In the analysis of the experimental data on the transition-metal ions with the d N configuration, the following Hamiltonian is used: 

$${H_{F - I}} = \sum\limits_{k = 2,4} {{F^{(k)}}} {h_k} + \alpha L(L + 1) + \zeta \sum\limits_{i = 1}^N {{l_i}} {s_i}$$

(1)

with 

$${h_k} = \sum\limits_{i,j > i}^N {\sum\limits_{q = - k}^k {C_{kq}^*(i){C_{kq}}(j)}}$$

and 

$${C_{kq}}(i) = \sqrt {{{4\pi } \over {2k + 1}}} {Y_{kq}}({\theta _i},{\phi _i}).$$

Also 

$$C_{kq}^* = {( - 1)^q}{C_{k - q}}.$$

Theory and Data

Spectroscopic investigations of the structure of highly ionised atoms have undergone significant developments in recent years. The experimental progress is largely due to the introduction of several powerful light sources, such as laser-produced plasmas. Tokamaks and beams of fast, excited ions. The results obtained with these laboratory devices complement the data from astrophysical observations of the solar corona and solar flares. The experimental techniques are described in some detail. The results are discussed with respect to energy level studies along isoelectronic sequences, inner-shell excited levels, forbidden transitions, lifetimes and transition probabilities as well as the results of spectroscopic studies of quantum electrodynamics, QED. The experimental results are compared with theoretical predictions.

http://iopscience.iop.org/article/10.1088/0034-4885/52/2/002/pdf

The spectroscopy of highly ionised atoms

: A revised and updated annotated bibliography on atomic transition probabilities covering the literature from 1914 through October 1977 is presented It contains approximately 2400 references and is divided into four main sections, with each article assigned a number The first section contains a listing, by number, of articles of general interest The second section lists by number all articles containing numerical data; it is arranged by element and stage of ionization and is further subdivided according to theoretical and experimental methods, comments, and compilations The third section contains a listing of all articles, including number, authors, title, and journal reference; it is arranged by year of publication and alphabetically by authors names within the year All foreign language papers are identified, and their titles are translated into English The final section contains a listing of all authors and the numbers of the papers they have authored or co-authored

Bibliography on Atomic Transition Probabilities: 1914 Through October 1977

Calculations of energies and transition probabilities are reported for forbidden lines in the ground configurations of the germanium (4p2) and arsenic (4p3) isoelectronic sequences up to silver (Z = 47). Configuration interaction and relativistic effects were included in the framework of the HXR and HFR self-consistent-field methods. Transition probabilities have been obtained in intermediate coupling using parameter values for the 4p2 and 4p3 configurations obtained either by fitting or by extra-(inter)polation when experimental energy levels are missing. Except for Ge I and As I, transition probabilities are reported for the first time for all these ions. A note concerning transition probabilities for Fe XII is also appended.

http://iopscience.iop.org/article/10.1088/0031-8949/33/2/006/pdf

Magnetic-Dipole and Electric-Quadrupole Transitions in the Ground-State Configurations of the Germanium and Arsenic Isoelectronic Sequences

Multiconfiguration relativistic Dirac–Fock (MCDF) values have been computed for the first four ionization potentials (IPs) of element 104 (unnilquadium) and of the other group 4 elements (Ti, Zr, and Hf). Factors were calculated that allowed correction of the systematic errors between the MCDF IPs and the experimental IPs. Single ‘‘experimental’’ IPs evaluated in eV (to ±0.1 eV) for element 104 are: [104(0),6.5]; [104(1+),14.8]; [104(2+),23.8]; [104(3+),31.9]. Multiple experimental IPs evaluated in eV for element 104 are: [(0−2+),21.2±0.2]; [(0−3+),45.1±0.2]; [(0−4+),76.8±0.3]. Our MCDF results track 11 of the 12 experimental single IPs studied for group 4 atoms and ions. The exception is Hf(2+). We submit our calculated IP of 22.4±0.2 eV as much more accurate than the value of 23.3 eV derived from experiment.

/pdf/ionization-potentials-and-radii-of-atoms-and-ions-of-element-3c5d0wipej.pdf

Ionization potentials and radii of atoms and ions of element 104 (unnilquadium) and of hafnium (2 +) derived from multiconfiguration Dirac-Fock calculations

On recordings made in the Physics Department of Lund University, we have identified 64, 65, 63 and 71 4p-4d transitions in Y VI, Zr VII, Nb VIII and Mo IX, respectively, establishing 23 levels of 4p34d in each case. In Y VII, Zr VIII, Nb IX and Mo X we have identified 54, 53, 48 and 57 4p-4d transitions, establishing 19 levels of 4p24d in each spectrum. The number of 4p-4d transitions identified in Y VIII, Zr IX, Nb X and Mo XI is 28, 27, 27 and 31; they establish all the 11 4p4d levels that can combine with the ground levels. In addition, two levels of 4s4p3 could be found from 4s-4p transitions.

The 4p-4d Transitions of Y VI, VII, VIII, Zr VII, VIII, IX, Nb VIII, IX, X and Mo IX, X, XI

The spectra of Y VII, VIII, Zr VIII, IX, Nb X and Mo X, XI are studied for the first time and our 1971 analysis of Nb IX is improved. By analyses of the transitions 4s24pk-4s24pk-15s all the levels of the configurations 4p3, 4p25s, 4p2 and 4p5s are established in the spectra concerned.

4p-5s Transitions in Y VII, VIII, Zr VIII, IX, Nb IX, X and Mo X, XI

Based on Lund recordings, this communication reports 380 classified lines of the doubly ionized zirconium atoms. These classifications led us to confirm the energy levels belonging to the configurations 4s24p64d2, 4d5s, 4d6s, 4d5p, 4d5d, 4d4f, 5s6s, 5s5p, 5s5d, 5s4f and 5p2. All the levels of 4d6p and 5s2 have been revised, along with 1H5 of 4d4f. The configurations 4d6d, 4d5f, 5s6p and 5s5f have been newly worked out to almost completeness. The total number of the known energy levels of Zr III is now 137 including 41 levels freshly added. We derive from nd series the ionization energy of Zr III to be 186 400 ± 500 cm-1 (23.11 ± 0.06 eV).

Classified Lines and Energy Levels of Doubly Ionized Zirconium (Zr III)

With the help of the spectra recorded in the Physics Department of Lund University, Y VI, Zr VII, Nb VIII and Mo IX are freshly analysed. The five 4s24p4 ground levels and the ten 4s24p35s levels of previous analyses are confirmed in the first three spectra, except for revising in Y VI the 4p4 1S0 and 4p35s(4S3/2)2 levels and interchanging 5s(2D3/2)1 with 5s(2D3/2)2. All level values are improved due to our new measurements. A new analysis of Mo IX establishing all the 4p4 and 4p35s levels is being reported.

The Transitions 4p-5s in Y VI, Zr VII, Nb VIII and Mo IX

The analysis of the RbI-like spectrum Mo VI has been extended to include a total of some 110 classified lines and 44 energy levels belonging to the one-electron configurations 4s24p6(1S) nl with n ranging up to 9 and l up to 7. The analysis is based on recordings of vacuum spark spectra made at Lund in the region 230-2350 A, complemented by a list of lines from 2193 to 6336 A observed and identified by Romanov and Striganov in a Penning type arc discharge. The one-electron level system is partly mixed with core-excited configurations, not treated in the present paper. Especially the nf series is strongly perturbed by 4s24p54d2, and an anomalous behaviour of the ng series is explained by interaction with the 2G term of 4s4p64d2. The ionization limit, derived from 6h, 7i and 8k by means of the polarization formula, is found to be 555 132 ± 2 cm-1.

K Rahimullah

Papers

The 4p-4d Transitions of Y VI, VII, VIII, Zr VII, VIII, IX, Nb VIII, IX, X and Mo IX, X, XI

4p-5s Transitions in Y VII, VIII, Zr VIII, IX, Nb IX, X and Mo X, XI

Classified Lines and Energy Levels of Doubly Ionized Zirconium (Zr III)

The Transitions 4p-5s in Y VI, Zr VII, Nb VIII and Mo IX

Extended Analysis of Mo VI