• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Master's Dissertation
DOI
10.11606/D.43.2009.tde-23042010-123947
Document
Author
Full name
Débora Machado Andrade
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2009
Supervisor
Committee
Hussein, Mahir Saleh (President)
Chamon, Luiz Carlos
Oliveira, Manuel Maximo Bastos Malheiro de
Title in Portuguese
Desigualdade de Jensen aplicada à probabilidade de fusão nuclear
Keywords in Portuguese
Análise matemática
Física nuclear
Fusão nuclear
Reações nucleares
Abstract in Portuguese
Discutimos o problema de tunelamento quântico em sistemas físicos com muitos graus de liberdade. Aplicamos a desigualdade de Jensen ao cálculo analítico semi-clássico da probabilidade de fusão entre dois núcleos, onde consideramos graus de liberdade intrínsecos. Utilizamos diferentes barreiras de potencial de tunelamento e trabalhamos analiticamente com cada uma delas. Provamos matematicamente então a validade de uma desigualdade de caráter geral que relaciona a probabilidade de tunelamento de um sistema com vários graus de liberdade com a probabilidade de tunelamento do mesmo sistema aproximado para um modelo unidimensional, ou seja, com todos os graus de liberdade, exceto o radial, sendo tomados em média. Tal desigualdade já é conhecida empiricamente, através de cálculo numérico para diferentes modelagens, e tem particular relevância no problema da fusão de íons pesados a energias próximas da barreira de potencial. Mostramos que uma desigualdade envolvendo reflexão sobre a barreira de potencial, derivada por R. Johnson e C. Goebel, e utilizada para estimar o efeito de breakup no espalhamento elástico de núcleos halo, é uma consequ ência imediata da desigualdade de Jensen. Uma generalização das idéias contidas no referido trabalho de Johnson e Goebel, possibilitada pela aplicação da desigualdade de Jensen, enriquece a compreensão acerca de limites superiores e inferiores para a probabilidade de tunelamento quântico em sistemas com vários graus de liberdade.
Title in English
Jensen inequality applied to nuclear fusion probability
Keywords in English
Mathematical analysis
Nuclear fusion
Nuclear physics
Nuclear reactions
Abstract in English
We discuss the quantum tunneling problem in physical systems involving many degrees of freedom. We apply the Jensen inequality to the semi-classical analytical probability of fusion between two nuclei, where we considered intrinsic degrees of freedom. We employed different tunneling potential barriers and analytically worked on each of them. We have mathematically proven then the validity of a general inequality which relates the tunneling probability for a sub-system of the many-degrees-of-freedom system when compared to the sub-system alone (with the coupling to the reservoir being averaged). Such inequality is already empirically well-known through numerical calculations for different models, and has a particular relevance in the problem of heavy ion fusion at sub-barrier energies. We have shown that an inequality derived by R. Johnson and C. Goebel, which involves the reflection over a potential barrier and was used to estimate the breakup effect on the elastic scattering of halo nuclei, is but an immediate consequence of the Jensen inequality. A generalization of the ideas contained in the refered work of Johnson and Goebel, which was made possible by using the Jensen inequality, enriches the comprehension towards upper and lower boundaries for tunneling probabilities in systems with many degrees of freedom.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
andrade.pdf (607.57 Kbytes)
Publishing Date
2010-05-12
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
Centro de Informática de São Carlos
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2021. All rights reserved.