Nuclear Shape-Phase Transitions and the Sextic Oscillator

This review delves into the utilization of a sextic oscillator within the degree of freedom of the Bohr Hamiltonian to elucidate critical-point solutions in nuclei, with a specific emphasis on the critical point associated with the shape variable, governing transitions from spherical to deformed nuc...

Descripción completa

Detalles Bibliográficos
Autores: Lévai, Géza, Arias Carrasco, José Miguel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/151481
Acceso en línea:https://hdl.handle.net/11441/151481
https://doi.org/10.3390/sym15112059
Access Level:acceso abierto
Palabra clave:Nuclear structure models and methods
Collective models
Bohr Hamiltonian
Quasi-exactly solvable models
Sextic potential
id ES_548b899c8a3421ad69ade88d5ffbd5af
oai_identifier_str oai:idus.us.es:11441/151481
network_acronym_str ES
network_name_str España
repository_id_str
spelling Nuclear Shape-Phase Transitions and the Sextic OscillatorLévai, GézaArias Carrasco, José MiguelNuclear structure models and methodsCollective modelsBohr HamiltonianQuasi-exactly solvable modelsSextic potentialThis review delves into the utilization of a sextic oscillator within the degree of freedom of the Bohr Hamiltonian to elucidate critical-point solutions in nuclei, with a specific emphasis on the critical point associated with the shape variable, governing transitions from spherical to deformed nuclei. To commence, an overview is presented for critical-point solutions E(5), X(5), X(3), Z(5), and Z(4). These symmetries, encapsulated in simple models, all model the degree of freedom using an infinite square-well (ISW) potential. They are particularly useful for dissecting phase transitions from spherical to deformed nuclear shapes. The distinguishing factor among these models lies in their treatment of the degree of freedom. These models are rooted in a geometrical context, employing the Bohr Hamiltonian. The review then continues with the analysis of the same critical solutions but with the adoption of a sextic potential in place of the ISW potential within the degree of freedom. The sextic oscillator, being quasi-exactly solvable (QES), allows for the derivation of exact solutions for the lower part of the energy spectrum. The outcomes of this analysis are examined in detail. Additionally, various versions of the sextic potential, while not exactly solvable, can still be tackled numerically, offering a means to establish benchmarks for criticality in the transitional path from spherical to deformed shapes. This review extends its scope to encompass related papers published in the field in the past 20 years, contributing to a comprehensive understanding of critical-point symmetries in nuclear physics. To facilitate this understanding, a map depicting the different regions of the nuclide chart where these models have been applied is provided, serving as a concise summary of their applications and implications in the realm of nuclear structure.Junta de Andalucía P20-01247, US-1380840Ministerio de Ciencia e Innovación (MICIN). España PID2019-104002GB-C22, PID2020-114687GBI00, PID2022-136228NB-C22European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) PID2019-104002GB-C22, PID2020-114687GBI00, PID2022-136228NB-C22National Research, Development and Innovation Office (NKFIH).Hungary K128729MDPIFísica Atómica, Molecular y NuclearJunta de AndalucíaMinisterio de Ciencia e Innovación (MICIN). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)National Research, Development and Innovation Office (NKFIH).Hungary2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/151481https://doi.org/10.3390/sym15112059reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésSymmetry Basel, 15 (11), 2059.P20-01247US-1380840PID2019-104002GB-C22PID2020-114687GBI00PID2022-136228NB-C22K128729https://doi.org/10.3390/sym15112059info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1514812026-06-17T12:51:07Z
dc.title.none.fl_str_mv Nuclear Shape-Phase Transitions and the Sextic Oscillator
title Nuclear Shape-Phase Transitions and the Sextic Oscillator
spellingShingle Nuclear Shape-Phase Transitions and the Sextic Oscillator
Lévai, Géza
Nuclear structure models and methods
Collective models
Bohr Hamiltonian
Quasi-exactly solvable models
Sextic potential
title_short Nuclear Shape-Phase Transitions and the Sextic Oscillator
title_full Nuclear Shape-Phase Transitions and the Sextic Oscillator
title_fullStr Nuclear Shape-Phase Transitions and the Sextic Oscillator
title_full_unstemmed Nuclear Shape-Phase Transitions and the Sextic Oscillator
title_sort Nuclear Shape-Phase Transitions and the Sextic Oscillator
dc.creator.none.fl_str_mv Lévai, Géza
Arias Carrasco, José Miguel
author Lévai, Géza
author_facet Lévai, Géza
Arias Carrasco, José Miguel
author_role author
author2 Arias Carrasco, José Miguel
author2_role author
dc.contributor.none.fl_str_mv Física Atómica, Molecular y Nuclear
Junta de Andalucía
Ministerio de Ciencia e Innovación (MICIN). España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
National Research, Development and Innovation Office (NKFIH).Hungary
dc.subject.none.fl_str_mv Nuclear structure models and methods
Collective models
Bohr Hamiltonian
Quasi-exactly solvable models
Sextic potential
topic Nuclear structure models and methods
Collective models
Bohr Hamiltonian
Quasi-exactly solvable models
Sextic potential
description This review delves into the utilization of a sextic oscillator within the degree of freedom of the Bohr Hamiltonian to elucidate critical-point solutions in nuclei, with a specific emphasis on the critical point associated with the shape variable, governing transitions from spherical to deformed nuclei. To commence, an overview is presented for critical-point solutions E(5), X(5), X(3), Z(5), and Z(4). These symmetries, encapsulated in simple models, all model the degree of freedom using an infinite square-well (ISW) potential. They are particularly useful for dissecting phase transitions from spherical to deformed nuclear shapes. The distinguishing factor among these models lies in their treatment of the degree of freedom. These models are rooted in a geometrical context, employing the Bohr Hamiltonian. The review then continues with the analysis of the same critical solutions but with the adoption of a sextic potential in place of the ISW potential within the degree of freedom. The sextic oscillator, being quasi-exactly solvable (QES), allows for the derivation of exact solutions for the lower part of the energy spectrum. The outcomes of this analysis are examined in detail. Additionally, various versions of the sextic potential, while not exactly solvable, can still be tackled numerically, offering a means to establish benchmarks for criticality in the transitional path from spherical to deformed shapes. This review extends its scope to encompass related papers published in the field in the past 20 years, contributing to a comprehensive understanding of critical-point symmetries in nuclear physics. To facilitate this understanding, a map depicting the different regions of the nuclide chart where these models have been applied is provided, serving as a concise summary of their applications and implications in the realm of nuclear structure.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/151481
https://doi.org/10.3390/sym15112059
url https://hdl.handle.net/11441/151481
https://doi.org/10.3390/sym15112059
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Symmetry Basel, 15 (11), 2059.
P20-01247
US-1380840
PID2019-104002GB-C22
PID2020-114687GBI00
PID2022-136228NB-C22
K128729
https://doi.org/10.3390/sym15112059
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869408191317540864
score 15,300719

Similares en LA Referencia