Abstract
The pair interaction function has been derived for the following metals: Li, Na, K, Al. It is obtained via a second order perturbation expansion of the wave functions of the conduction electrons using a self-consistent pseudo-potential. Exchange and correlations between those electrons have been ignored. Such an interaction is only valid at constant volume and depends on a single experimental parameter, namely the ionic volume. Its main features are a pronounced minimum in the vicinity of the nearest neighbours, especially marked in alkaline metals, and an asymptotic decrease of the form cos(2k{sub F}r)/r{sup 3}. This interaction gives the correct crystalline structure of these metals at 0 K as well as a good approximation of the phonon spectrum of an alkaline. The validity of the perturbation technique is discussed. We prove that the pair interaction function is correctly given to second order in the pseudo-potential despite the various approximations and errors involved by such a method. (author) [French] L'interaction de paire effective entre ions a ete calculee dans les metaux Li, Na, K et Al. Elle est obtenue par un developpement en serie de perturbation des fonctions d'onde des electrons de conduction. Le developpement est pousse au deuxieme ordre et utilise
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Pick, R
[1]
- Commissariat a l'Energie Atomique, Saclay (France). Centre d'Etudes Nucleaires
Citation Formats
Pick, R.
Study of the pair-interaction function in some normal metals; Etude de l'interaction de paire dans quelques metaux normaux.
France: N. p.,
1965.
Web.
Pick, R.
Study of the pair-interaction function in some normal metals; Etude de l'interaction de paire dans quelques metaux normaux.
France.
Pick, R.
1965.
"Study of the pair-interaction function in some normal metals; Etude de l'interaction de paire dans quelques metaux normaux."
France.
@misc{etde_20650661,
title = {Study of the pair-interaction function in some normal metals; Etude de l'interaction de paire dans quelques metaux normaux}
author = {Pick, R}
abstractNote = {The pair interaction function has been derived for the following metals: Li, Na, K, Al. It is obtained via a second order perturbation expansion of the wave functions of the conduction electrons using a self-consistent pseudo-potential. Exchange and correlations between those electrons have been ignored. Such an interaction is only valid at constant volume and depends on a single experimental parameter, namely the ionic volume. Its main features are a pronounced minimum in the vicinity of the nearest neighbours, especially marked in alkaline metals, and an asymptotic decrease of the form cos(2k{sub F}r)/r{sup 3}. This interaction gives the correct crystalline structure of these metals at 0 K as well as a good approximation of the phonon spectrum of an alkaline. The validity of the perturbation technique is discussed. We prove that the pair interaction function is correctly given to second order in the pseudo-potential despite the various approximations and errors involved by such a method. (author) [French] L'interaction de paire effective entre ions a ete calculee dans les metaux Li, Na, K et Al. Elle est obtenue par un developpement en serie de perturbation des fonctions d'onde des electrons de conduction. Le developpement est pousse au deuxieme ordre et utilise un pseudo-potentiel self-consistant. Les phenomenes d'echange et de correlations entre ces electrons ont ete negliges. L'interaction calculee n'a de sens qu'a volume constant. Elle depend d'un seul parametre experimental, le volume ionique. Elle se caracterise par un minimum prononce de l'energie de paire pour les proches voisins, surtout marque chez les alcalins. Elle decroit asymptotiquement en cos(2k{sub F}r)/r{sup 3}. Elle permet de predire la structure cristalline la plus stable a 0 K; elle donne le spectre de phonons des alcalins avec une assez bonne precision. Par ailleurs, la validite de la methode de perturbation du deuxieme ordre est discutee. On montre qu'elle donne correctement l'interaction de paire au meme ordre d'approximation, les differents defauts de la methode n'apparaissant qu'a des ordres plus eleves. (auteur)}
place = {France}
year = {1965}
month = {Jun}
}
title = {Study of the pair-interaction function in some normal metals; Etude de l'interaction de paire dans quelques metaux normaux}
author = {Pick, R}
abstractNote = {The pair interaction function has been derived for the following metals: Li, Na, K, Al. It is obtained via a second order perturbation expansion of the wave functions of the conduction electrons using a self-consistent pseudo-potential. Exchange and correlations between those electrons have been ignored. Such an interaction is only valid at constant volume and depends on a single experimental parameter, namely the ionic volume. Its main features are a pronounced minimum in the vicinity of the nearest neighbours, especially marked in alkaline metals, and an asymptotic decrease of the form cos(2k{sub F}r)/r{sup 3}. This interaction gives the correct crystalline structure of these metals at 0 K as well as a good approximation of the phonon spectrum of an alkaline. The validity of the perturbation technique is discussed. We prove that the pair interaction function is correctly given to second order in the pseudo-potential despite the various approximations and errors involved by such a method. (author) [French] L'interaction de paire effective entre ions a ete calculee dans les metaux Li, Na, K et Al. Elle est obtenue par un developpement en serie de perturbation des fonctions d'onde des electrons de conduction. Le developpement est pousse au deuxieme ordre et utilise un pseudo-potentiel self-consistant. Les phenomenes d'echange et de correlations entre ces electrons ont ete negliges. L'interaction calculee n'a de sens qu'a volume constant. Elle depend d'un seul parametre experimental, le volume ionique. Elle se caracterise par un minimum prononce de l'energie de paire pour les proches voisins, surtout marque chez les alcalins. Elle decroit asymptotiquement en cos(2k{sub F}r)/r{sup 3}. Elle permet de predire la structure cristalline la plus stable a 0 K; elle donne le spectre de phonons des alcalins avec une assez bonne precision. Par ailleurs, la validite de la methode de perturbation du deuxieme ordre est discutee. On montre qu'elle donne correctement l'interaction de paire au meme ordre d'approximation, les differents defauts de la methode n'apparaissant qu'a des ordres plus eleves. (auteur)}
place = {France}
year = {1965}
month = {Jun}
}