Abstract
A unified theory for the spectra of nuclei with closed shells, based on the elementary particle-hole excitation of these systems, is applied to a study of carbon-12, oxygen-16 and calcium-40. Two approximations are made. The first consists in diagonalizing the residual two-body interaction in a limited sub-space having one particle and one hole configurations. Its validity depends on the high energy necessary for exciting a particle-hole pair. The second approximation consists in re-summing the infinite sub-series of the particle-hole diagrams. It is equivalent to the Hartree-Fock method depending on the time, or to Quasi-Boson method. Its domain of validity in the nuclear case is not thoroughly Understood. The summed diagrams are preponderant at the high density limit, when the nuclear density is about unity. The violation of the Pauli principle in this approximation is only justified if the number of excited pairs is small with respect to the number of particle states available; in the case of light nuclei the degeneracies of the shells are small. Nevertheless this approximation, which postulates the existence of an average nuclear field, varying slowly with time with respect to the nucleons periods has the merit of being self-consistent, of giving orthogonal proper states in
More>>
Gillet, V
[1]
- Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires
Citation Formats
Gillet, V.
Spectra theory for nuclei with closed shells (1962); Theorie des spectres des noyaux a couches completes (1962).
France: N. p.,
1962.
Web.
Gillet, V.
Spectra theory for nuclei with closed shells (1962); Theorie des spectres des noyaux a couches completes (1962).
France.
Gillet, V.
1962.
"Spectra theory for nuclei with closed shells (1962); Theorie des spectres des noyaux a couches completes (1962)."
France.
@misc{etde_20757674,
title = {Spectra theory for nuclei with closed shells (1962); Theorie des spectres des noyaux a couches completes (1962)}
author = {Gillet, V}
abstractNote = {A unified theory for the spectra of nuclei with closed shells, based on the elementary particle-hole excitation of these systems, is applied to a study of carbon-12, oxygen-16 and calcium-40. Two approximations are made. The first consists in diagonalizing the residual two-body interaction in a limited sub-space having one particle and one hole configurations. Its validity depends on the high energy necessary for exciting a particle-hole pair. The second approximation consists in re-summing the infinite sub-series of the particle-hole diagrams. It is equivalent to the Hartree-Fock method depending on the time, or to Quasi-Boson method. Its domain of validity in the nuclear case is not thoroughly Understood. The summed diagrams are preponderant at the high density limit, when the nuclear density is about unity. The violation of the Pauli principle in this approximation is only justified if the number of excited pairs is small with respect to the number of particle states available; in the case of light nuclei the degeneracies of the shells are small. Nevertheless this approximation, which postulates the existence of an average nuclear field, varying slowly with time with respect to the nucleons periods has the merit of being self-consistent, of giving orthogonal proper states in the non-physical state of the mass centre, and of improving the calculation of the summation rules. In order to determine and to limit the role of phenomenology in the results obtained using these approximations, a maximum amount of experimental data is calculated. By applying method of least squares to fourteen energy levels of oxygen and carbon, the region of optimum agreement in the effective interaction parameters is determined. This region is in part a function of the numerical approximations made. We hope that it will keep its significance when the theory is improved. It is compatible with certain characteristics of free nucleon-nucleon scattering. The present research favours the second approximation which alone leads to a region of optimum agreement identical for both carbon and oxygen. An excellent general agreement is obtained with the known spectra of these two nuclei. The importance of higher order terms in the calculation of the 3{sup -} and 5{sup -} collective states for calcium 40 is demonstrated; furthermore it is possible to explain these levels only by the second approximation. Certain forecasts are made using the effective forces thus found. (author) [French] On applique une theorie unifiee des spectres des noyaux a couches completes, fondee sur les excitations elementaires particule-trou de ces systemes, a l'etude du carbone 12, de l'oxygene i6 et du calcium.40. Deux approximations sont utilisees. La premiere consiste a diagonaliser l'interaction residuelle a deux corps dans un sous-espace limite de configurations a une particule et un trou. Sa validite repose sur l'energie importante exigee pour l'excitation d'une paire particule-trou. La seconde approximation consiste a resommer la sous-serie infinie des diagrammes particule-trou. Elle est equivalente a la methode de Hartree-Fock dependante du temps ou a la methode des Quasi-Bosons. Son domaine de validite, dans le cas nucleaire, n'est pas bien compris. Les diagrammes sommes sont preponderants a la limite des fortes densites, alors que la densite nucleaire est de l'ordre de l'unite. La violation des Principe de Pauli, dans cette approximation, n'est justifiee que si le nombre de paires excitees est petit par rapport au nombre d'etats de particule disponibles; or, dans les noyaux legers les degenerescences des couches sont petites. Neanmoins cette approximation qui postule l'existence d'un champ nucleaire moyen, lentement variable dans le temps par rapport aux periodes des nucleons a le merite d'etre self-consistante, de donner des etats propres orthogonaux a l'etat non physique du centre de masse et d'ameliorer le calcul des regles de somme. Pour determiner et limiter le role de la phenomenologie danns les resultats obtenus avec ces approximations on calcule un nombre maximum de faits experimentaux. Une recherche aux moindres carres portant sur quatorze niveaux de l'oxygene et du carbone determine la region d'accord optimum dans l'espace des parametres de l'interaction effective. Cette region est en partie une fonction des approximations numeriques utilisees. On espere qu'elle conservera une signification avec les ameliorations de la theorie. Elle est compatible avec certaines caracteristiques de la diffusion nucleon-nucleon libre. Cette recherche est en faveur de la seconde approximation qui seule conduit a une region d'accord optimum qui soit identique dans le carbone et l'oxygene. On obtient un accord general remarquablement bon avec les spectres connus de ces deux noyaux. Pour le calcium 40 on met en evidence l'importance de termes d'ordre superieur dans le calcul des etats collectifs 3{sup -} et 5{sup -}; par ailleurs seule l'approximation II permet d'expliquer ces niveaux. Des predictions sont faites avec les forces effectives ainsi obtenues. (auteur)}
place = {France}
year = {1962}
month = {Jul}
}
title = {Spectra theory for nuclei with closed shells (1962); Theorie des spectres des noyaux a couches completes (1962)}
author = {Gillet, V}
abstractNote = {A unified theory for the spectra of nuclei with closed shells, based on the elementary particle-hole excitation of these systems, is applied to a study of carbon-12, oxygen-16 and calcium-40. Two approximations are made. The first consists in diagonalizing the residual two-body interaction in a limited sub-space having one particle and one hole configurations. Its validity depends on the high energy necessary for exciting a particle-hole pair. The second approximation consists in re-summing the infinite sub-series of the particle-hole diagrams. It is equivalent to the Hartree-Fock method depending on the time, or to Quasi-Boson method. Its domain of validity in the nuclear case is not thoroughly Understood. The summed diagrams are preponderant at the high density limit, when the nuclear density is about unity. The violation of the Pauli principle in this approximation is only justified if the number of excited pairs is small with respect to the number of particle states available; in the case of light nuclei the degeneracies of the shells are small. Nevertheless this approximation, which postulates the existence of an average nuclear field, varying slowly with time with respect to the nucleons periods has the merit of being self-consistent, of giving orthogonal proper states in the non-physical state of the mass centre, and of improving the calculation of the summation rules. In order to determine and to limit the role of phenomenology in the results obtained using these approximations, a maximum amount of experimental data is calculated. By applying method of least squares to fourteen energy levels of oxygen and carbon, the region of optimum agreement in the effective interaction parameters is determined. This region is in part a function of the numerical approximations made. We hope that it will keep its significance when the theory is improved. It is compatible with certain characteristics of free nucleon-nucleon scattering. The present research favours the second approximation which alone leads to a region of optimum agreement identical for both carbon and oxygen. An excellent general agreement is obtained with the known spectra of these two nuclei. The importance of higher order terms in the calculation of the 3{sup -} and 5{sup -} collective states for calcium 40 is demonstrated; furthermore it is possible to explain these levels only by the second approximation. Certain forecasts are made using the effective forces thus found. (author) [French] On applique une theorie unifiee des spectres des noyaux a couches completes, fondee sur les excitations elementaires particule-trou de ces systemes, a l'etude du carbone 12, de l'oxygene i6 et du calcium.40. Deux approximations sont utilisees. La premiere consiste a diagonaliser l'interaction residuelle a deux corps dans un sous-espace limite de configurations a une particule et un trou. Sa validite repose sur l'energie importante exigee pour l'excitation d'une paire particule-trou. La seconde approximation consiste a resommer la sous-serie infinie des diagrammes particule-trou. Elle est equivalente a la methode de Hartree-Fock dependante du temps ou a la methode des Quasi-Bosons. Son domaine de validite, dans le cas nucleaire, n'est pas bien compris. Les diagrammes sommes sont preponderants a la limite des fortes densites, alors que la densite nucleaire est de l'ordre de l'unite. La violation des Principe de Pauli, dans cette approximation, n'est justifiee que si le nombre de paires excitees est petit par rapport au nombre d'etats de particule disponibles; or, dans les noyaux legers les degenerescences des couches sont petites. Neanmoins cette approximation qui postule l'existence d'un champ nucleaire moyen, lentement variable dans le temps par rapport aux periodes des nucleons a le merite d'etre self-consistante, de donner des etats propres orthogonaux a l'etat non physique du centre de masse et d'ameliorer le calcul des regles de somme. Pour determiner et limiter le role de la phenomenologie danns les resultats obtenus avec ces approximations on calcule un nombre maximum de faits experimentaux. Une recherche aux moindres carres portant sur quatorze niveaux de l'oxygene et du carbone determine la region d'accord optimum dans l'espace des parametres de l'interaction effective. Cette region est en partie une fonction des approximations numeriques utilisees. On espere qu'elle conservera une signification avec les ameliorations de la theorie. Elle est compatible avec certaines caracteristiques de la diffusion nucleon-nucleon libre. Cette recherche est en faveur de la seconde approximation qui seule conduit a une region d'accord optimum qui soit identique dans le carbone et l'oxygene. On obtient un accord general remarquablement bon avec les spectres connus de ces deux noyaux. Pour le calcium 40 on met en evidence l'importance de termes d'ordre superieur dans le calcul des etats collectifs 3{sup -} et 5{sup -}; par ailleurs seule l'approximation II permet d'expliquer ces niveaux. Des predictions sont faites avec les forces effectives ainsi obtenues. (auteur)}
place = {France}
year = {1962}
month = {Jul}
}