Coupled-channel analysis of high-energy electron scattering by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Sm</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>152</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Er

Cardman, L. S.; Dowell, D. H.; Gulbranson, R. L.; Ravenhall, D. G.; Mercer, R.L.

doi:10.1103/physrevc.18.1388

Cited by 15 publications

(4 citation statements)

References 16 publications

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“…With exception of the term which refers to the ground state of the target nucleus, (α = g) these terms represent dispersion corrections to elastic and inelastic electron scattering. Some of the couplings to the bound-state excitations have been included in the literature in the calculation of dispersion corrections to elastic electron scattering by means of explicit coupled channel equations [21], [22], but explicit coupling to the continuum states, which contain the effect of the (e,e'N) reactions on the elastic or inelastic electron scattering, and which arise from the terms γ = β in the sum in Eq. (3.7a), have up to now been ignored.…”

Section: Correctionsmentioning

confidence: 99%

Inclusion of virtual nuclear excitations in the formulation of the(e,e′N)reaction

Rawitscher

1997

Phys. Rev. C

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A wave-function framework for the theory of the (e,e'N) reaction is presented in order to justify the use of coupled channel equations in the usual Feynman matrix element. The overall wave function containing the electron and nucleon coordinates is expanded in a basis set of eigenstates of the nuclear Hamiltonian, which contain both bound states as well as continuum states.. The latter have an ingoing nucleon with a variable momentum Q incident on the daughter nucleus as a target, with as many outgoing channels as desirable.The Dirac Eqs. for the electron part of the wave function acquire inhomogeneous terms, and require the use of distorted electron Green's functions for their solutions. The condition that the asymptotic wave function contain only the appropriate momentum Q k for the outgoing nucleon, which corresponds to the electron momentum k through energy conservation, is achieved through the use of the steepest descent saddle point method, commonly used in three-body calculations. I. INTRODUCTION.The commonly accepted starting point for writing down the (e,e'N) matrix element is a Feynman diagram. The Feynman diagram consists of two vertices: one in which a nucleon is detached from the target nucleus, and the other which represents the electron-nucleon interaction, which scatters the nucleon into the appropriate final state. In 1970 Gross and Lipperheide [1] wrote down such a matrix element, and Boffi and collaborators [2] based their work [3] on this approach. Walecka and collaborators [4], as well as Donnelly and co-workers [5] also start from this type of approach. Additional refinements were gradually introduced. The optical model, initially used to describe the nucleon-nucleus distortion [2], was later refined by using the Random Phase Approximation for the nuclear excitations [6], electron spin variables were introduced [5], the relativistic nucleon-nucleus interaction was considered [7], and two-step processes (or coupled channel effects) were included [8], [9].Many good reviews of the (e,e'N) formalism exist, the latest one being due to Kelly [10].The objective of the present paper is to formulate the (e,e' N) reaction in terms of a wave function expansion, rather than Feynman-diagram matrix elements This treatment permits one a) to understand the assumptions which underlie the coupled-channel treatment of the hadron-nucleus channels, which are commonly inserted into the Feynman matrix elements, b) to include the effect of the (e,e' N) channels into the treatment of dispersion corrections to electron-nucleus scattering, c) to provide a foundation for the treatment of the (e,e' 2N) processes.The wave function method described here is similar in nature to the expansions employed in three-body reaction theory [11], [12], [13]. In particular, the saddle-point method is used to obtain the asymptotic limit of the wave function for the two particles in the continuum (the electron and the emitted nucleon), thus making contact with the matrix element written conventionally for the Feynman diagram mentioned ...

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Section: Correctionsmentioning

confidence: 99%

Inclusion of virtual nuclear excitations in the formulation of the(e,e′N)reaction

Rawitscher

1997

Phys. Rev. C

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“…3 1 and r rms experimental values provided in [25][26][27]. We have also analyzed electron-nucleus elastic and inelastic scattering data, and experimental transition densities, obtained from [18][19][20][21][22][23][24]. Finally, also the experimental energy-level structure of the low-lying quadrupole states was included in the data set.…”

Section: Experimental and Theoretical Results For Electron-nucleus Sc...mentioning

confidence: 99%

“…However, it is necessary to impose the limits of application of the DWBA itself. A comparison between the results of CC and DWBA calculations, for the scattering of electrons on 152 Sm and 166 Er, was performed in [22]. The difference between these theoretical calculations was found to be small for scattering involving the l = 0 and 2 multipole contributions, and significantly larger for cases with l = 4 and 6, where sequential excitations can occur.…”

Section: Electron-nucleus Scatteringmentioning

confidence: 99%

Transition densities in the context of the generalized rotation-vibration model

Botero

Chamon

Carlson

2017

J. Phys. G: Nucl. Part. Phys.

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A collective model for the description of heavy-ion nuclear structure, called the generalized rotation-vibration model (GRVM), was proposed in an earlier paper. In the present work, we use this model to study transition densities for the low-lying states of several nuclei. In order to evaluate the accuracy of the model, we test the GRVM transition densities in the description of experimental results corresponding to elastic and inelastic electron–nucleus scattering. We also compare the GRVM densities with those arising from microscopic Dirac–Hartree–Bogoliubov theoretical calculations. The GRVM transition densities can be used in future works to calculate folding-type coupling potentials in coupled-channel data analyses for heavy-ion systems.

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“…. dos núcleos 32 S,40 Ca,52 Cr,58 Ni e 70 Ge. Na coluna da direita são apresentados os respectivos fatores de forma elásticos calculados dentro da aproximação PWBA.Figura5.0.9: O mesmo da figura 5.0.8, para os núcleos 88 Sr, 108 Pd, 120 Sn, 152 Sm e 208 Pb.…”

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Cálculo de canais acoplados com o modelo generalizado de rotação-vibração

Botero¹

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No presente trabalho, foram realizados cálculos de canais acoplados (CC) para reações nucleares que envolvem íons pesados. Nesses cálculos assumimos o Modelo Generalizado de Rotação-Vibração (GRVM), que é um modelo coletivo de estrutura nuclear desenvolvido recentemente [1]. Fizemos algumas modificações no GRVM, que tornam o modelo mais simples e consistente com o objeto de estudo. Assumimos esse modelo de estrutura nuclear para calcular as densidades de transição de carga e de matéria entre estados nucleares. Relacionamos as densidades de transição de carga teóricas com resultados experimentais de espalhamento elástico e inelástico de sistemas elétron-núcleo, o que permitiu testar a precisão do GRVM. Como mais um teste que reforça a confiabilidade do GRVM, comparamos os respectivos resultados com aqueles obtidos com o modelo de estrutura nuclear microscópico de Dirac-Hartree-Bogoliubov (DHB). Dentro do contexto do GRVM, também foi desenvolvido o formalismo de cálculos CC. As densidades de transição, anteriormente calculadas, foram usadas para obter, com precisão, potenciais de acoplamento (próprios de cálculos CC), considerando o método de duplaconvolução descrito em [2]. Em todos esses cálculos, as densidades nucleares foram expandidas até segunda ordem na deformação e foram levados em conta valores finitos para as difusividades das densidades, os quais são desprezados na maioria dos modelos de estrutura nuclear. Foi elaborado um programa computacional para o cálculo de seções de choque de diversos processos, o qual foi utilizado na analise de dados de espalhamentos elástico e inelástico de sistemas de núcleos pesados, bem como de dados de fusão nuclear.

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Coupled-channel analysis of high-energy electron scattering bySm152andEr

Cited by 15 publications

References 16 publications

Inclusion of virtual nuclear excitations in the formulation of the(e,e′N)reaction

Inclusion of virtual nuclear excitations in the formulation of the(e,e′N)reaction

Transition densities in the context of the generalized rotation-vibration model

Cálculo de canais acoplados com o modelo generalizado de rotação-vibração

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