# 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 »

- Authors:

- Physics Department, University of Nevada, Reno, NV 89557 (United States). E-mail: usafrono@nd.edu
- Physics Department, University of Nevada, Reno, NV 89557 (United States)
- Physics Department, Hashemite University, Zerga (Jordan)
- 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}

}