E1, E2, M1, and M2 transitions in the nickel isoelectronicsequence

Abstract

A relativistic many-body method is developed to calculate energy and transition rates for multipole transitions in many-electron ions. This method is based on relativistic many-body perturbation theory (RMBPT), agrees with MCDF calculations in lowest order, includes all second-order correlation corrections, and includes corrections from negative-energy states. Reduced matrix elements, oscillator strengths, and transition rates are calculated for electric-dipole (E1) and electric-quadrupole (E2) transitions, and magneticdipole (M1) and magnetic-quadrupole (M2) transitions in Ni-like ions with nuclear charges ranging from Z = 30 to 100. The calculations start from a 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order E1, M1, E2, and M2 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations.Résumé : Nous développons une méthode relativiste à N corps pour calculer l'énergie et les taux de transitions multiples dans les atomes multi-électroniques. Cette méthode, qui est basée sur la théorie perturbative relativiste (RMBPT), est en accord avec les calculs MCDF à l'ordre le plus bas, inclut toutes les corrections de corrélation du second ordre et les corrections pour les états d'énergie négative. Nous calculons les éléments de matrice réduits, les forces d'oscillateur et les taux de transition pour les transitions dipolaires électriques (E1), dipolaires magnétiques (M1), quadripolaires électriques (E2) et quadripolaires magnétiques (M2) dans les ions de type Ni avec charges nucléaires dans le domaine Z = 30-100. Le calcul démarre avec un potentiel Dirac-Fock 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 . Nous utilisons les perturbation au premier ordre pour obtenir les coefficients de couplage intermédiaire et au deuxième ordre RMBPT pour obtenir les éléments de matrice. Les contributions des états d'énergie négative sont inclues dans les éléments de matrice E1, M1, E2 et M2. Nous comparons nos énergies et taux de transition avec les résultats expérimentaux et avec les résultats calculés par d'autre sauteurs.[Traduit par la Rédaction]

Correlation and relativistic effects in actinide ions

“…[13] for calculation of energies, in Refs. [6,[13][14][15][16][17][18][19] for calculation of multipole matrix elements for transitions from excited states to the ground state, and in Refs. [6,[20][21][22] for calculation of multipole matrix elements for transitions between excited states.…”

Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, and M3) transition wavelengths and rates between 3l−14l′ excited and ground states in nickel-like ions

“…We refer to a set of states of the same parity and the same J as a complex of states. Strong mixing for the 3l j 4l ′ j ′ (J) hole-particle states was discussed in many papers (see, for example, [33,39]). It should be noted that the 3l j 5l ′ j ′ (J) states are less mixed than the 3l j 4l ′ j ′ (J) states.…”

“…Reduced matrix elements, oscillator strengths, and transition rates into the ground state for all allowed and forbidden electric-and magnetic-dipole and electric-and magnetic-quadrupole transitions (E1, M1, E2, M2) in Ni-like ions were presented by Hamasha et al in Ref. [33]. Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, M3) transition wavelengths and rates between 3l −1 4l ′ excited and ground states in nickel-like ions were recently reported by Safronova et al in Ref.…”

The importance of EBIT data for Z-pinch plasma diagnostics

“…The energies for the excited states for the trans itions 3l-4l', 3l-5l'', and 3l-6l''' as well as radiative transition probabilities in Ni-like W were also determined to second order in Relativistic Many Body Perturbation Theory (RMBPT) [18][19][20]. The calculations start from a clos ed-shell Dirac-Fock potential, and include second-order Coulomb a nd Breit-C oulomb interactions.…”