skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, and M3) transition wavelengths and rates between 3l{sup -1}4l' excited and ground states in nickel-like ions

Abstract

Wavelengths, transition rates, and line strengths are calculated for the 76 possible multipole (E1, M1, E2, M2, E3, and M3) transitions between the excited 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 1}4l, and 3s3p{sup 6}3d{sup 1}4l and the ground 3s{sup 2}3p{sup 6}3d{sup 1} states in Ni-like ions with the nuclear charges ranging from Z = 30 to 100. The relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in hole-particle systems. This method is based on relativistic many-body perturbation theory, agrees with MCDF calculations in lowest-order, includes all second-order correlation corrections, and includes corrections from negative energy states. The calculations start from a 1s{sup 2}2s{sup 2}2p{sup 6}3s{sup 2}3p{sup 6}3d{sup 1} Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and the 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, M2, E3, and M3 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. As a result, we present wavelengths and transition rates data for the selected transitions that include the 76 possiblemore » multipole (E1, M1, E2, M2, E3, and M3) transitions between the excited 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 1}4l, and 3s3p{sup 6}3d{sup 1}4l states and the ground 3s{sup 2}3p{sup 6}3d{sup 1} state in Ni-like ions. Trends of the line strengths for the 76 multipole transitions and oscillator strengths for the 13 E1 transitions as function of Z are illustrated graphically. The Z-dependence of the energy splitting for all triplet terms of the 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 1}4l, and 3s3p{sup 6}3d{sup 1}4l configurations are shown in the range of Z = 30-100.« less

Authors:
 [1];  [2];  [3];  [4]
  1. Physics Department, University of Nevada, Reno, NV 89557 (United States). E-mail: usafrono@nd.edu
  2. Physics Department, University of Nevada, Reno, NV 89557 (United States)
  3. Physics Department, Hashemite University, Zerga (Jordan)
  4. Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States)
Publication Date:
OSTI Identifier:
20761890
Resource Type:
Journal Article
Resource Relation:
Journal Name: Atomic Data and Nuclear Data Tables; Journal Volume: 92; Journal Issue: 1; Other Information: DOI: 10.1016/j.adt.2005.09.001; PII: S0092-640X(05)00053-7; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CORRECTIONS; E1-TRANSITIONS; E2-TRANSITIONS; E3-TRANSITIONS; EXCITED STATES; GROUND STATES; INTERMEDIATE COUPLING; M1-TRANSITIONS; M2-TRANSITIONS; M3-TRANSITIONS; MANY-BODY PROBLEM; MATRIX ELEMENTS; NEGATIVE ENERGY STATES; NICKEL IONS; NUCLEAR DATA COLLECTIONS; OSCILLATOR STRENGTHS; PERTURBATION THEORY; RELATIVISTIC RANGE

Citation Formats

Safronova, U.I., Safronova, A.S., Hamasha, S.M., and Beiersdorfer, P.. Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, and M3) transition wavelengths and rates between 3l{sup -1}4l' excited and ground states in nickel-like ions. United States: N. p., 2006. Web. doi:10.1016/j.adt.2005.09.001.
Safronova, U.I., Safronova, A.S., Hamasha, S.M., & Beiersdorfer, P.. Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, and M3) transition wavelengths and rates between 3l{sup -1}4l' excited and ground states in nickel-like ions. United States. doi:10.1016/j.adt.2005.09.001.
Safronova, U.I., Safronova, A.S., Hamasha, S.M., and Beiersdorfer, P.. Sun . "Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, and M3) transition wavelengths and rates between 3l{sup -1}4l' excited and ground states in nickel-like ions". United States. doi:10.1016/j.adt.2005.09.001.
@article{osti_20761890,
title = {Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, and M3) transition wavelengths and rates between 3l{sup -1}4l' excited and ground states in nickel-like ions},
author = {Safronova, U.I. and Safronova, A.S. and Hamasha, S.M. and Beiersdorfer, P.},
abstractNote = {Wavelengths, transition rates, and line strengths are calculated for the 76 possible multipole (E1, M1, E2, M2, E3, and M3) transitions between the excited 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 1}4l, and 3s3p{sup 6}3d{sup 1}4l and the ground 3s{sup 2}3p{sup 6}3d{sup 1} states in Ni-like ions with the nuclear charges ranging from Z = 30 to 100. The relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in hole-particle systems. This method is based on relativistic many-body perturbation theory, agrees with MCDF calculations in lowest-order, includes all second-order correlation corrections, and includes corrections from negative energy states. The calculations start from a 1s{sup 2}2s{sup 2}2p{sup 6}3s{sup 2}3p{sup 6}3d{sup 1} Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and the 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, M2, E3, and M3 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. As a result, we present wavelengths and transition rates data for the selected transitions that include the 76 possible multipole (E1, M1, E2, M2, E3, and M3) transitions between the excited 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 1}4l, and 3s3p{sup 6}3d{sup 1}4l states and the ground 3s{sup 2}3p{sup 6}3d{sup 1} state in Ni-like ions. Trends of the line strengths for the 76 multipole transitions and oscillator strengths for the 13 E1 transitions as function of Z are illustrated graphically. The Z-dependence of the energy splitting for all triplet terms of the 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 1}4l, and 3s3p{sup 6}3d{sup 1}4l configurations are shown in the range of Z = 30-100.},
doi = {10.1016/j.adt.2005.09.001},
journal = {Atomic Data and Nuclear Data Tables},
number = 1,
volume = 92,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}
  • Wavelengths, transition rates, and line strengths are calculated for the 76 possible multipole (E1, M1, E2, M2, E3, M3) transitions between the excited 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 10}4l, and 3s3p{sup 6}3d{sup 10}4l and the ground 3s{sup 2}3p{sup 6}3d{sup 10} states in Ni-like ions with the nuclear charges ranging from Z = 30 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in hole-particle systems. This method is based on relativistic many-body perturbation theory, agrees with MCDF calculations in lowest-order, includes all second-order correlation correctionsmore » and includes corrections from negative energy states. The calculations start from a 1s{sup 2}2s{sup 2}2p{sup 6}3s{sup 2}3p{sup 6}3d{sup 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, M2, E3, and M3 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. As a result, we present wavelengths and transition rates data for the selected transitions that includes the 76 possible multipole (E1, M1, E2, M2, E3, M3) transitions between the excited 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 10}4l, and 3s3p{sup 6}3d{sup 10}4l states and the ground 3s{sup 2}3p{sup 6}3d{sup 10} state in Ni-like ions. Trends of the line strengths for the 76 multipole transitions and oscillator strengths for the 13 E1 transitions as function of Z are illustrated graphically. The Z dependence of the energy splitting for all triplet terms of the 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 10}4l, and 3s3p{sup 6}3d{sup 10}4l configurations are shown in the range of Z = 30-100.« less
  • 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-multipole (dipole (E1), quadrupole (E2), and octupole (E3)) and magnetic-multipole (dipole (M1), quadrupole (M2), and octupole (M3)) transitions between 3l{sup -1}5l{prime} excited and ground states in Ni-like ions with nuclear charges ranging from Z = 30 to 100. The calculations start from amore » 1s{sup 2}s{sup 2}2p{sup 6}3s{sup 2}3p{sup 6}3d{sup 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. A detailed discussion of the various contributions to the dipole matrix elements and energy levels is given for nickel-like tungsten (Z = 74). The contributions from negative-energy states are included in the second order E1, M1, E2, M2, E3 and M3 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. These atomic data are important in modeling of M-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in M-shell diagnostics of plasmas.« less
  • Transition rates and line strengths are calculated for electric-multipole (E2 and E3) and magnetic-multipole (M1, M2, and M3) transitions between 3s{sup 2}3p{sup 6}3d{sup 10}, 3s{sup 2}3p{sup 6}3d{sup 9}4l, 3s{sup 2}3p{sup 5}3d{sup 10}4l, and 3s3p{sup 6}3d{sup 10}4l states (with 4l = 4s, 4p, 4d, and 4f) in Ni-like ions with the nuclear charges ranging from Z = 34 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded multipole matrix elements. Transition energies used in the calculation of line strengths and transition rates are from second-order RMBPT. Lifetimes of the 3s{sup 2}3p{sup 6}3d{sup 9}4s levelsmore » are given for Z = 34-100. Taking into account that calculations were performed in a very broad range of Z, most of the data are presented in graphs as Z-dependencies. The full set of data is given only for Ni-like W ion. In addition, we also give complete results for the 3d4s{sup 3}D{sub 2}-3d4s {sup 3}D{sub 1} magnetic-dipole transition, as the transition may be observed in future experiments, which measure both transition energies and radiative rates. These atomic data are important in the modeling of radiation spectra from Ni-like multiply-charged ions generated in electron beam ion trap experiments as well as for laboratory plasma diagnostics including fusion research.« less
  • Transition rates, oscillator strengths, and line strengths are calculated for electric-dipole (E1) transitions between odd-parity 3s{sup 2}3p{sup 6}3d{sup 9}4{ell}{sub 2}, 3s{sup 2}3p{sup 5}3d{sup 10}4{ell}{sub 2}, and 3s3p{sup 6}3d{sup 10}4{ell}{sub 1} states and even-parity 3s{sup 2}3p{sup 6}3d{sup 9}4{ell}{sub 2}, 3s{sup 2}3p{sup 5}3d{sup 10}4{ell}{sub 1}, and 3s3p{sup 6}3d{sup 10}4{ell}{sub 2} (with 4{ell}{sub 1} = 4p; 4f and 4{ell}{sub 2} = 4s; 4d) in Ni-like ions with the nuclear charges ranging from Z = 34 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start frommore » a 1s{sup 2}2s{sup 2}2p{sup 6}3s{sup 2}3p{sup 6}3d{sup 10} Dirac-Fock potential. First-order RMBPT is used to obtain intermediate coupling coefficients and second-order RMBPT is used to calculate transition matrix elements. Contributions from negative-energy states are included in the second-order E1 matrix elements to ensure the gauge independence of transition amplitudes. Transition energies used in the calculation of oscillator strengths and transition rates are from second-order RMBPT. Lifetimes of the 3s{sup 2}3p{sup 6}3d{sup 9}4d levels are given for Z = 34-100. Transition rates, line strengths, and oscillator strengths are compared with critically evaluated experimental values and with results from other recent calculations. These atomic data are important in modeling of M-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in M-shell diagnostics of plasmas.« less
  • Based on relativistic wavefunctions from multiconfiguration Dirac–Hartree–Fock and configuration interaction calculations, E1, M1, E2, and M2 transition rates, weighted oscillator strengths, and lifetimes are evaluated for the states of the (1s{sup 2})2s{sup 2}2p{sup 3},2s2p{sup 4}, and 2p{sup 5} configurations in all nitrogen-like ions between F III and Kr XXX. The wavefunction expansions include valence, core–valence, and core–core correlation effects through single–double multireference expansions to increasing sets of active orbitals. The computed energies agree very well with experimental values, with differences of only 300–600 cm{sup −1} for the majority of the levels and ions in the sequence. Computed transitions rates aremore » in close agreement with available data from MCHF-BP calculations by Tachiev and Froese Fischer [G.I. Tachiev, C. Froese Fischer, A and A 385 (2002) 716].« less