Abstract
We have presented a perturbative construction method of the periodic orbits of the time-dependent Hartree-Fock equations (TDHF). The solutions are found in the form of a power series in the amplitude of the collective motion. We have performed calculations using third order expansions to determine the splitting of two-phonon states of the low-lying octupole vibration in oxygen-16 and calcium-40. We have also investigated giant quadrupole vibrations. We had to generalize our method in order to account for the resonant coupling between the two-phonon state and one-phonon states in the continuum. This was done by introducing admixture of the resonant mode in the first order expression of the periodic orbit. Our results demonstrate that the method of quantization of periodic orbits of TDHF equation is a powerful tool to investigate the energy spectra of many-body systems. We have used our method to build the classical periodic orbits of a Skyrmion. The method, used up to second order, has been applied to the Roper resonance described in terms of monopole vibrations. To first order the method is equivalent to linear response theory and we find that the response function displays a well developed peak. We have also presented a powerful method which
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Citation Formats
Abada, Abdellatif.
Perturbative construction of the periodic orbits of the mean-field equations in nuclear physics; Construction perturbative des orbites periodiques des equations de champ moyen en physique nucleaire.
France: N. p.,
1992.
Web.
Abada, Abdellatif.
Perturbative construction of the periodic orbits of the mean-field equations in nuclear physics; Construction perturbative des orbites periodiques des equations de champ moyen en physique nucleaire.
France.
Abada, Abdellatif.
1992.
"Perturbative construction of the periodic orbits of the mean-field equations in nuclear physics; Construction perturbative des orbites periodiques des equations de champ moyen en physique nucleaire."
France.
@misc{etde_10127995,
title = {Perturbative construction of the periodic orbits of the mean-field equations in nuclear physics; Construction perturbative des orbites periodiques des equations de champ moyen en physique nucleaire}
author = {Abada, Abdellatif}
abstractNote = {We have presented a perturbative construction method of the periodic orbits of the time-dependent Hartree-Fock equations (TDHF). The solutions are found in the form of a power series in the amplitude of the collective motion. We have performed calculations using third order expansions to determine the splitting of two-phonon states of the low-lying octupole vibration in oxygen-16 and calcium-40. We have also investigated giant quadrupole vibrations. We had to generalize our method in order to account for the resonant coupling between the two-phonon state and one-phonon states in the continuum. This was done by introducing admixture of the resonant mode in the first order expression of the periodic orbit. Our results demonstrate that the method of quantization of periodic orbits of TDHF equation is a powerful tool to investigate the energy spectra of many-body systems. We have used our method to build the classical periodic orbits of a Skyrmion. The method, used up to second order, has been applied to the Roper resonance described in terms of monopole vibrations. To first order the method is equivalent to linear response theory and we find that the response function displays a well developed peak. We have also presented a powerful method which uses the knowledge of periodic orbits to construct a collective Bohr-type Hamiltonian. We have applied it to the case of monopole vibrations of the Skyrmion and derived the corresponding first anharmonic terms in the collective Hamiltonian.}
place = {France}
year = {1992}
month = {Jun}
}
title = {Perturbative construction of the periodic orbits of the mean-field equations in nuclear physics; Construction perturbative des orbites periodiques des equations de champ moyen en physique nucleaire}
author = {Abada, Abdellatif}
abstractNote = {We have presented a perturbative construction method of the periodic orbits of the time-dependent Hartree-Fock equations (TDHF). The solutions are found in the form of a power series in the amplitude of the collective motion. We have performed calculations using third order expansions to determine the splitting of two-phonon states of the low-lying octupole vibration in oxygen-16 and calcium-40. We have also investigated giant quadrupole vibrations. We had to generalize our method in order to account for the resonant coupling between the two-phonon state and one-phonon states in the continuum. This was done by introducing admixture of the resonant mode in the first order expression of the periodic orbit. Our results demonstrate that the method of quantization of periodic orbits of TDHF equation is a powerful tool to investigate the energy spectra of many-body systems. We have used our method to build the classical periodic orbits of a Skyrmion. The method, used up to second order, has been applied to the Roper resonance described in terms of monopole vibrations. To first order the method is equivalent to linear response theory and we find that the response function displays a well developed peak. We have also presented a powerful method which uses the knowledge of periodic orbits to construct a collective Bohr-type Hamiltonian. We have applied it to the case of monopole vibrations of the Skyrmion and derived the corresponding first anharmonic terms in the collective Hamiltonian.}
place = {France}
year = {1992}
month = {Jun}
}