"false\">)</mo></math></span><span></span> and <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>O</mi><mo stretchy=\"false\">(</mo><mn>1</mn><mn>0</mn><mo stretchy=\"false\">)</mo><mo>↔</mo><mi>U</mi><mo stretchy=\"false\">(</mo><mn>9</mn><mo stretchy=\"false\">)</mo></math></span><span></span>, respectively. We offer that this method can be used to study <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi><mi>α</mi><mo>+</mo><mi>x</mi></math></span><span></span> nucleon structures with <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>k</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></span><span></span> and <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>x</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo></math></span><span></span> in specific <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mi>x</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span><span></span> such as structures <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow></mrow><mrow><mn>9</mn></mrow></msup><mstyle><mtext mathvariant=\"normal\">Be</mtext></mstyle></math></span><span></span>, <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow></mrow><mrow><mn>9</mn></mrow></msup><mstyle><mtext mathvariant=\"normal\">B</mtext></mstyle></math></span><span></span>, <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow></mrow><mrow><mn>1</mn><mn>0</mn></mrow></msup><mstyle><mtext mathvariant=\"normal\">B</mtext></mstyle></math></span><span></span>; <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow></mrow><mrow><mn>1</mn><mn>3</mn></mrow></msup><mstyle><mtext mathvariant=\"normal\">C</mtext></mstyle></math></span><span></span>, <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow></mrow><mrow><mn>1</mn><mn>3</mn></mrow></msup><mstyle><mtext mathvariant=\"normal\">N</mtext></mstyle></math></span><span></span>, <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow></mrow><mrow><mn>1</mn><mn>4</mn></mrow></msup><mstyle><mtext mathvariant=\"normal\">N</mtext></mstyle></math></span><span></span>; <span><math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow></mrow><mrow><mn>1</mn><mn>7</mn></mrow></msup><mstyle><mtext mathvariant=\"normal\">O</mtext></mstyle></math></span><span></span>, <span><math altimg=\"eq-00016.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow></mrow><mrow><mn>1</mn><mn>7</mn></mrow></msup><mstyle><mtext mathvariant=\"normal\">F</mtext></mstyle></math></span><span></span>. Numerical extraction to the energy levels, the expectation value of the boson number operator, and the behavior of the overlap of the ground state wave function within the control parameters of this evaluated Hamiltonian are presented. The effect of the coupling of the odd particle to an even–even boson core is discussed along the shape transition and, in particular, at the critical point.</p>","PeriodicalId":18752,"journal":{"name":"Modern Physics Letters A","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic cluster model calculations for shape phase transitions of boson-fermion systems\",\"authors\":\"M. Ghapanvari, N. Amiri, M. A. Jafarizadeh, M. 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We schemed a solvable extended transitional Hamiltonian based on affine <span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mstyle><mtext mathvariant=\\\"normal\\\">SU</mtext></mstyle><mo stretchy=\\\"false\\\">(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo stretchy=\\\"false\\\">)</mo></math></span><span></span> Lie algebra within the framework for two-, three- and four-body algebraic cluster models that explains both regions <span><math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>O</mi><mo stretchy=\\\"false\\\">(</mo><mn>4</mn><mo stretchy=\\\"false\\\">)</mo><mo>↔</mo><mi>U</mi><mo stretchy=\\\"false\\\">(</mo><mn>3</mn><mo stretchy=\\\"false\\\">)</mo></math></span><span></span>, <span><math altimg=\\\"eq-00003.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>O</mi><mo stretchy=\\\"false\\\">(</mo><mn>7</mn><mo stretchy=\\\"false\\\">)</mo><mo>↔</mo><mi>U</mi><mo stretchy=\\\"false\\\">(</mo><mn>6</mn><mo stretchy=\\\"false\\\">)</mo></math></span><span></span> and <span><math altimg=\\\"eq-00004.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>O</mi><mo stretchy=\\\"false\\\">(</mo><mn>1</mn><mn>0</mn><mo stretchy=\\\"false\\\">)</mo><mo>↔</mo><mi>U</mi><mo stretchy=\\\"false\\\">(</mo><mn>9</mn><mo stretchy=\\\"false\\\">)</mo></math></span><span></span>, respectively. 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Numerical extraction to the energy levels, the expectation value of the boson number operator, and the behavior of the overlap of the ground state wave function within the control parameters of this evaluated Hamiltonian are presented. 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引用次数: 0

摘要

代数簇模型(ACM)是一种相互作用玻色子模型,它给出了簇构型的相对运动,其中所有振动和旋转自由度从一开始就存在。我们在二体、三体和四体代数簇模型的框架内,基于仿射苏(1,1)李代数设计了一个可解的扩展过渡哈密顿,分别解释了O(4)↔U(3)、O(7)↔U(6)和O(10)↔U(9)区域。我们提出,这种方法可以用来研究 kα+x 核子结构,k=2,3,4 和 x=1,2,......,特别是 x=1,2,如 9Be、9B、10B;13C、13N、14N;17O、17F 结构。报告介绍了能级的数值提取、玻色子数算子的期望值以及在此评估哈密顿控制参数范围内基态波函数的重叠行为。讨论了奇数粒子与偶偶数玻色子核的耦合在形状转变过程中的影响,特别是在临界点上的影响。
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Algebraic cluster model calculations for shape phase transitions of boson-fermion systems

The Algebraic Cluster Model (ACM) is an interacting boson model that gives the relative motion of the cluster configurations in which all vibrational and rotational degrees of freedom are present from the outset. We schemed a solvable extended transitional Hamiltonian based on affine SU(1,1) Lie algebra within the framework for two-, three- and four-body algebraic cluster models that explains both regions O(4)U(3), O(7)U(6) and O(10)U(9), respectively. We offer that this method can be used to study kα+x nucleon structures with k=2,3,4 and x=1,2,, in specific x=1,2 such as structures 9Be, 9B, 10B; 13C, 13N, 14N; 17O, 17F. Numerical extraction to the energy levels, the expectation value of the boson number operator, and the behavior of the overlap of the ground state wave function within the control parameters of this evaluated Hamiltonian are presented. The effect of the coupling of the odd particle to an even–even boson core is discussed along the shape transition and, in particular, at the critical point.

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来源期刊
Modern Physics Letters A
Modern Physics Letters A 物理-物理:核物理
CiteScore
3.10
自引率
7.10%
发文量
186
审稿时长
3 months
期刊介绍: This letters journal, launched in 1986, consists of research papers covering current research developments in Gravitation, Cosmology, Astrophysics, Nuclear Physics, Particles and Fields, Accelerator physics, and Quantum Information. A Brief Review section has also been initiated with the purpose of publishing short reports on the latest experimental findings and urgent new theoretical developments.
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