M. Ghapanvari, N. Amiri, M. A. Jafarizadeh, M. Seidi
{"title":"玻色子-费米子系统形状相变的代数簇模型计算","authors":"M. Ghapanvari, N. Amiri, M. A. Jafarizadeh, M. Seidi","doi":"10.1142/s0217732324500214","DOIUrl":null,"url":null,"abstract":"<p>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 <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":"20 1","pages":""},"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. Seidi\",\"doi\":\"10.1142/s0217732324500214\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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 <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\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-04-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Modern Physics Letters A\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1142/s0217732324500214\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Modern Physics Letters A","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1142/s0217732324500214","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
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 Lie algebra within the framework for two-, three- and four-body algebraic cluster models that explains both regions , and , respectively. We offer that this method can be used to study nucleon structures with and in specific such as structures , , ; , , ; , . 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.
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.