The Ritz variational-perturbational method is developed for calculating relativistic energy levels of ions embedded in plasmas. With a review of the one-electron atom problem, hydrogen-like ions are studied, and He-like and Li-like ions are studied at the effective charge approximation. For the outer shell excited states, the results agree well with other theoretical results and experimental data. PACS Nos.: 52.25.Vy, 52.40.Mj, 52.27.Gr. Résumé : Nous développons la méthode variation-perturbation de Ritz pour calculer les niveaux d'énergie relativistes d'ions dans du plasma. Suite à une revue du problème de l'atome à un électron, nous étudions les atomes de type hydrogène, alors que les ions de type He et Li sont étudiés dans l'approximation de la charge effective. Pour les états dans les couches extérieures, les résultats agréent avec l'expérience et d'autres théories. [Traduit par la Rédaction]
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