Abstract
An important parameter in the nuclear equation of state is the nuclear matter incompressibility. This parameter is related to the giant monopole resonance (GMR) energy. The present work concerns a simple vibrational model for calculating the GMR energy in {sup 16}O. For extrapolations to infinite nuclear matter it is necessary to use also heavier nuclei than {sup 16}O. The present model could be applicable to such systems as well. The basic idea of this model is to describe the wave function bar{Psi}> of the nucleus as a superposition of states:bar{Psi}>={Sigma}c{sub i}bar{Phi}{sup v}i>, where bar{Phi}{sup v}i> is a nuclear wave function with a specific value v{sub i} of some collective vibrational parameter. As a generator for the non-ortogonal basis (bar{Phi}{sup v}i>), a single particle shell model is used and the single particle potential gives candidates for the collective vibrational parameter. Evaluation of the state bar{Psi}> is accomplished by solving the (discrete) Hill-Wheeler equation, with Skyrme type interactions. There are as many solutions, i.e. different states bar{Psi}>, to the Hill-Wheeler equation as there are states in the basis (bar{Phi}{sup v}i>). The energy spectrum for these solutions is in its lower part approximately harmonic and the energy difference between states in this part
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Citation Formats
Hellmans, R.
A calculation of the giant monopole resonance energy in {sup 16}O.
Sweden: N. p.,
1994.
Web.
Hellmans, R.
A calculation of the giant monopole resonance energy in {sup 16}O.
Sweden.
Hellmans, R.
1994.
"A calculation of the giant monopole resonance energy in {sup 16}O."
Sweden.
@misc{etde_10124477,
title = {A calculation of the giant monopole resonance energy in {sup 16}O}
author = {Hellmans, R}
abstractNote = {An important parameter in the nuclear equation of state is the nuclear matter incompressibility. This parameter is related to the giant monopole resonance (GMR) energy. The present work concerns a simple vibrational model for calculating the GMR energy in {sup 16}O. For extrapolations to infinite nuclear matter it is necessary to use also heavier nuclei than {sup 16}O. The present model could be applicable to such systems as well. The basic idea of this model is to describe the wave function bar{Psi}> of the nucleus as a superposition of states:bar{Psi}>={Sigma}c{sub i}bar{Phi}{sup v}i>, where bar{Phi}{sup v}i> is a nuclear wave function with a specific value v{sub i} of some collective vibrational parameter. As a generator for the non-ortogonal basis (bar{Phi}{sup v}i>), a single particle shell model is used and the single particle potential gives candidates for the collective vibrational parameter. Evaluation of the state bar{Psi}> is accomplished by solving the (discrete) Hill-Wheeler equation, with Skyrme type interactions. There are as many solutions, i.e. different states bar{Psi}>, to the Hill-Wheeler equation as there are states in the basis (bar{Phi}{sup v}i>). The energy spectrum for these solutions is in its lower part approximately harmonic and the energy difference between states in this part of the spectrum gives the GMR energy E{sub GMR}. As can be seen the three main ingredients are: shell model generator, Skyrme type interaction and the Hill-Wheeler equation. They will be discussed in detail in the next section. The main subject of this work is to investigate monopole resonance (MR) generated through bulk density vibrations, but some indications of using this model for studying the importance of surfacedensity vibrations as well as coupled bulk and surface density vibrations will be given. The results obtained with this model appear to be comparable with the results Gleissl et al obtain in their density variational approach.}
place = {Sweden}
year = {1994}
month = {Nov}
}
title = {A calculation of the giant monopole resonance energy in {sup 16}O}
author = {Hellmans, R}
abstractNote = {An important parameter in the nuclear equation of state is the nuclear matter incompressibility. This parameter is related to the giant monopole resonance (GMR) energy. The present work concerns a simple vibrational model for calculating the GMR energy in {sup 16}O. For extrapolations to infinite nuclear matter it is necessary to use also heavier nuclei than {sup 16}O. The present model could be applicable to such systems as well. The basic idea of this model is to describe the wave function bar{Psi}> of the nucleus as a superposition of states:bar{Psi}>={Sigma}c{sub i}bar{Phi}{sup v}i>, where bar{Phi}{sup v}i> is a nuclear wave function with a specific value v{sub i} of some collective vibrational parameter. As a generator for the non-ortogonal basis (bar{Phi}{sup v}i>), a single particle shell model is used and the single particle potential gives candidates for the collective vibrational parameter. Evaluation of the state bar{Psi}> is accomplished by solving the (discrete) Hill-Wheeler equation, with Skyrme type interactions. There are as many solutions, i.e. different states bar{Psi}>, to the Hill-Wheeler equation as there are states in the basis (bar{Phi}{sup v}i>). The energy spectrum for these solutions is in its lower part approximately harmonic and the energy difference between states in this part of the spectrum gives the GMR energy E{sub GMR}. As can be seen the three main ingredients are: shell model generator, Skyrme type interaction and the Hill-Wheeler equation. They will be discussed in detail in the next section. The main subject of this work is to investigate monopole resonance (MR) generated through bulk density vibrations, but some indications of using this model for studying the importance of surfacedensity vibrations as well as coupled bulk and surface density vibrations will be given. The results obtained with this model appear to be comparable with the results Gleissl et al obtain in their density variational approach.}
place = {Sweden}
year = {1994}
month = {Nov}
}