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Dirac-Fock-Slater calculations for the elements Z = 100, fermium, to Z = 173
ATOMIC
DATA AND
NUCLEAR
DATA
TABLES
19, 83-95 (1977)
DIRAC-FOCK-SLATER FOR
THE
ELEMENTS
CALCULATIONS
Z = 100, FERMIUM,
TO Z = 173*
B. FRICKE Theoretische
Physik, Gesamthochschule D35-Kassel, Germany
Kassel
and G. SOFF Institut
fur Theoretische D6-Frankfurt
Physik, Universitat am Main, Germany
Frankfurt
Listed here for the elements Z = 100, fermium, to Z = 173 are energy eigenvalues and total energies found from relativistic Dirac-Fock-Slater calculations. The effect of high ionization on the energy eigenvalues is presented for two examples. The use of these tables in connection with the energy levels of superheavy elements and molecular orbital (MO) x-ray transitions in superheavy quasiatoms, is discussed. In addition, a brief comparison between the results of the Dirac-Fock-Slater and Dirac-Fock calculations is given.
*Work supported by Gesellschaft fur Schwerionenforschung (GSI), Germany, the Bundesministerium fur Forschung und Technologie (BMFT)
Copyright 0 1977 by Academic Press, inc. All rights of reproduction in any form reserved.
83
Atomic
Data
and partially
and
Nuclear
Data
Tables,
(G.S.) by
Vol.
19,
No.
1, January
1977
B. FRICKE and G. SOFF
DFS Energy Eigenvalues 100 5 Z 2 173
CONTENTS
INTRODUCTION Atomic Physics of Superheavy Elements Method of Calculation Comments on the Results EXPLANATION
OF TABLES
TABLES I. Electron Occupation z = 173 II. Energy Eigenvalues III.
Numbers
for the Elements
Z = 100 to
and Total Energies, Z = 100 to Z = 173
Energy Eigenvalues for Z = 100 from DF and DFS Calculations and Binding Energies from Experiment
IV. Energy Eigenvalues for 2 = 139 and Z = 170 in Various States of Ionization
The discussion of the existence of elements near Z = 126 has been brought up again by recent experimental results.7 Also, new theoretical Hartree-Fock calculations8 indicate that stability around Z = 126 is more probable than at Z = 114.
INTRODUCTION
Within the last fifteen years several tables with the results of self-consistent-field (SCF) atomic calculations have been published. Such calculations can be nonrelativistic or relativistic and can make use either of Slater’s exchange approximation or exact exchange. Thus there are four major ways to perform the calculations. In the following we give for each of the four possible methods the best known reference, a short description of the listed results, and the elements covered.
Atomic Physics of Superheavy Elements
Two groups99 lo extended SCF atomic calculations to even higher elements mainly to get results for the ground-state configurations, the first ionization potentials, and the principal maxima and radii of the outerelectron wavefunctions. The data, together with extrapolations from the known elements, were used to get an idea of the chemical behavior’l of the superheavy elements up to Z = 172. A model calculation12 including quantum electrodynamical effects was used to go even to Z = 184. From an atomic-physics point of view, elements with very large proton numbers are especially interesting because many of the corrections, which have to be added to the SCF calculations, are known only in perturbation theory, where the expansion parameter is Za(a = l/137). These corrections take account of the quantum electrodynamical effects, vacuum polarization and vacuum fluctuation, and the so-called Breit interaction which includes magnetic effects and retardation. The accuracy of the experimental binding energies for elements like uranium and plutonium is now better than 1 eV.15 A theoretical calculation with such a small error must include the correlation energy as well as SCF effects of the contributions just mentioned. Comparisons between experiment and calculation of the binding energies of the innermost levels of fermium, which yield a
Nonrelativistic Hartree-Fock-Slater (HFS) calculations by F. Herman and S. Skillman’ with energy eigenvalues, potentials, wavefunctions, and relativistic corrections to the energy eigenvalues, for all elements up to Z = 103. Nonrelativistic Hartree-Fock (HF) calculations by J. B. Mann2 with energy eigenvalues, total energies, radii, two-electron integrals, and wavefunctions for all elements up to Z = 103. See also Refs. 3 and 4. Relativistic Hartree-Fock-Slater (rel. HFS) or DiracFock-Slater (DFS) calculations by C. Lu et a1.5 with energy eigenvalues, total energies, radii, and potentials for all elements up to Z = 126. Relativistic Hartree-Fock (rel. HF) or Dirac-Fock (DF) calculations by J. P. Desclaux6 with energy eigenvalues, radii, wavefunctions, and radial expectation values for all elements up to Z = 126. The tables of Refs. 5 and 6 present results for elements up to Z = 126. This number was chosen because several years ago Z = 126 was assumed to be the center of an island of nuclear stability. Later calculations of the late sixties shifted this island to Z = 114, but 126 was kept as a good endpoint in the tables of Refs. 5 and 6. 84
Atomit
Data
and
Nuckor
Dota
Tables,
Vol.
19,
No.
I,
Januory
1977
B. FRICKE
and G. SOFF
DFS
good agreement, 131r4show that at 2 = 100 the corrections already are of the order of percent. In the region of the superheavy elements they would be even larger. Even if no superheavy elements are found near 2 = 114 or Z = 126 at least the atomic clouds of superheavy elements can be produced for a very short time. The method is that of heavy-ion collision, where the energy is large enough so that two nuclei approach each other so closely that the electron clouds of both ions combine and the electrons feel a nuclear charge Z, + Z, in their center. Brief combination is possible because the velocity, at least for the inner electrons, is much larger than the velocity of the two nuclei approaching each other. If, by some process, an electron hole can be created in the inner level of either atom and thus of the combined atomic cloud, it is possible to observe an x-ray transition during the time of collision. The change of the electrons from the levels of the separated atoms to the levels of the combined system, is shown in the so-called correlation diagram, which has been discussed qualitatively in some detail by Lichteni6 as well as by Barat and Lichten.i7 Ab initio calculations within the adiabatic approximation, based on the Roothaan-Hartree-Fock method, have been made for small-Z systems.i8 For systems with Z >, 40 only relativistic many-electron molecular calculations lead to good results, which are given by Rosen et al. lg For the innermost 1s electrons one-electron calculations by Mtiller et alzO may give a good first approximation. Explanation of the experimentally observed molecular orbital (MO) M-x-ray spectrum by taking into account all possible transitions of the molecular system I-Au, with a combined Z = 132, provides the first evidence of the quasiatomic levels of superheavy elements.21 As already mentioned the behavior of the energy levels as function of the distance between the two nuclei is given in the correlation diagrams, in which the levels of the separated systems are linked with the levels of the combined system. Thus the knowledge of the levels of the atomic systems involved is the first step in the construction of the diagrams. The main purpose of this paper is to give the energy levels of the atoms with Z > 100 (the energy levels of the atoms with Z < 100 may be taken from any of the other tables). A secondary purpose is to give a first orientation for the expected transition energies for the x-ray spectra of possible superheavy elements since these offer the best means of detecting such elements in small quantities.
Method
The Hamiltonian follows :
Energy
Eigenvalues
100 5 Z 5 173
H=CT,--g+x i
e2 i
i
l’i
-rjI
= HO + Hint.
(1)
Using a fully antisymmetrized determinantal wavefunction, one obtains, after the variation of the total energy, the Hartree-Fock equation, which can be written in the form
J/i69
I
~:~~~klrl,cr)) ,,,ezy,, d7’h(r) I
#T(rN/i(r)
= E&(r).
(2)
The total energy is given by the expression
x bb&)d&‘>- &@‘)&@)I~
(3) We have used in this calculation the relativistic Hartree-Fock-Slater approximation [usually called DiracFock-Slater (DFS) calculation] in which the last term on the left side of Eq. (2), the exchange term, is approximated by22 3a 2a
Vexch(r) = - -q37?p(r)]l’3.
(4)
This is a very good description as long as the total electron density p(r) is not too small. For very large radii the total potential l/r is used. This procedure results in the so-called Latter correction.23 We have used here a, = 2/3.
Since we are interested in very heavy elements the wavefunctions have to be found by using the relativistic Dirac operator T = coup + firnc’ in Eq. (2). Because (Y and /? are four component matrices this leads to the set of coupled differential equations
-KJY
of Calculation
a[ci
-
W-)1
=
-a[~
of the atomic problem is given as
-
V(r)] + f
where cx is the fine-structure
85
Atomic
Data
(5)
Ki/r
and Nuclear
constant,
Data
Table.,
Vol.
~~
19, No.
the Dirac
1, January
,977
B. FRICKE
DFS
and G. SOFF
Energy
(6)
with the surface thickness t = 2.2 fm and the number of nucleonsA = 0.0073 Z2 + 1.3 Z + 63.6. For the equivalent radius we required R,, = 1.2 AlI3 fm, which determines the half-density radius c. For further details of the actual calculations and numerical procedures we refer to Refs. l-6 and 24. Comments
on the Results
Listed in Table I are the electron occupation numbers of the elements Z = 100 to Z = 173 found from the present DFS calculations. Given are the configurations with the smallest total energies. These are expected to be the ground-state configurations of the free atoms.
- 1MeVt 110
100
120
100 2 Z 5 173
There are only a few minor discrepancies between the results of the Dirac-Fock’O and the Dirac-FockSlater calculations for the differences of the total energies of the lowest states. Of course, the first method is more exact but it needs about an order-of-magnitude more computer time and the differences in the results are negligible for many purposes. For only four elements the lowest configurations came out differently in the two calculations but the difference between the total energies of the two lowest configurations is very small, of the order of 0.1 eV. In the case of the inner levels the additional corrections already noted in the text have to be added. They are small for small Z and of the order of a percent at Z=: 100. First estimates of the quantum electrodynamical corrections for elements near Z z 170 show25 that their influence remains below a few percent of the binding energies. The uncertainty due to the unknown nuclear-charge distribution in this region also is of the same order of magnitude.s In suite of the uncertainties in the DFS results, the listed eneigy eigenvalues of the elements in Table II are expected to give good approximations to the binding energies in the region where one does not know the appropriate corrections. They may be used to construct correlation diagrams and to get a first idea of the ex-
quantum number, and Fi and Gi the small and large components of the wavefunction i, respectively. The quantity ci in Eq. (5) represents the energy required to remove an electron from shell i if all other electrons remain unchanged. Therefore, usually it is called the “binding energy” in the sense of Koopmans’ theorem. Because the Dirac equation for a point nucleus leads to a singularity for the 1s level at 2 = 137 we have used an extended nucleus with a Fermi-type nuclear charge distribution p(r) = po{ 1 + exp [4 in 3(r - c)/t]}-l
Eigenvalues
130
lul
150
160 Atomic
Fig.
1. Energy
eigenvalues
for the inner
electrons
of the elements
86
Z = 100, fermium,
170 Number
-
to Z = 173
Atomic Data and Nuclear Data Tables. Vol. 19, No. I, January
1977
B. FRICKE
and G. SOFF
DFS
petted x-ray transition energies in the combined system during a heavy-ion collision or in a superheavy element which may be found in nature or a physics laboratory. In the DFS calculations there is one parameter in front of Slater’s exchange approximation in Eq. (4) which can be chosen within some narrow limits to yield an optimal agreement with those values one is looking for. Lu et a1.5 have chosen the original value used by Slater namely cy, = 1. This leads to energy eigenvalues which are good approximations for the ionization energies for the outer electrons. The more correct value as = 2/3 is used by most other authors, but this value has the disadvantage that the ionization energies for the outer electrons have to be calculated with the various corrections. Nearly independent of the value of (Y, are the energy eigenvalues of the inner electrons calculated with the DFS approximation which by chance lead to a better agreement with the experimental results than do the exact DF calculations. The differences can be seen in Table III, where we have listed the energy eigenvalues for DF and the DFS calculations for the inner electrons of fermium together with the known experimental results.13*‘” The DFS results seem to be closer to the experimental results. But if all known corrections to the DF calculations are added they, of course, come out to be much more superior. In order to obtain a general view we give the position of the energy eigenvalues in Fig. 1. The sequence of the levels, which is still normal at Z = 100, changes considerably with the higher elements. We see particularly the strong binding of the s and pi/z levels
Energy
Eigenvalues
100 < 2 5 173
with the same principal quantum number. The reason for this is twofold. The wavefunctions of the electrons with a total angular momentum l/2 are drawn nearer to the nucleus. This is the so-called direct relativistic effect. In response to this the other electrons are more strongly shielded and thus pushed away from the nucleus. This is the so-called indirect relativistic effect. The two effects together lead to a very unusual ordering of the levels. Figure 2 shows the energy eigenvalues of the outer electrons of the same elements. The behavior of the levels looks very normal for the elements up to Z z 120 and above Z =: 160. In the intermediate region the onset of the filling of the shells, as well as their behavior with increasing Z, is very complicated. The total energies in Table II provide an idea of how much energy may be gained from the electron cloud when the two atoms combine during a heavy-ion collision. To give an example we assume that Hg combines with Th to form the superheavy quasi atom z = 170:
ET(170) - E&90) - E&80) = (5.878 - 0.721 - 0.534) MeV = 4.623 MeV. This gain in energy is found for the most optimistic case that all electrons are present and contribute to the binding here amounting to more than 4.6 MeV. The total energies also are shown in Fig. 3 where the sharp rise for large Z can be seen even better. In heavy-ion collisions the incoming projectile ion
atomic number2 Fig. 2. Energy
eigenvalues
for the outer
electrons
of the elements
87
Z = 100, fermium,
Atomic
to Z = 173
Dato
and
Nuclear
Data
Tables,
Vol.
19,
No.
1, January
1977
B. FRICKE and G. SOFF
DFS Energy Eigenvalues 100< Z 5 173
is highly ionized and, because of strong ionization processes during the collision, an even higher ionization of the combined system is expected. To give an idea of the effect of this ionization on the energy levels, we have listed in Table IV the energy eigenvalues of elements 2 = 139 and 2 = 170 in various highly ionized states. The table shows that the medium and outer electrons are very strongly affected whereas the innermost electrons are shifted by a considerable amount only for very large ionizations or for ionization of the inner electron shells.
References 1. F. Herman and S. Skillman, Atomic Structure Calculations, (Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963) 2. J. B. Mann,
“Atomic Structure Calculations,” Los Alamos Scientific Reports No. LA-3690 (1967) and LA-3691 (1968)
3. C. Froese Fischer, ATOMIC DATA 4, 301 (1972) 4. J. B. Mann, ATOMIC DATA AND NUCLEAR DATA TABLES 12, 1 (1973)
Acknowledgment We thank Profs. W. Greiner and J. T. Waber for their continuous interest and support.
5. C. C. Lu et al., ATOMIC DATA 3, 1 (1971) 6. J. P. Desclaux, ATOMIC DATA AND NUCLEAR DATA TABLES 12, 3 11 (1973) 7. R. V. Gentry et al., Phys. Rev. Lett. 37, 11 (1976) 8. D. Kolb, to be published
6 E,[MeVI 1
9. B. Fricke and W. Greiner,
Physics Lett. B 30, 317 (1969); B. Fricke, W. Greiner, and J. T. Waber, Theor. Chim. Acta 21, 235 (1971)
energyofatomsas function of theatomicnumber
10. J. B. Mann, Proceedings of the Robert A. Welsh Foundation Conference. XIII. The Transuranium Elements, edited by W. 0. Milligan (Houston, Tex., Nov. 1969) p. 430 11. B. Fricke and J. T. Waber, Actinides Review 1, 433 (1971); B. Fricke, Structure and Bonding 21, 89 (1975) 12. B. Fricke and J. T. Waber, J. Chem. Phys. 57, 371 (1972) 13. M. S. Freedman, F. T. Porter, and J. B. Mann, Phys. Rev. Lett. 28, 711 (1972) 14. B. Fricke, J. P. Desclaux, and J. T. Waber, Phys. Rev. Lett. 28, 714 (1972) 15. G. L. Borchert, Z. Naturforsch.
A 31, 102 (1976)
16. W. Lichten, Phys. Rev. 164, 13 1 (1967) 17. M. Barat and W. Lichten, Phys. Rev. A 6,211 (1972) 18. E. W. Thulstrup and H. Johansen, Phys. Rev. A 6, 206 (1972); F. P. Larkins, lSt Int. Conf. on Inner Shell Ionization Phenomena, Atlanta, Ga. (1972); for more information see W. Lichten, Atomic Physics 4, edited by G. zu Putlitz, E. W. Weber, and A. Winnacker, (Plenum Press, New York, 1975), p. 249
Atomic number O 50I
I
70 I
I
90I
I
19. A. Rosen, D. Ellis, B. Fricke, and T. Morovic, Abstracts of Contributed Papers, 2nd Int. Conf. Inner Shell Ionization Phenomena, Freiburg (1976) p. 18
110 I I 130 I l 150 l l 170 , c
Fig. 3. Total energies of the atoms up to Z = 173
88
DFS Energy Eigenvalues 100 < Z 2 173
B. FRICKE and G. SOFF
Phys. Rev. 137, A27 (1965); D. A. Liberman, D. T. Cromer, and J. T. Waber, Comp. Phys. Comm. 2, 107 (1971); I. P. Grant, Adv. Phys. 19, 747 (1970). For a summary of references see C. Froese Fischer, Comp. Phys. Comm. 5, 147 (1973)
20. B. Mullet-, J. Rafelski, and W. Greiner, Phys. Lett. B 47, 5 (1973); B. Mtiller and W. Greiner, Z. Naturforsch. A 31, 1 (1976) 21. B. Fricke, T. Morovic, W. D. Sepp, A. Rosen, and D. Ellis, to be published
25. G. A. Rinker and L. Wilets, Phys. Rev. A 12, 748 (1975); M. Gyulassy, Phys. Rev. Lett. 33, 921 (1974); K. T. Cheng and W. R. Johnson, Phys. Rev., in print
22. J. C. Slater, Phys. Rev. 81, 385 (1951) 23. R. Latter, Phys. Rev. 99, 510 (1955) 24. D. A. Liberman,
J. T. Waber, and D. T. Cromer,
EXPLANATION TABLE
OF TABLES
I. Electron Occupation Numbers for the Elements 2 = 100 to Z = 173
Values from present DFS (Dirac-Fock-Slater) TABLE
calculations
II. Energy Eigenvalues and Total Energies, Z = 100 to Z = 173 (in eV)
Values from present DFS (Dirac-Fock-Slater)
calculations
c,t
Nuclear-change density parameters c and t in Eq. (6) in fm (lo-l3 cm)
E,
Total energy
TABLE
III.
Energy Eigenvalues (in eV) for Z = 100 from DF and DFS Calculations and Binding Energies from Experiment
DF
Dirac-Fock
Corrections
Magnetic contribution, retardation, vacuum fluctuation, vacuum polarization, and rearrangement effect including rearrangement in the magnetic contribution
Experiment
From conversion electron energies in the beta decay of 254mEs from F. T. Porter and M. S. Freedman, Phys. Rev. Lett. 27,293 (197 1). The experimental error bars are between 7 and 14 eV
DFS RESULT
Dirac-Fock-Slater
TABLE
CT
results of present authors
values of present authors
IV. Energy Eigenvalues (in eV) for Z = 139 and Z = 170 in Various States of Ionization Same as c,t in TABLE
89
II
B. FRICKE
TABLE 2
5F7/2
100 101 102
8
103
8
1
104
8
2
105
8
106
Energy
Eigenvalues
100 5 2 < 173
I. Electron Occupation Numbers for the Elements (Rn core plus 7S2 and 5F5/26) 6133/Z
6D5/2
7P1/2
7P3/2
6
119
8
4
6
2
4
1
7
120
8
4
6
2
4
2
121
8
4
6
2
4
2
1
122
8
4
6
2
4
2
1
1
123
8
4
6
2
4
2
1
1
3
124
8
4
6
2
4
2
1
8
4
125
8
4
6
2
4
2
1
107
8
4
126
8
4
6
2
4
2
1
108
8
4
2
127
8
4
6
2
4
2
109
8
4
3
128
8
4
6
2
4
2
110
8
4
4
129
8
4
6
2
4
111
8
4
5
130
8
4
6
2
112
8
4
6
1
131
8
4
6
2
113
8
4
6
2
132
8
4
6
114
8
4
6
2
133
8
4
6
115
8
4
6
2
1
134
8
4
6
116
8
4
6
2
2
117
8
4
6
2
3
118
8
4
6
2
4
5G9/2
6F5/2
7D3/2
6F7/2
2
569/Z
6F5/2
7D3/2
6F7/2
135
1
4
154
10
6
2
6
136
2
4
155
IO
6
2
7
2
8
3
3
7Pl/2
7P3/2
Z = 100 to Z = 173
5~712
137
6D5/2
DFS
2
z
6D3/2
and G. SOFF
1
156
10
6
8sl/2
8P1/2
7D3/2
6F5/2
3
1
2
2
2
2
3
2
2
4
2
2
2
5
4
2
2
2
6
4
2
2
2
7
2
4
2
2
2
8
2
4
2
2
3
8
2
4
2
2
4
8
833/Z
951/Z
71)5/Z
1
9P1/2
138
4
3
1
157
10
6
3
8
5
2
2
158
10
6
4
8
140
6
3
1
159
10
6
4
8
141
7
2
2
160
10
6
4
8
1
142
8
2
2
161
10
6
4
8
2
143
9
2
2
162
10
6
4
8
4
144
10
1
3
163
10
6
4
8
5
145
10
3
2
164
10
6
4
8
6
146
10
4
2
165
10
6
4
8
6
147
10
5
2
166
10
6
4
8
6
2
167
IO
6
4
8
6
2
1
4
8
6
2
2
10
6
2
149
10
6
3
168
10
150
10
6
4
169
10
6
4
8
6
2
2
151
lo
6
3
2
170
10
6
4
8
6
2
2
152
lo
6
3
3
171
10
6
4
8
6
2
2
153
lo
6
2
5
172
10
6
4
8
6
2
2
173
10
6
4
8
6
2
2
89 for
Explanation
of Tables
90
6G7/2
1
6
See page
1 3
139
148
X7/2
1
B. FRICKE and G. SOFF
DFS Energy Eigenvalues 100 5 2 2 173
TABLE II. Energy Eigenvalues and Total Energies, 2 = 100 to Z = 173 (in eV)
lSl/Z ZSl/P 2P1/2 2P3/2 3Sll2 3P1/2 3P3/2 3[33/2 305/Z 451/Z 4P1/2 4P3/2 403/Z 4D5/2 4FW2 4F7f2 5S1/2 5P1/2 5P3/2 503/Z 5D5/2 5F5/2 5F7/2 6Sl/2 6Pl/2 6P3/2 6D3/2 7S1/2 7Pl/P ET
lSl/P 251/o 2P1/2 2P3/2 3S1/2 3Pi/2 3P3/2 303/2 3D5/2 4S1/2 4Pl/2 4P3/2 403/Z 405/2 4F5/2 4F7/2 5s1/2 5P1/2 5P3/2 5D3/2 5D5/2 5F5/2 5F7/2 6Sl/2 bP1/2 6P3/2 683/Z bD5/2 7Sl/2 7P1/2 ET
ZIlOO
Z=101
21102
23103
Z-104
z-105
2=106
z=107
2=1oe
Z=109
c=7.000 T-2.2
C-7.252 T=%.E
cc7.399 Tr2.2
Cr7.427 T"2.2
(317.455 T=2.2
c17.483 Tr2.2
cr7.511 T=X.2
c17.538 1=2.2
C-7.566 112.2
c=7.594 Tr2.2
142049.7 27409.6 26555.4 20715.1 7095.7 6694.6 5320.0 4685.2 4420.9 1889.3 1701.9 1328.5 1031.5 965.2 573.4 555.0 433.2 355.5 258.1 144.1 129.8 5.9 3.9 59.5 36.4 21.8
145656.9 28220.2 27355.9 21204.2 7325.6 6918.1 5466.6 ke2i .6 4544.7 1950.8 1768.5 1372.5 1069.6 999.7 600.1 580.6 451.0 371.0 266.9 149.7 134.4 6.4 4.3 61.4 37.6 22.0
4.9
5.0
948461
973705
149346.1 29052.9 28117.9 21699.3 7561.8 7147.5 5615.2 4959.9 4670.0 2032.2 1836.9 1417.0 :E-: . 627.2 606.4 469.1 387.0 275.7 155.4 139.1 7.0 4.6 63.4 38.8 22.3 5.1
999468
153129.4 29915.6 29029.1 22206.7 7811.3 7389.9 5772.6 5106.9 4803.5 2113.3 1914.0 1468.9 1154.1 1076.5 661.3 639.3 494.5 410.1 291.1 167.5 150.1 13.1 10.4 70.4 44.6 2h.2 2.5 5.9
156995.1 30802.8 29905.2 22721.8 8068.9 7640.7 5933.9 5257.7 4940.3 2198.2 1994.8 1523.1 1202.3 1120.7 697.6 674.4 522.0 435.3 308.1 181.2 162.7 20.7 17.7 78.6 51.6 31.1 4.3 7.1 3.5
1025766
1052586
151/z 2s1/2 PP112 PP3/2 351/Z 3P1/2 3P3/2 3D3/2 3D5/2 4S1/2 4P1/2 4P3/2 4D3/2 4D5/2 4F5/2 4F7/2 5S1/2 5P1/2 5P3/2 5D3/2 5D5/2 5F5/2 5F7/2 6Sl/P 6P112 6P3/2 603/2 751/Z 6D5/2 ET
160940.5 31709.8 30801.8 23239.2 a329.7 7894.7 6093.7 5406.9 5075.1 2281.6 2074.1 1574.4 1247.4 1161.6 730.6 706.1 546.5 457.4 321.5 191.2 171.4 24.4 21.1 82.9 54.6 31.9 3.8 6.8
i64974.2 32643.6 31726.3 23765.0 8597.8 8158.2 6258.1 5560.h 5213.9 2368.5 2157.9 162a.6 1295.6 1305.4 766.5 740.6 573.9 482.5 337.3 203.6 182.5 30.5 26.8 89.3 59.7 34.6 4.5 7.2
169097.2 33503.7 32678.1 24297 ,a 8877.9 8429.9 6425.4 5717.3 5355.1 2460.6 2244.0 1684.5 1345.3 1250.5 803.7 776.4 602.8 509.0 354.0 216.8 194.4 37.3 33.3 96.3 65.4 37.7 5.5 4.0 7.6
173312.1 34590.4 33658.0 24837.0 9163.9 8709.7 6595.4 5876.3 5498.2 2554.5 2334.9 1741.3 1396.0 1296.4 841.7 812.9 632.6 536.5 371.0 230.4 206.5 44.4 39.9 103.6 71.3 40.8 6.5 4.b 8.1
177621.7 35604.9 34667.1 25382.6 9458.0 8997.9 6767.9 6037.9 5643.3 2651.2 2427.5 1799.2 1447.6 1343.2
1079942
1107844
1136306
1165342
1194968
eao.5 850.1
663.4 564.9 388.4 244.2 218.9 51.7 46.8 111.1 77.3 43.8 7.4 5.3 a.5
Z-110
z-111
z=112
Z-113
2=114
z-115
Z=116
z=117
z=lle
21119
C17.621 Ts2.2
C17.649 1=2.2
C=7.676 T=2*2
c=7.704 T=2.2
c=7.731 T+2.2
cE7.758 Tt2.2
C=7.786 1=2.2
c17.813 T=2.2
c=7.840 Tn2.2
C=7.867 1x2.2
ie2029.4 36648.2 35706.9 25934.7 9760.4 9294.9 6943.0 6202.1 5790.4 2750.7 2523.2 1858.2 1500.4 1390.8 920.1
186538.3 37721.4 36778.9 26493.2 10071.6 9h00.9 7120.7 6368.6 5939.3 2853.3 2622.0 19la.2 1554.0 1439.1 960.4 926.7 728.3 625.1 424.4 273.0 244.5 67.1 61.4 126.7 90.1 49.8 9.4 6.6 9.4
i9iisi.e 38825.9 37884.6 27058.2 10391.7 991b.6 7301.0 6537.9 6090.3 2959.0 2724.0 1979.3 1608.7 1488.4 1OOl.b
195276.6 39965.7 39028.6 27632.5 10724.1 10245.1 7486.8 6712.3 6245.9 3070.8 2832.3 2044.3 1667.3 1541.3 1046.4 1009.2 800.6 692.7 464.7 306.1 274.0 80.6 79.8 146.4 106.9 58.6 13.8 10.1 11.6 4.9
200713.8 41139.6 40210.3 28213.5 11066.4 10584.3 7675.4 6889.6 6403.9 3186.2 2944.3 2110.6 1727.2 1595.3 1092.3 1053.3 e40.9 730.0 487.2 324.9 291.0 98.4 91.1 158.3 117.4 64.6 17.3 13.0 13.5 5.7
205b69.4 42350.7 41433.2 28803.0 ii420.e 10936.4 7868.7 7071.5 6565.8 3307.1 3062.0 2ieo.o 1790.1 1652.0 1141.0 1100.0 883.1 770.6 511.9 345.9 310.0 112.4 104.5 172.6 130.1 72.4 22.7 17.7 16.9 7.8 3.8
210745.9 43598.9 42697.9 29399.2 11786.0 11300.2 eo64.R 7256.1 6729.8 3431.7 3183.8 2250.7 la54.2 1709.9 1190.7 1147.7 927.5 812.7 537.3 367.6 329.6 126.9 lie.4 187.4 143.4 80.5 28.2 22.6 20.3 10.1 4.4
215947.7 44ea5.5 44006.6 30002.0 12162.1 11676.2 8263.7 7443.4 6895.8 3560.2 3309.7 2322.5 1919.5 1768.6 1241.3 1196.2 973.3 856.4 563.2 389.6 349.6 141.7 132.7 202.6 157.1 ea.6 33.7 27.5 23.7 12.4 5.2
221279.4 46212.4 45362.0 30611.4 12549.6 12065.1 8465.3 7633.4 7063.8 3692.7 3439.9 2395.6 1985.9 1828.3 i292.e 1245.5 1020.5 901.7 589.5 4lp.2 369.9 157.0 147.2 214.3 171.4 96.8 39.4 32.4 27.2 14.9 h.0
226748.8 47583.6 46769.2 31229.9 12951.5 12470.0 8672.2 7828.5 7236.4 3831.8 3577.2 2472.3 2056.0 1891.3 1347.6 1298.2 1072.0 951.2 618.9 437.7 393.1 175.1 lb4.6 237.1 lee.7 107.5 47.6 39.9 33.1 19.7 a.4 3.6
1256051
1287542
1319687
1352505 1386015
1420239
1455201
1490925
1527433
eea. i
695.4 594.5 406.2 258.5 231.6 59.3 54.0 lie.7 83.6 46.8 a.4
5.9 a.9
1225199
966.2
762.4 656.8 442.9 287.9 257.7 75.3 69.0 134.9 96.9 52.8 10.4 7.3 9.8
lS1/2 2s1/2 2P1/2 2P3/2 351/i? 3Pl/P 3P3/2 3D3/2 305/P 4s1/2 4P1/2 4P3/2 4D3/2 4D5/2 4F5/2 4F7/2 551/P 5P1/2 5P3/2 503/2 SDS/Z 5F5/2 5F7/2 6Sl/E bPl/Z 6P3/2 6D3/2 605/2 ISl/P 7Pl/2 7P3/2 asl/z ET
See page 89 for Explanation of Tables
91
Atomic Dota and Nuclear
DD+D Tables, Vol. 19, No. 1, Jonuory
1977
B. FRICKE and G. SOFF
TABLE
151/2 2s1/2 2P1/2 2PW2 35112 3P1/2 JP3/2 303/E 3D5/2 4-9112 4P1/2 4P3/2 403/E 405/i! 4F5/2 4f7/2 5S1/2 5Pl/P 5P3/2 503/2 5DS/P 5F5/2 5F7/2 65112 6P1/2 6P3/2 603/2 605/2 7s1/2 ?Pl/2 7P3/2 as1/2 0P1/2 703/2 6F5/2
15112 251/2 PP1/2 2P3/2 351/2 3P1/2 3?3/2 30312 305/2 451/2 4P1/2 4P3/2 403/2 405/2 4F5/2 4F7/2 5S1/2 5P1/2 5P3/2 50312 50512 5F5/2 5F7/2 5G7/2 651/2 6Pl/2 6P3/2 60312 60512 6F5/2 7S1/2 7P1/2 7P3/2 85112 0P1/2 ET
and Total Energies, Z = 100 to Z = 173 (in eV)
2.120
z--121
Z=l22
2=123
21124
z=125
21126
Z=127
z=120
Z=129
Cx7.094 TI2.2
Cl7.921 1=2.2
c17.940 T=2.2
C37.975 1-2.2
c=0.002 r12.2
C18.029 Tr2.2
C~E.056 1=2.2
c=a.082 1=2.2
c=a.109 112.2
C10.136 1=2.2
244024.3 51971.2 51321.9 33127.6 14236.2 13775.9 9312.2 0432.0 7766.7 4270.0 4021.3 2712.4 2275.9 2008.7 1520.3 1463.7 1238.7 1113.0 712.4 519.6 467.6 234.1 221.5 299.2 246.7 142.9 75.3 64.9 53.4 36.7 17.7 6.2 3.3 3.3
250086.7 53526.8 52957.0 3377n.o 14607.1 14239.2 952K.7 0635.2 7945.6 4431.6 4175.7 2790.5 2347.1 2151.9 1575.2 1516.1 1293.4 1166.5 740.2 543.5 400.7 250.1 236.7 316.9 213.0 150.7 80.6 69.4 56.9 39.4 18.4 6.4 3.4 3.4 4.7
256309.9 55130.9 5465b.2 34413.2 15148.6 14716.4 9739.9 0036.3 0120.5 4506.1 4331.9 2865.7 2415.4 2212.0 1626.9 1565.2 1346.1 1218.2 764.6 563.Y 506.4 262.6 240.4 331.3 276.2 154.9 82.5 70.5 57.6 39.7 17.4 b.l 3.3
262670.4 56777.2 56413.2 35053.6 15618.1 15205.1 9950.0 9033.9 0291.4 4741.2 4409.6 2938.1 2480.9 2269.1 1675.6 1611.3 1398.1 1269.b 788.3 583.8 523.8 275.4 260.5 8.6 340.6 292.6 163.9 90.1 77.5 a.9 65.4 47.0 23.1 10.6 6.8
289270.9 58499.0 58271.0 35714.0 16100.6 15720.4 10165.2 9237.7 8467.0 4098.6 4651.3 3006.7 2542.a 2321.9 1720.4 1653.2 1444.3 1315.6 803.9 595.h 532.0 279.7 264.0 6.1 357.6 300.9 164.3 89.1 76.1 5.9 64.0 45.9 20.2 7.4 3.9 3.6
276024.4 b0268.7 60198.3 36371.2 16609.8 16250.7 10378.9 9439.3 0639.9 5059.0 4810.0 3075.9 2605.0 2374.9 1765.3 1695.1 1493.4 1364.9 821.4 609.2 543.7 205.8 269.4 5.6 369.0 311.6 166.7 90.1 76.6 5.4 66.5 47.3 20.2 7.5 3.9
282971.4 62100.6 62215.4 37034.5 17127.5 16803.3 10594.9 9643.1 8814.3 5226.2 4991.5 3145.6 2667.0 2420.3 1810.4 1737.2 1544.1 1416.2 038.9 622.9 554.5 291.9 274.7 5.0 300.9 322.9 169.1 91.1 77.2 4.9 68.4 48.8 20.2 7.6 4.0
290120.5 63997.7 64329.5 37703.7 17662.5 17379.7 10813.1 9049.1 8989.9 5398.0 5172.2 3216.0 2731.2 2481.9 1855.0 1779.5 1596.5 1469.0 856.4 636.6 565.2 297.8 279.9
1681088
1722777 1764622
1007556
1851536
la96636
1942905
232359.0 4P999.4 46229.4 31855.6 13366.4 12809.7 8882.5 0027.0 7411.6 3975.0 3719.9 2550.9 2127.9 1955.9 1404.0 1352.3 1125.6 1003.0 649.3 464.2 417.3 194.1 183.0 257.0 207.1 119.0 56.5 47.9 39.6 25.1 11.3 4.2
ET
II. Energy Eigenvalues
DFS Energy Eigenvalues 100 2 Z 5 173
1564753
238116.4 50462.0 49746.5 32408.9 13795.2 13325.5 9096.h 8229.2 7509.7 4125.2 3860.6 2631.7 2201.9 2022.5 1462.4 1400.2 1181.9 1057.7 601.2 492.3 442.9 214.5 202.7 270.4 227.2 131.5 66.5 57.0 47.1 31.4 15.1 5.4 3.0
1602913
1642191
lS1/2 ES1/2 2P1/2 2P3/2 35112 3Pl/P 3P3/2 303/2 30512 451/2 4P1/2 4P3/2 40312 405/2 4F5/2 4f7/2 5.5112 5P1/2 5P3/2 503/2 505/P 5F5/2 5f7/2 5G7/2 6S1/2 bPl/Z bP3/2 603/2 685/2 6F5/2 7S1/2 7P1/2 7P3/2 asi/ BPI/E 70312
3.4
ET
393:: 334.7 171.5 92.1 77.b 4.4 70.2 50.3 20.2 7.7 4.0
21130
25131
2.132
Z=133
21134
z-135
Z=136
z=137
21138
z=139
Cr0.162 TI2.2
CI0.189 Tl2.2
C38.215 r=2.2
C10.242 1=2.2
C=8.268 T=2.2
C=8.295 T=2.2
C=8.321 TE2.2
csa.347 T=2.2
c=a.374 1x2.2
e-a.400 1.2.2
337800.4 76937.4 79564.3 41862.0 21292.7 21453.7 12188.7 11149.2 10090.1 6575.8 6457.5 3673.7 3145.7 2831.8 2155.2 2058.4 1972.5 1869.0 903.6 739.6 648.2 351.1 327.7 13.5 9.4 492.3 435.4 195.1 105.4 86.8 3.6 87.8 66.0 21.1
346b37.3 79379.8 82620.4 42574.1 21969.9 22249.5 12423.7 11371.4 10275.7 6792.6 6704.6 3749.5 3214.2 2888.3 2203.3 2102.6 2039.7 1944.0 1002.3 754.2 b59.P 357.1 332.8 12.5 a.2 500.7 453.1 197.7 106.5 87.2 3.0 90.5 68.R 21.1
365183.9 84546.2 89339.3 44019.8 23398.7 23967.5 12904.3 11826.2 10654.4 7252.1 7230.7 390fJ.7 3356.6 3005.0 2303.9 2195.4 2184.0 2110.0 1043.6 787.1 604.6 372.6 346.3 13.7 9.0 546.8 495.1 206.2
8.0 4.6
9.0 4.7
355762.4 81917.7 85883.6 43296.1 22b74.4 23089.4 12665.0 11599.9 10466.6 7020.7 6967.5 3029.0 3287.2 2940.9 2255.5 2151.0 2113.1 2027.4 1025.9 772.6 673.9 366.9 341.6 15.1 10.6 529.4 475.5 203.9 111.1 91.1 4.9 96.6 74.8 22.9 3.3 10.1 5.3 2362114
2421754
297400.6 65962.9 b6548.2 30379.1 18215.4 17981.5 11033.6 10057.4 9167.0 5575.5 5360.7 3287.1 2795.2 2536.0 1901.5 1822.0 1650.7 1525.9 074.2 650.4 576.0 303.8 285.1 3.6 405.9 347.2 173.9 93.1 78.1 3.9 72.2 52.0 20.2 7.9 4.1
305061.0 67999.3 60800.4 39060.5 18787.1 10610.6 11256.5 10267.9 9345.5 5758.9 5557.5 3359.0 2060.0 2590.4 1947.6 1064.8 1706.9 1584.6 092.0 664.3 506.9 309.8 290.3 2.8 419.1 360.3 176.3 94.1 78.4 3.5 74.3 53.8 20.2 8.0 4.1
312871.4 70110.1 71335.6 39748.0 19378.3 19268.6 11481.7 10480.6 9525.4 5940.6 5763.1 3431.6 2925.5 2645.2 1994.1 1908.0 1765.1 1646.3 910.1 670.5 597.8 315.9 295.5 2.0 433.0 374.3 178.8 95.2 79.1 3.0 76.5 55.8 20.2 a.2 4.3
320928.7 72305.8 73931.2 40440.8 19997.6 19965.5 11717.5 10703.7 9714.7 6153.7 5987.2 3514.5 3001.1 2710.0 2050.4 1960.7 1035.0 1720.4 937.3 701.4 617.2 330.2 300.8 8.0 454.3 395.9 185.6 99.7 82.7 3.6 80.7 59.5 20.6 a.4 4.3
329237.0 74583.0 76672.4 41156.1 20638.3 20695.9 11956.2 10929.5 9906.0 6366.2 6221.8 3598.0 3078.1 2775.0 2107.6 2014.5 1907.8 1790.b 965.1 725.2 637.3 345.1 322.6 14.5 476.6 418.8 192.7 104.4 86.3 4.1 85.1 63.5 21.1 8.6 4.4
1990396
2039193
2009267
2140769
2193732
lSl/Z PSI/P 2P1/2 2P3/2 351/2 3P1/2 3P3/2 303/E 3D5/2 4Sl/E 4P1/2 4P3/2 4D3/2 40512 4F5/2 4F7/2 55112 5P1/2 5P3/2 50312 505/2 5F5/2 5F7/2 50712 50412 6S1/2 6Pl/2 6P3/2 603/P 605/2 6F5j.2 75112 7P1/2 7P3/2 70312 as112 8P1/2 ET
See page 89 for Explanation
2240236
2304354
'2.: . 4.2 99.5 77.7 22.0 3.1 10.3 5.4
374916.4 07274.1 93019.0 44750.4 24140.5 24891.8 13146.7 12055.4 10844.2 7491.8 7523.8 3984.9 3427.4 3063.5 2353.1 2240.5 2259.6 2197.4 1062.0 802.2 695.7 378.7 351.4 12.5 7.6 565.3 516.2 208.7 113.0 91.7 10::: 01.1 22.0 3.0 10.5 5.6 2483211
of Tables
92
Atomic
Data and Nuclwr
Da+o TobIer, Vol. 19, No. 1, Jmuary
1977
DFS Energy Eigenvalues 100 5 Z < 173
B. FRICKE and G. SOFF
TABLE
ISI/ 251/2 2P1/2 2P3/2 351/P 3P1/2 3P3/2 303/2 305/C 451/2 4P1/2 4P3/2 403/2 40512 4F5/2 4F?/2 ss1/2 5P112 5P3/2 5D3/2 505/P 5FS/E SF712 56712 509/i? 65112 6P1/2 6P3/2 6D3/2 6DS/E 6FW2 751/t 7Pl/2 7P3/2 70312 851/2 BP]/2 ET
lSl/Z 2Sl/E 2P1/2 2P3/2 351/2 3P1/2 3P3/2 3D3/2 30512 4S1/2 4P1/2 4P3/2 4D3/2 4D5/2 4FW2 4F7/2 551/z 5P1/2 5P3/2 5D3/2 505/2 5F5/2 5F7/2 SG7/2 50912 65112 6P1/2 6P3/2 6D3/2 6D5/2 6F5/2 6F7/2 75112 7Pl/2 7P3/2 703/2 BSl/E 8P1/2 ET
See
page
II. Energy Eigenvalues
and Total Energies, Z = 100 to Z = 173 (in eV)
2=140
25141
21142
z=143
Z=144
Z=145
Z=146
z--147
Z.=l48
z=149
C18.426 Tr2.2
C=8.452 T12.2
c-8.476 T=2.2
CEB.504 T=2.2
we.530 T12.2
C18.556 712.2
C=8.582 T=2.2
C=8.60R T-2.2
GE.634 T-2.2
c=8.660 T=2.2
440669.5 105918.2 121067.2 49278.6 29225.7 31548.7 14666.7 13494.5 12023.9 9120.6 9563.2 4485.5 3881.9 3431.9 2669.8 2530.3 2781.9 2838.8 1195.5 908.7 776.0 427.9 393.6 15.7 9.2 704.7 604.2 232.8 126.7 100.6 3.5 130.9 112.8 25.0 3.0 13.7 8.1
453003.5 109438.7 126990.7 50062.3 30178.R 32869.6 14936.0 13749.7 12232.1 9430.7 9967.9 4579.9 3968.3 3502.7 2731.6 2587.3 21387.5 2972.6 1225.8 934.6 796.7 443.1 407.5 22.1 15.1 737.4 724.4 240.4 131.8 104.2 4.1 138.1 121.2 25.5
465773.5 113083.8 133351.6 50853.3 31162.6 34254.7 15208.5 14007.9 12442.1 9750.7 10390.6 4675.8 4056.1 3574.4 2794.4 2645.1 2996.9 3112.7 1256.8 960.9 817.9 458.7 421.7 28.9 21.4 771.5 766.9 248.1 136.9 107.9
478997.2 116855.5 140183.9 51651.8 32177.6 35705.1 15484.3 14269.3 12654.0 10080.7 10831.3 4773.1 4145.2 3647.0 2858.0 2703.6 3109.9 3259.0 1288.5 987.9 839.4 474.7 436.2 35.9 LB.0 806.9 811.5 255.9 142.1 111.6 5.2 153.4 139.5 26.4 2.8 15.5 9.9
492696.0 120759.7 147526.4 52461.6 33228.1 37225.3 15767.4 14537.8 12871.8 10424.6 11294.1 4875.7 4239.6 3724.4 2926.4 2766.7 3230.6 3415.5 1324.6 1019.3 865.3 495.0 454.9 47.1 38.7 847.5 862.3 267.6 151.2 118.9 8.3 165.1 153.1 28.6 3.3 17.2 11.5
2896743
2974135
3054251
3137210
3223127
386752.9 90713.3 97819.9 45768.9 25147.5 26142.7 13515.2 12416.8 11150.1 7833.0 7932.1 4118.0 3553.7 3170.4 2451.4 2332.2 2374.8 2331.8 1106.4 840.3 127.9 403.2 374.1 23.6 18.1 601.7 557.0 221.1 122.4 99.7 7.3 112.8 91.5 26.0 4.6 13.0 7.6
397219.3 93673.4 102063.1 46518.1 25959.4 27180.4 13767.4 12655.A 11347.1 8095.0 8253.1 4201.9 3630.1 3232.8 2505.3 2381.7 2459.6 2433.6 1129.9 859.6 743.0 413.2 383.0 26.2 20.5 625.9 585.1 227.6 127.2 103.7 9.2 119.8 98.8 27.7 5.3 14.2 6.5
408040.0 96739.7 106597.1 47269.8 26794.9 28268.0 14018.1 12893.2 11541.5 8361.6 8585.6 4282.7 3703.3 3291.7 2555.7 2427.6 2543.3 2536.4 1149.7 875.0 754.1 419.2 387.9 24.7 18.8 646.9 610.7 230.1 128.2 103.9 8.5 123.4 103.1 27.7 5.1 14.6 a.9
419234.0 99919.4 111451.9 48028.1 27658.5 29412.1 14271.5 13133.3 11737.4 8637.1 8934.3 4364.5 3777.4 3351.1 2606.5 2473.8 2630.1 2644.6 1169.7 890.7 765.3 425.3 392.8 23.2 17.0 660.8 637.8 232.6 129.2 104.2 7.8 127.3 107.6 27.6 4.9 15.0 9.2
430821.0 103219.4 116659.4 48796.8 28555.1 30619.0 14531.7 13379.9 11938.8 8925.6 9303.6 4451.2 3856.4 3415.0 2661.7 2524.3 2723.9 2762.3 1193.9 910.6 780.6 435.4 401.7 25.7 19.3 695.7 670.6 239.3 134.1 108.2 9.7 134.9 116.0 29.4 5.5 16.4 10.4
2546574
2612051
2679692
2749602
2821893
Z=150
z=151
Z-152
z-153
z-154
z.155
Z=156
21157
Z'15R
21159
c=8.686 Tr2.2
csu.711 T=2.2
C18.737 T=2.2
C10.763 T=2.?
C=8.780 T=2.2
C=0.814 T=2.2
C18.839 T=2.2
C18.865 T=2.2
cIa.890 T=2.2
C18.916 712.2
585797.1 146938.4 204200.2 57465.3 40188.0 47703.0 17512.2 16191.8 14193.1 12677.5 14415.2 5495.6 4808.6 4180.9 3327.5 3133.8 4007.8 4456.0 1526.9 1192.3 1000.7 596.0 545.5 93.0 81.1 1093.8 1187.0 313.2 180.3 137.0 7.9 2.5 217.5 222.7 28.1 2.0 20.2 15.4
603310.9 151773.6 216080.9 58333.8 41468.5 49676.4 17820.6 16484.5 14425.2 13094.3 14999.1 5609.0 4913.2 4265.0 3402.1 3202.2 4155.6 4654.6 1567.4 1227.8 1029.2 618.7 566.3 106.2 93.8 1144.6 1253.5 325.9 190.1 144.6 11.5 5.b 232.2 241.3 30.5 2.4 22.8 18.1
621441.6 156741.7 228740.9 59211.6 42782.6 51710.1 18133.3 16781.2 14659.7 13521.9 15599.0 5724.3 5019.6 4350.2 3477.9 3271.7 4307.5 4859.0 1608.8 1264.1 1058.3 641.9 587.5 119.9 106.8 1197.1 1322.3 338.9 200.1 152.3 15.2 8.6 247.5 260.7 32.8 2.9 25.1 20.8
640205.8 161841.7 242207.2 60098.A 44130.3 53802.7 18450.1 17081.9 14996.7 13960.3 16214.5 5R41.6
659621.6 167078.2 256513.7 61003.2 45519.4 55960.5 18778.6 17394.2 15143.6 14416.6 16852.6 5967.2 5244.4 4530.8 3639.6 3420.1 4630.2 5291.0 1700.3 1345.1 1124.2 695.8 637.3 154.6 140.1 1313.1 1472.8 371.6 226.6 173.9 28.5 20.5 285.6 308.0 42.3 7.9 34.9 31.7 4.0
3807237
3917011
4030583
506885.0 124794.6 155411.6 53279.6 34311.1 38812.3 16054.1 14809.8 13091.9 10779.1 11775.3 4980.1 4335.7 3803.0 2995.9 2831.0 3355.4 3578.6 1361.6 1051.6 891.8 515.9 474.2 58.9 50.0 889.9 915.6 279.8 160.5 126.4 11.7 177.4 167.6 30.7 3.7 18.9 13.1
521579.0 128958.2 163472.1 54102.1 35422.8 40462.3 16340.R 15081.6 13310.3 11140.2 12270.8 5082.4 4429.7 3879.0 3062.8 2892.4 3480.5 3744.3 1395.7 1080.9 915.1 533.5 490.2 67.5 58.0 930.1 967.7 288.5 166.5 130.6 12.6 8.0 186.7 179.4 31.2 3.6 19.R 14.1
536796.7 133251.6 172943.9 54929.4 36563.7 42174.8 16627.2 15353.0 13527.0 11507.9 lPTR0.3 5182.5 4521.3 3952.2 3126.7 2950.7 3605.6 3912.4 1426.7 1107.0 935.1 547.8 502.7 72.6 62.5 968.0 10!8.3 293.6 168.9 131.4 10.9 6.2 193.1 188.4 30.2 3.1 19.8 14.3
552562.7 137682.0 182669.0 55768.4 37741.0 43956.0 16920.9 15631.5 13749.4 11B89.8 13310.8 5287.7 4618.1 4030.0 3195.2 3013.5 3738.3 4090.2 1461.9 1137.3 959.1 566.0 519.2 81.6 70.9 1010.9 1074.8 302.4 175.0 135.6 11.8 h.7 203.1 201.6 30.7 3.0 20.8 15.5
568823.9 142223.2 193032.9 56606.4 38941.6 45789.1 17212.2 15907.2 13967.9 12276.2 13851.7 5390.1 4711.7 4104.3 3260.2 3072.6 3870.5 4269.3 1493.9 1164.4 979.6 580.8 532.2 87.2 75.9 1051.5 1129.6 307.6 177.4 136.1 9.0 4.6 209.9 211.6 29.7
3404311
3499814
3598731
3701115
3312120
lSl/2 PS1/2 2P1/2 2P3/2 3S1/2 3P1/2 3P3/2 303/2 3D5/2 4.51/2 4P1/2 4P3/2 40312 4DW2 4F5/2 4F7/2 551/2 SP1/2 SP3/2 503/E 5D5/2 5F5/2 5F7/2 507/P 5G9/2 65112 6P1/2 bP3/2 6D3/2 6DW2 6FS/2 751/2 7Pl/2 7P3/2 7D3/2 851/2 8P1/2 ET
15112 251/2 2Pl/2 2P3/2 3Sl/2 3P1/2 3P3/2 3D3/2 3D5/2 451/2 4P1/2 4P3/2 403/2 405/i! 4F5/2 4F7/2 551/2 5P1/2 5P3/2 50312 SDS/2 5F5/2 5F7/2 507/P 509/Z 6S1/2 6Pl/P bP3/2 6D3/2 6D5/2 bF5/2 6F7/2 75112 7P1/2 7P3/2 7D3/2 851/E 8P1/2 95112
2::: 15.9
ET
89 for
Explanation
1::: 8.7
14::: 130.0 26.0 2.9 14.9 9.3
XT . 3554.9 3342.2 4463.7 5069.1 1651.1 1301.1 1087.9 665.6 609.1 134.1 120.3 1251.2 1393.4 352.2 210.4 160.2 19.1 11.9 263.4 281.1 35.0 3.3 27.5 23.7
4148031
4269367
of Tables
93
Atomic Dota and Nuclear
Dota Tables, Vol. 19, No. 1, Jonuory
1977
B. FRICKE and G. SOFF
TABLE
lS1/2 PSl/2 2Pl/E 2P3/2 3S1/2 3P1/2 3P3/2 303/2 30512 451/2 4Pl/P 4P3/2 403/Z 4D5/2 4F5/2 4F7/2 5S1/2 5P1/2 5P3/2 5[33/2 5D5/2 5F5/2 5F7/2 5G7/2 50912 LSl/P 6P1/2 6P3/2 bD3/2 bD5/2 6F5/2 6F7/2 7S1/2 7Pl/2 7P3/2 7D3/2 7D5/2 BSl/E 8Pl/P 9S1/2 ET
II. Energy Eigenvalues
DFS Energy Eigenvalues 100 < 2 5 173
and Total Energies, Z = 100 to Z = 173 (in eV)
21160
21161
Z-162
Z=l63
Z=164
21165
21166
Z=167
Z=l68
Z=169
C=8.941 1=2.2
C18.966 Tat.2
C18.992 TE2.2
c19.017 TI2.2
C19.042 TSP.2
C=9.068 7-2.2
co9.093 1=2.2
Ci9.118 T12.2
c19.143 1=2.2
C19.168 112.2
679704.4 172439.7 271668.2 61912.4 46931.0 50169.4 19105.9 17705.1 15387.2 14878.4 17500.1 6090.0 5358.0 4621.4 3720.4 3494.1 4796.3 5513.7 1745.9 1385.4 1156.5 722.2 661.4 171.3 156.0 1372.3 1550.1 387.0 239.0 183.6 34.0 25.4 304.3 331.6 45.7 9.3 5.0 38.6 36.0 4.1
700462.9 177927.3 287696.7 62830.2 48386.5 60431.9 19437.1 18019.4 15632.7 15350.4 18161.7 6214.1 5472.9 4712.6 3802.0 3568.7 4966.1 5741.1 1791.9 1426.1 1189.1 748.6 685.6 188.0 171.9 1432.8 1629.1 402.5 251.3 193.2 39.5 30.1 323.4 355.8 49.0 10.6 5.6 42.3 40.5 4.3
721909.6 183529.8 304608.6 63750.0 49862.2 62740.3 19766.2 18331.3 15874.2 15827.0 18831.1 6334.7 5584.1 4799.5 3879.1 3638.7 5134.7 5968.2 1834.1 1462.9 1217.4 771.0 705.7 200.6 183.8 1490.4 1705.6 414.1 259.8 198.9 41.1 31.1 338.9 376.7 48.5 8.6 3.5 42.4 41.5
744064.2 189261.7 322430.9 64687.6 5137R.6 65110.3 20106.2 18654.2 16124.6 16320.4 19521.1 6462.8 5702.6 4893.1 3962.9 3715.2 5312.6 6205.9 1881.9 1505.2 1251.1 796.5 730.8 218.1 200.5 1554.4 1788.9 430.2 272.7 20H.9 46.9 36.1 359.3 402.7 51.7 9.8 3.9 46.3 46.3
766933.7 195112.3 341169.2 65635.4 52928.2 67533.5 20450.9 18981.4 16377.5 16824.6 20225.2 6592.9 5823.1 4987.9 4047.8 3792.6 5494.0 6448.8 1930.5 1548.3 1285.2 826.5 756.4 236.1 217.7 1620.0 1874.4 446.7 285.9 219.0 52.8 41.2 380.3 429.6 54.9 11.1 4.4 50.3 51.4
4394763
4524233
4657079
4795616
4937547
15112 2.5112 PPl/P 2P3/2 3S1/2 3P1/2 3P3/2 3D312 3D5/2 4S1/2 4P1/2 4P3/2 4D3/2 4DW2 4F5/2 4F7/2 5S1/2 5P1/2 5P3/2 5D3/2 5D5/2 5F5/2 5F7/2 5G7/2 5G9/2 6S1/2 6Pl/2 6P3/2 60312 6D5/2 6F5/2 6F7/2 7S1/2 7P1/2 7P3/2 7D3/2 7D5/2 8S1/2 8P1/2 9S1/2 9Pl/P 8P3/2 ET
lS1/2 2s1/2 2Pl/E 2P3/2 35112 3P1/2 3P3/2 3D3/2 3D5/2 45112 4P1/2 4P3/2 403/2 405/2 4F5/2 4F7/2 5s1/2 5P1/2 5P3/2
790530.3 201081.6 360834.6 66596.1 54513.6 70012.3 20802.7 19315.5 16635.4 17342.1 20945.9 6727.5 5948.0 5086.3 4136.3 3873.4 5683.6 6699.3 1982.6 1594.8 1322.4 G57.5 784.9 257.0 237.7 1689.9 1964.6 466.0 301.9 231.8 61.4 49.0 404.6 459.8 60.6 14.6 6.8 56.9 59.3 4.5
814861.0 207165.0 3131431.9 67568.2 56132.9 72545.2 21160.2 19655.1 16896.8 17871.3 21681.5 6865.2 6075.6 5187.0 4227.0 3956.2 5877.5 6955.9 2036.5 1643.1 1361.2 990.0 a14.8 279.3 259.1 1762.5 2057.8 406.6 319.1 245.8 71.1 57.8 430.5 492.0 67.3 19.0 10.0 64.6 68.4 5.2
839932.1 213359.4 402964.8 68551.3 57785.9 75132.2 21522.9 19999.8 17161.2 18411.7 22431.8 7005.4 6206.1 5289.4 4319.3 4040.5 6076.1 7218.1 2091.8 1692.7 1400.9 923.5 845.6 302.5 281.5 1837.4 2153.8 507.9 337.1 260.4 81.4 67.3 457.6 525.5 74.4 23.8 13.5 72.8 78.2 6.1 4.5
865749.2 219661.4 425434.8 69545.0 59471.6 77773.5 21890.4 2034R.9 17428.0 18962.9 23196.2 7147.6 6338.2 5392.8 4412.7 4125.6 6278.7 7485.4 2148.0 1743.0 1441.1 957.4 676.8 326.0 304.0 1913.8 2251.7 529.6 355.3 275.0 91.8 76.7 485.2 559.8 81.4 28.4 16.8 81.1 88.1 7.0 5.4
892316.7 226068.5 440642.2 70549.7 61190.7 80470.1 22262.9 20702.8 17697.6 19525.0 23975.2 7292.2 6472.6 5497.7 4507.4 4211.9 6485.7 7758.1 2205.3 1794.5 1482.1 992.0 908.6 350.2 327.2 1992.3 2352.1 551.7 374.1 290.0 102.5 86.5 513.8 595.2 80.6 33.2 20.2 89.8 98.6 8.0 6.5 5.6
5083690
5234064
5388684
5547557
5710683
z=170
z=171
Zr172
z=173
11170
21171
Z=172
z=173
c19.193 Tr2.2
W9.463 b2.2
Cs9.243 T=2.2
C19.268 Tr2.2
cr9.193 T=P.P
C19.463 Tr2.2
09.243 T=2.2
C19.268 Tr2.2
919638.3 232578.3 473186.8 71566..0 62943.6 83223.8 22641.4 21062.4 17970.5 20098.8 24769.6 7439.9 6609.9 5604.7 4604.2 4300.1 6697.9 8037.0 2264.4
938807.3 237306.9 490782.6 72617.0 64299.3 85410.8 23032.7 21434.1 18251.3 20558.9 25420.1 7591.9 6751.3 5714.2 4703.1 4389.9 6871.6 8269.6 2324.5
967112.1 243942.1 516427.1 73655.4 66100.2 8G252.7 23420.9 21802.9 18528.9 21149.0 26237.5 7743.5 bG92.3 5823.2 4801.8 4479.5 7090.0 8556.7 2385.0
1006175.0 252712.6 551833.0 74685.2 68406.9 91842.9 23810.7 22173.5 18808.5 21890.2 27247.8 7899.8 7038.2 5937.0 4905.5 4574.1 7363.8 8910.2 2451.4
5D3/2 5D5/2 5F5/2 5F7/2 5G7/2 5G9/2 651/P 6Pl/2 6Pi/E 6D3/2 6D5/2 6F5/2 6F7/2 75112 7P1/2 7P3/2 7D3/2 7D5/2 8S1/2 8P1/2 8P3/2 9S1/2 9P1/2 6G7/2 ET
See page 89 for Explanation
1847.7 1524.5 1028.0 941.7 375.6 351.7 2073.4 2455.6 575.2 394.0 306.1 114.3 97.3 544.0 632.5 96.7 38.9 24.5 99.5 110.2 6.6 9.4
1901.7 1567.1 1064.0 974.6 400.7 375.7 2140.9 2543.0 598.0 413.2 321.3 125.1 107.0 569.1 664.2 103.5 43.3 27.4 106.9 119.5 1::: 8.7
6006887
1956.2 1610.1 1100.5 1008.1 426.5 400.5 2224.4 2649.8 621.6 433.2 337.2 136.6 117.5 600.0 702.5 111.1 48.5 31.1 116.4 131.2 7.6 11.2 10.1
6180167
2016.5 1658.9 1143.0 1047.5 458.4 431.3 2331.4 2783.6 651.4 459.4 359.2 154.4 134.2 642.8 753.9 124.9 60.0 41.1 133.7 151.0 13.9 18.4 17.7 n.5 6405743
of Tables
94
Atomic Doto and Nuclwr
Data Tables, Vol. 19, No. 1, January
1977
B. FRICKE
TABLE
DFS
and G. SOFF
lSl/2
143028
2s1/2
27803
2Pl/2
26868
2P3/2
Corrections
21017
56::: 516.2 200.7 113.0 91.7 3.6 102.6 81.1 22.0
-91 -153 -92
+41 +8
-457
+155
-96
+13
-9
+11
+3
100 5 Z 5 173
+26 +4 0
SUP?
Experiment
DFS Result
-99
141953
141963
-69
27581
27573
27410
-77
26646
26664
26555
-70
20869
20868
20715
142050
+6
-42
7213
7200
7096
+1
-49
6783
6779
6695
0 -46
5411
5408
5320
4814
4746
4685
3D5/2
4540
4484
4421
451/2
1993
1940
1889
4P1/2
1793
1743
1702
4P3/2
1411
1371
1328
4D3/2
1099
1059
1031
4D5/2
1031
989
965
7292
-19
+1
3Pl/2
6864
-33
+3
-3
3P3/2
5474
-20
+2
+1
3D3/2
21139
374916.4 07274.2 93019.1 44750.4 24148.5 24891.8 13146.7 12055.4 10844.2 7491.8 7523.0 3984.9 3427.4 3063.5 2353.1 2240.5 2259.6 2197.4 1062.8 802.2 695.7 378.7 351.4 12.5
-715
3S1/2
TABLE
lSl/2 2s1/2 2Pl/2 2P3/2 351/2 w1/2 3P3/2 303/2 305/2 4Sl/2 4Pl/2 4P3/2 403/2 4DW2 4f5/2 4f7/2 5Sl/2 SPllP 5P3/2 5D3/2 SDS/2 5f5/2 5f7/2 507/2 5G9/2 6Sl/P bPl/Z 6P3/2 6D3/2 6DW2 6fW2 751/2 7Pl/2 7P3/2 703/2 i351/2 8P1/2
Eigenvalues
III. Energy Eigenvalues (in eV) for Z = 100 from DF and DFS Calculations and Binding Energies from Experiment DF Result
NEUTRAL
Energy
IV. Energy-- Eigenvalues (in eV) for Z = 139 and Z = 170 in Vkious States of Ionization
c-e.4
.s*
-25
1=2.2 17*
2=170
29+
3s*
375016.1 87373.9 93118.7 44850.3 24248.6 24991.0 13246.6 12155.4 10944.2 7591.3 7623.4 4Q04.2 3526.7 3162.7 2452.5 2339.9 2356.7 2296.5 1161.9 901.3 794.9 477.8 450.5 111.3 106.4 664.5 615.4 307.4 211.0 189.1
375254.5 07b14.7 93350.6 45092.3 24494.1 25236.2 13494.9 12402.2 11191.7 7844.1 7875.4 4339.3 3701.3 3417.7 2706.9 2594.5 2613.1 2551.1 1409.9 1148.4 1039.8 720.9 692.5 317.0
375734.0 88093.7 93837.0 45572.7 24982.2 25722.0 13989.0 12892.6 11684.0 8340.0 8377.6 4845.5 4207.0 3923.4 3212.4 3100.3 3110.0 3049.5 1882.3 1618.5 1503.1 1180.6 1148.9
375974.5 RO335.3 94070.4 45813.8 25219.1 25960.1 14223.3 13128.6 11919.2 8578.5 8608.8 5072.6 4514.9 4150.3 3440.4 3327.9 3331.9 3272.0 2098.0 1833.9 1717.0 1393.8 1361.4
898.4 849.6 517.9 414.0 387.0
1281.9 893.8 777.2 739.9
1535.5 1488.7 1084.2 963.8
198.6 176.5 109.5
385.1 361.1
NEUTRAL lSl/2 251/2 2Pl/P 2P3/2 351/2 3P112 3P3/2 3D3/2 305/2 451/2 4Pl/2 4P3/2 603/2 4D5/2 4f5/2 4f7/2 551/2 5Pl/2 5P3/2 5D3/2 SDS/2 5fW2 5f7/2 SG7/2 5G9/2 651/P 6Pl/2 6P3/2 6D3/2 6D5/2 6f5/2 6f7/2 751/2 7Pl/2 7P3/2 7D3/2 7D5/2 BSl/2 BPl/2 EP3/2 951/2
1::: 5.6
See page 89 for Explanation of Tables
95
919638.3 232578.8 473186.0 71566.1 62943.6 83223.8 22641.4 21062.4 17970.5 20098.9 24769.7 7439.9 6609.9 5604.8 4604.3 4300.1 6697.9 8037.0 2264.4 1847.7 1524.5 1020.0 941.7 375.6 351.7 2073.4 2455.6 575.2 394.0 306.1 114.3 97.3 544.0 632.5 96.7 38.9 24.5 99.5 110.2 6.6 9.4
c19.193 36* 920676.6 233594.2 474222.2 72568.5 63943.1 84229.3 23630.1 22053.8 18959.3 21084.2 25759.0 0412.2 7503.9 6576.1 5570.4 5272.9 7667.4 9010.5 3219.1 ERO2.3 2475.1 1978.2 1889.9 1322.4 1297.2 3024.5 3411.7 1481.4 1291.6 1187.9 972.9
112.2 701
1oa*
14e*
923114.4 235966.5 476654.1 74096.4 66257.1 86367.8 25903.7 24337.1 21232.4 23346.7 28037.5 10620.4 9800.4 8776.8 7794.9 7453.2 9855.9 11225.0 5245.6 4830.0 4458.3 3967.2 3319.0
927970.4 240711.2 4815OO.n 79535.7 70846.5 91232.4 30311.4 28806.0 25650.7 27683.7 32466.9 14632.8 13863.5 12761.5 11877.6 11531.5 13770.0
940986.6 253012.2 494454.2 91190.1 82149.7 103050.0 40218.8 39230.0
DATA AND
NUCLEAR
DATA
TABLES
19, 83-95 (1977)
DIRAC-FOCK-SLATER FOR
THE
ELEMENTS
CALCULATIONS
Z = 100, FERMIUM,
TO Z = 173*
B. FRICKE Theoretische
Physik, Gesamthochschule D35-Kassel, Germany
Kassel
and G. SOFF Institut
fur Theoretische D6-Frankfurt
Physik, Universitat am Main, Germany
Frankfurt
Listed here for the elements Z = 100, fermium, to Z = 173 are energy eigenvalues and total energies found from relativistic Dirac-Fock-Slater calculations. The effect of high ionization on the energy eigenvalues is presented for two examples. The use of these tables in connection with the energy levels of superheavy elements and molecular orbital (MO) x-ray transitions in superheavy quasiatoms, is discussed. In addition, a brief comparison between the results of the Dirac-Fock-Slater and Dirac-Fock calculations is given.
*Work supported by Gesellschaft fur Schwerionenforschung (GSI), Germany, the Bundesministerium fur Forschung und Technologie (BMFT)
Copyright 0 1977 by Academic Press, inc. All rights of reproduction in any form reserved.
83
Atomic
Data
and partially
and
Nuclear
Data
Tables,
(G.S.) by
Vol.
19,
No.
1, January
1977
B. FRICKE and G. SOFF
DFS Energy Eigenvalues 100 5 Z 2 173
CONTENTS
INTRODUCTION Atomic Physics of Superheavy Elements Method of Calculation Comments on the Results EXPLANATION
OF TABLES
TABLES I. Electron Occupation z = 173 II. Energy Eigenvalues III.
Numbers
for the Elements
Z = 100 to
and Total Energies, Z = 100 to Z = 173
Energy Eigenvalues for Z = 100 from DF and DFS Calculations and Binding Energies from Experiment
IV. Energy Eigenvalues for 2 = 139 and Z = 170 in Various States of Ionization
The discussion of the existence of elements near Z = 126 has been brought up again by recent experimental results.7 Also, new theoretical Hartree-Fock calculations8 indicate that stability around Z = 126 is more probable than at Z = 114.
INTRODUCTION
Within the last fifteen years several tables with the results of self-consistent-field (SCF) atomic calculations have been published. Such calculations can be nonrelativistic or relativistic and can make use either of Slater’s exchange approximation or exact exchange. Thus there are four major ways to perform the calculations. In the following we give for each of the four possible methods the best known reference, a short description of the listed results, and the elements covered.
Atomic Physics of Superheavy Elements
Two groups99 lo extended SCF atomic calculations to even higher elements mainly to get results for the ground-state configurations, the first ionization potentials, and the principal maxima and radii of the outerelectron wavefunctions. The data, together with extrapolations from the known elements, were used to get an idea of the chemical behavior’l of the superheavy elements up to Z = 172. A model calculation12 including quantum electrodynamical effects was used to go even to Z = 184. From an atomic-physics point of view, elements with very large proton numbers are especially interesting because many of the corrections, which have to be added to the SCF calculations, are known only in perturbation theory, where the expansion parameter is Za(a = l/137). These corrections take account of the quantum electrodynamical effects, vacuum polarization and vacuum fluctuation, and the so-called Breit interaction which includes magnetic effects and retardation. The accuracy of the experimental binding energies for elements like uranium and plutonium is now better than 1 eV.15 A theoretical calculation with such a small error must include the correlation energy as well as SCF effects of the contributions just mentioned. Comparisons between experiment and calculation of the binding energies of the innermost levels of fermium, which yield a
Nonrelativistic Hartree-Fock-Slater (HFS) calculations by F. Herman and S. Skillman’ with energy eigenvalues, potentials, wavefunctions, and relativistic corrections to the energy eigenvalues, for all elements up to Z = 103. Nonrelativistic Hartree-Fock (HF) calculations by J. B. Mann2 with energy eigenvalues, total energies, radii, two-electron integrals, and wavefunctions for all elements up to Z = 103. See also Refs. 3 and 4. Relativistic Hartree-Fock-Slater (rel. HFS) or DiracFock-Slater (DFS) calculations by C. Lu et a1.5 with energy eigenvalues, total energies, radii, and potentials for all elements up to Z = 126. Relativistic Hartree-Fock (rel. HF) or Dirac-Fock (DF) calculations by J. P. Desclaux6 with energy eigenvalues, radii, wavefunctions, and radial expectation values for all elements up to Z = 126. The tables of Refs. 5 and 6 present results for elements up to Z = 126. This number was chosen because several years ago Z = 126 was assumed to be the center of an island of nuclear stability. Later calculations of the late sixties shifted this island to Z = 114, but 126 was kept as a good endpoint in the tables of Refs. 5 and 6. 84
Atomit
Data
and
Nuckor
Dota
Tables,
Vol.
19,
No.
I,
Januory
1977
B. FRICKE
and G. SOFF
DFS
good agreement, 131r4show that at 2 = 100 the corrections already are of the order of percent. In the region of the superheavy elements they would be even larger. Even if no superheavy elements are found near 2 = 114 or Z = 126 at least the atomic clouds of superheavy elements can be produced for a very short time. The method is that of heavy-ion collision, where the energy is large enough so that two nuclei approach each other so closely that the electron clouds of both ions combine and the electrons feel a nuclear charge Z, + Z, in their center. Brief combination is possible because the velocity, at least for the inner electrons, is much larger than the velocity of the two nuclei approaching each other. If, by some process, an electron hole can be created in the inner level of either atom and thus of the combined atomic cloud, it is possible to observe an x-ray transition during the time of collision. The change of the electrons from the levels of the separated atoms to the levels of the combined system, is shown in the so-called correlation diagram, which has been discussed qualitatively in some detail by Lichteni6 as well as by Barat and Lichten.i7 Ab initio calculations within the adiabatic approximation, based on the Roothaan-Hartree-Fock method, have been made for small-Z systems.i8 For systems with Z >, 40 only relativistic many-electron molecular calculations lead to good results, which are given by Rosen et al. lg For the innermost 1s electrons one-electron calculations by Mtiller et alzO may give a good first approximation. Explanation of the experimentally observed molecular orbital (MO) M-x-ray spectrum by taking into account all possible transitions of the molecular system I-Au, with a combined Z = 132, provides the first evidence of the quasiatomic levels of superheavy elements.21 As already mentioned the behavior of the energy levels as function of the distance between the two nuclei is given in the correlation diagrams, in which the levels of the separated systems are linked with the levels of the combined system. Thus the knowledge of the levels of the atomic systems involved is the first step in the construction of the diagrams. The main purpose of this paper is to give the energy levels of the atoms with Z > 100 (the energy levels of the atoms with Z < 100 may be taken from any of the other tables). A secondary purpose is to give a first orientation for the expected transition energies for the x-ray spectra of possible superheavy elements since these offer the best means of detecting such elements in small quantities.
Method
The Hamiltonian follows :
Energy
Eigenvalues
100 5 Z 5 173
H=CT,--g+x i
e2 i
i
l’i
-rjI
= HO + Hint.
(1)
Using a fully antisymmetrized determinantal wavefunction, one obtains, after the variation of the total energy, the Hartree-Fock equation, which can be written in the form
J/i69
I
~:
#T(rN/i(r)
= E&(r).
(2)
The total energy is given by the expression
x bb&)d&‘>- &@‘)&@)I~
(3) We have used in this calculation the relativistic Hartree-Fock-Slater approximation [usually called DiracFock-Slater (DFS) calculation] in which the last term on the left side of Eq. (2), the exchange term, is approximated by22 3a 2a
Vexch(r) = - -q37?p(r)]l’3.
(4)
This is a very good description as long as the total electron density p(r) is not too small. For very large radii the total potential l/r is used. This procedure results in the so-called Latter correction.23 We have used here a, = 2/3.
Since we are interested in very heavy elements the wavefunctions have to be found by using the relativistic Dirac operator T = coup + firnc’ in Eq. (2). Because (Y and /? are four component matrices this leads to the set of coupled differential equations
-KJY
of Calculation
a[ci
-
W-)1
=
-a[~
of the atomic problem is given as
-
V(r)] + f
where cx is the fine-structure
85
Atomic
Data
(5)
Ki/r
and Nuclear
constant,
Data
Table.,
Vol.
~~
19, No.
the Dirac
1, January
,977
B. FRICKE
DFS
and G. SOFF
Energy
(6)
with the surface thickness t = 2.2 fm and the number of nucleonsA = 0.0073 Z2 + 1.3 Z + 63.6. For the equivalent radius we required R,, = 1.2 AlI3 fm, which determines the half-density radius c. For further details of the actual calculations and numerical procedures we refer to Refs. l-6 and 24. Comments
on the Results
Listed in Table I are the electron occupation numbers of the elements Z = 100 to Z = 173 found from the present DFS calculations. Given are the configurations with the smallest total energies. These are expected to be the ground-state configurations of the free atoms.
- 1MeVt 110
100
120
100 2 Z 5 173
There are only a few minor discrepancies between the results of the Dirac-Fock’O and the Dirac-FockSlater calculations for the differences of the total energies of the lowest states. Of course, the first method is more exact but it needs about an order-of-magnitude more computer time and the differences in the results are negligible for many purposes. For only four elements the lowest configurations came out differently in the two calculations but the difference between the total energies of the two lowest configurations is very small, of the order of 0.1 eV. In the case of the inner levels the additional corrections already noted in the text have to be added. They are small for small Z and of the order of a percent at Z=: 100. First estimates of the quantum electrodynamical corrections for elements near Z z 170 show25 that their influence remains below a few percent of the binding energies. The uncertainty due to the unknown nuclear-charge distribution in this region also is of the same order of magnitude.s In suite of the uncertainties in the DFS results, the listed eneigy eigenvalues of the elements in Table II are expected to give good approximations to the binding energies in the region where one does not know the appropriate corrections. They may be used to construct correlation diagrams and to get a first idea of the ex-
quantum number, and Fi and Gi the small and large components of the wavefunction i, respectively. The quantity ci in Eq. (5) represents the energy required to remove an electron from shell i if all other electrons remain unchanged. Therefore, usually it is called the “binding energy” in the sense of Koopmans’ theorem. Because the Dirac equation for a point nucleus leads to a singularity for the 1s level at 2 = 137 we have used an extended nucleus with a Fermi-type nuclear charge distribution p(r) = po{ 1 + exp [4 in 3(r - c)/t]}-l
Eigenvalues
130
lul
150
160 Atomic
Fig.
1. Energy
eigenvalues
for the inner
electrons
of the elements
86
Z = 100, fermium,
170 Number
-
to Z = 173
Atomic Data and Nuclear Data Tables. Vol. 19, No. I, January
1977
B. FRICKE
and G. SOFF
DFS
petted x-ray transition energies in the combined system during a heavy-ion collision or in a superheavy element which may be found in nature or a physics laboratory. In the DFS calculations there is one parameter in front of Slater’s exchange approximation in Eq. (4) which can be chosen within some narrow limits to yield an optimal agreement with those values one is looking for. Lu et a1.5 have chosen the original value used by Slater namely cy, = 1. This leads to energy eigenvalues which are good approximations for the ionization energies for the outer electrons. The more correct value as = 2/3 is used by most other authors, but this value has the disadvantage that the ionization energies for the outer electrons have to be calculated with the various corrections. Nearly independent of the value of (Y, are the energy eigenvalues of the inner electrons calculated with the DFS approximation which by chance lead to a better agreement with the experimental results than do the exact DF calculations. The differences can be seen in Table III, where we have listed the energy eigenvalues for DF and the DFS calculations for the inner electrons of fermium together with the known experimental results.13*‘” The DFS results seem to be closer to the experimental results. But if all known corrections to the DF calculations are added they, of course, come out to be much more superior. In order to obtain a general view we give the position of the energy eigenvalues in Fig. 1. The sequence of the levels, which is still normal at Z = 100, changes considerably with the higher elements. We see particularly the strong binding of the s and pi/z levels
Energy
Eigenvalues
100 < 2 5 173
with the same principal quantum number. The reason for this is twofold. The wavefunctions of the electrons with a total angular momentum l/2 are drawn nearer to the nucleus. This is the so-called direct relativistic effect. In response to this the other electrons are more strongly shielded and thus pushed away from the nucleus. This is the so-called indirect relativistic effect. The two effects together lead to a very unusual ordering of the levels. Figure 2 shows the energy eigenvalues of the outer electrons of the same elements. The behavior of the levels looks very normal for the elements up to Z z 120 and above Z =: 160. In the intermediate region the onset of the filling of the shells, as well as their behavior with increasing Z, is very complicated. The total energies in Table II provide an idea of how much energy may be gained from the electron cloud when the two atoms combine during a heavy-ion collision. To give an example we assume that Hg combines with Th to form the superheavy quasi atom z = 170:
ET(170) - E&90) - E&80) = (5.878 - 0.721 - 0.534) MeV = 4.623 MeV. This gain in energy is found for the most optimistic case that all electrons are present and contribute to the binding here amounting to more than 4.6 MeV. The total energies also are shown in Fig. 3 where the sharp rise for large Z can be seen even better. In heavy-ion collisions the incoming projectile ion
atomic number2 Fig. 2. Energy
eigenvalues
for the outer
electrons
of the elements
87
Z = 100, fermium,
Atomic
to Z = 173
Dato
and
Nuclear
Data
Tables,
Vol.
19,
No.
1, January
1977
B. FRICKE and G. SOFF
DFS Energy Eigenvalues 100< Z 5 173
is highly ionized and, because of strong ionization processes during the collision, an even higher ionization of the combined system is expected. To give an idea of the effect of this ionization on the energy levels, we have listed in Table IV the energy eigenvalues of elements 2 = 139 and 2 = 170 in various highly ionized states. The table shows that the medium and outer electrons are very strongly affected whereas the innermost electrons are shifted by a considerable amount only for very large ionizations or for ionization of the inner electron shells.
References 1. F. Herman and S. Skillman, Atomic Structure Calculations, (Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963) 2. J. B. Mann,
“Atomic Structure Calculations,” Los Alamos Scientific Reports No. LA-3690 (1967) and LA-3691 (1968)
3. C. Froese Fischer, ATOMIC DATA 4, 301 (1972) 4. J. B. Mann, ATOMIC DATA AND NUCLEAR DATA TABLES 12, 1 (1973)
Acknowledgment We thank Profs. W. Greiner and J. T. Waber for their continuous interest and support.
5. C. C. Lu et al., ATOMIC DATA 3, 1 (1971) 6. J. P. Desclaux, ATOMIC DATA AND NUCLEAR DATA TABLES 12, 3 11 (1973) 7. R. V. Gentry et al., Phys. Rev. Lett. 37, 11 (1976) 8. D. Kolb, to be published
6 E,[MeVI 1
9. B. Fricke and W. Greiner,
Physics Lett. B 30, 317 (1969); B. Fricke, W. Greiner, and J. T. Waber, Theor. Chim. Acta 21, 235 (1971)
energyofatomsas function of theatomicnumber
10. J. B. Mann, Proceedings of the Robert A. Welsh Foundation Conference. XIII. The Transuranium Elements, edited by W. 0. Milligan (Houston, Tex., Nov. 1969) p. 430 11. B. Fricke and J. T. Waber, Actinides Review 1, 433 (1971); B. Fricke, Structure and Bonding 21, 89 (1975) 12. B. Fricke and J. T. Waber, J. Chem. Phys. 57, 371 (1972) 13. M. S. Freedman, F. T. Porter, and J. B. Mann, Phys. Rev. Lett. 28, 711 (1972) 14. B. Fricke, J. P. Desclaux, and J. T. Waber, Phys. Rev. Lett. 28, 714 (1972) 15. G. L. Borchert, Z. Naturforsch.
A 31, 102 (1976)
16. W. Lichten, Phys. Rev. 164, 13 1 (1967) 17. M. Barat and W. Lichten, Phys. Rev. A 6,211 (1972) 18. E. W. Thulstrup and H. Johansen, Phys. Rev. A 6, 206 (1972); F. P. Larkins, lSt Int. Conf. on Inner Shell Ionization Phenomena, Atlanta, Ga. (1972); for more information see W. Lichten, Atomic Physics 4, edited by G. zu Putlitz, E. W. Weber, and A. Winnacker, (Plenum Press, New York, 1975), p. 249
Atomic number O 50I
I
70 I
I
90I
I
19. A. Rosen, D. Ellis, B. Fricke, and T. Morovic, Abstracts of Contributed Papers, 2nd Int. Conf. Inner Shell Ionization Phenomena, Freiburg (1976) p. 18
110 I I 130 I l 150 l l 170 , c
Fig. 3. Total energies of the atoms up to Z = 173
88
DFS Energy Eigenvalues 100 < Z 2 173
B. FRICKE and G. SOFF
Phys. Rev. 137, A27 (1965); D. A. Liberman, D. T. Cromer, and J. T. Waber, Comp. Phys. Comm. 2, 107 (1971); I. P. Grant, Adv. Phys. 19, 747 (1970). For a summary of references see C. Froese Fischer, Comp. Phys. Comm. 5, 147 (1973)
20. B. Mullet-, J. Rafelski, and W. Greiner, Phys. Lett. B 47, 5 (1973); B. Mtiller and W. Greiner, Z. Naturforsch. A 31, 1 (1976) 21. B. Fricke, T. Morovic, W. D. Sepp, A. Rosen, and D. Ellis, to be published
25. G. A. Rinker and L. Wilets, Phys. Rev. A 12, 748 (1975); M. Gyulassy, Phys. Rev. Lett. 33, 921 (1974); K. T. Cheng and W. R. Johnson, Phys. Rev., in print
22. J. C. Slater, Phys. Rev. 81, 385 (1951) 23. R. Latter, Phys. Rev. 99, 510 (1955) 24. D. A. Liberman,
J. T. Waber, and D. T. Cromer,
EXPLANATION TABLE
OF TABLES
I. Electron Occupation Numbers for the Elements 2 = 100 to Z = 173
Values from present DFS (Dirac-Fock-Slater) TABLE
calculations
II. Energy Eigenvalues and Total Energies, Z = 100 to Z = 173 (in eV)
Values from present DFS (Dirac-Fock-Slater)
calculations
c,t
Nuclear-change density parameters c and t in Eq. (6) in fm (lo-l3 cm)
E,
Total energy
TABLE
III.
Energy Eigenvalues (in eV) for Z = 100 from DF and DFS Calculations and Binding Energies from Experiment
DF
Dirac-Fock
Corrections
Magnetic contribution, retardation, vacuum fluctuation, vacuum polarization, and rearrangement effect including rearrangement in the magnetic contribution
Experiment
From conversion electron energies in the beta decay of 254mEs from F. T. Porter and M. S. Freedman, Phys. Rev. Lett. 27,293 (197 1). The experimental error bars are between 7 and 14 eV
DFS RESULT
Dirac-Fock-Slater
TABLE
CT
results of present authors
values of present authors
IV. Energy Eigenvalues (in eV) for Z = 139 and Z = 170 in Various States of Ionization Same as c,t in TABLE
89
II
B. FRICKE
TABLE 2
5F7/2
100 101 102
8
103
8
1
104
8
2
105
8
106
Energy
Eigenvalues
100 5 2 < 173
I. Electron Occupation Numbers for the Elements (Rn core plus 7S2 and 5F5/26) 6133/Z
6D5/2
7P1/2
7P3/2
6
119
8
4
6
2
4
1
7
120
8
4
6
2
4
2
121
8
4
6
2
4
2
1
122
8
4
6
2
4
2
1
1
123
8
4
6
2
4
2
1
1
3
124
8
4
6
2
4
2
1
8
4
125
8
4
6
2
4
2
1
107
8
4
126
8
4
6
2
4
2
1
108
8
4
2
127
8
4
6
2
4
2
109
8
4
3
128
8
4
6
2
4
2
110
8
4
4
129
8
4
6
2
4
111
8
4
5
130
8
4
6
2
112
8
4
6
1
131
8
4
6
2
113
8
4
6
2
132
8
4
6
114
8
4
6
2
133
8
4
6
115
8
4
6
2
1
134
8
4
6
116
8
4
6
2
2
117
8
4
6
2
3
118
8
4
6
2
4
5G9/2
6F5/2
7D3/2
6F7/2
2
569/Z
6F5/2
7D3/2
6F7/2
135
1
4
154
10
6
2
6
136
2
4
155
IO
6
2
7
2
8
3
3
7Pl/2
7P3/2
Z = 100 to Z = 173
5~712
137
6D5/2
DFS
2
z
6D3/2
and G. SOFF
1
156
10
6
8sl/2
8P1/2
7D3/2
6F5/2
3
1
2
2
2
2
3
2
2
4
2
2
2
5
4
2
2
2
6
4
2
2
2
7
2
4
2
2
2
8
2
4
2
2
3
8
2
4
2
2
4
8
833/Z
951/Z
71)5/Z
1
9P1/2
138
4
3
1
157
10
6
3
8
5
2
2
158
10
6
4
8
140
6
3
1
159
10
6
4
8
141
7
2
2
160
10
6
4
8
1
142
8
2
2
161
10
6
4
8
2
143
9
2
2
162
10
6
4
8
4
144
10
1
3
163
10
6
4
8
5
145
10
3
2
164
10
6
4
8
6
146
10
4
2
165
10
6
4
8
6
147
10
5
2
166
10
6
4
8
6
2
167
IO
6
4
8
6
2
1
4
8
6
2
2
10
6
2
149
10
6
3
168
10
150
10
6
4
169
10
6
4
8
6
2
2
151
lo
6
3
2
170
10
6
4
8
6
2
2
152
lo
6
3
3
171
10
6
4
8
6
2
2
153
lo
6
2
5
172
10
6
4
8
6
2
2
173
10
6
4
8
6
2
2
89 for
Explanation
of Tables
90
6G7/2
1
6
See page
1 3
139
148
X7/2
1
B. FRICKE and G. SOFF
DFS Energy Eigenvalues 100 5 2 2 173
TABLE II. Energy Eigenvalues and Total Energies, 2 = 100 to Z = 173 (in eV)
lSl/Z ZSl/P 2P1/2 2P3/2 3Sll2 3P1/2 3P3/2 3[33/2 305/Z 451/Z 4P1/2 4P3/2 403/Z 4D5/2 4FW2 4F7f2 5S1/2 5P1/2 5P3/2 503/Z 5D5/2 5F5/2 5F7/2 6Sl/2 6Pl/2 6P3/2 6D3/2 7S1/2 7Pl/P ET
lSl/P 251/o 2P1/2 2P3/2 3S1/2 3Pi/2 3P3/2 303/2 3D5/2 4S1/2 4Pl/2 4P3/2 403/Z 405/2 4F5/2 4F7/2 5s1/2 5P1/2 5P3/2 5D3/2 5D5/2 5F5/2 5F7/2 6Sl/2 bP1/2 6P3/2 683/Z bD5/2 7Sl/2 7P1/2 ET
ZIlOO
Z=101
21102
23103
Z-104
z-105
2=106
z=107
2=1oe
Z=109
c=7.000 T-2.2
C-7.252 T=%.E
cc7.399 Tr2.2
Cr7.427 T"2.2
(317.455 T=2.2
c17.483 Tr2.2
cr7.511 T=X.2
c17.538 1=2.2
C-7.566 112.2
c=7.594 Tr2.2
142049.7 27409.6 26555.4 20715.1 7095.7 6694.6 5320.0 4685.2 4420.9 1889.3 1701.9 1328.5 1031.5 965.2 573.4 555.0 433.2 355.5 258.1 144.1 129.8 5.9 3.9 59.5 36.4 21.8
145656.9 28220.2 27355.9 21204.2 7325.6 6918.1 5466.6 ke2i .6 4544.7 1950.8 1768.5 1372.5 1069.6 999.7 600.1 580.6 451.0 371.0 266.9 149.7 134.4 6.4 4.3 61.4 37.6 22.0
4.9
5.0
948461
973705
149346.1 29052.9 28117.9 21699.3 7561.8 7147.5 5615.2 4959.9 4670.0 2032.2 1836.9 1417.0 :E-: . 627.2 606.4 469.1 387.0 275.7 155.4 139.1 7.0 4.6 63.4 38.8 22.3 5.1
999468
153129.4 29915.6 29029.1 22206.7 7811.3 7389.9 5772.6 5106.9 4803.5 2113.3 1914.0 1468.9 1154.1 1076.5 661.3 639.3 494.5 410.1 291.1 167.5 150.1 13.1 10.4 70.4 44.6 2h.2 2.5 5.9
156995.1 30802.8 29905.2 22721.8 8068.9 7640.7 5933.9 5257.7 4940.3 2198.2 1994.8 1523.1 1202.3 1120.7 697.6 674.4 522.0 435.3 308.1 181.2 162.7 20.7 17.7 78.6 51.6 31.1 4.3 7.1 3.5
1025766
1052586
151/z 2s1/2 PP112 PP3/2 351/Z 3P1/2 3P3/2 3D3/2 3D5/2 4S1/2 4P1/2 4P3/2 4D3/2 4D5/2 4F5/2 4F7/2 5S1/2 5P1/2 5P3/2 5D3/2 5D5/2 5F5/2 5F7/2 6Sl/P 6P112 6P3/2 603/2 751/Z 6D5/2 ET
160940.5 31709.8 30801.8 23239.2 a329.7 7894.7 6093.7 5406.9 5075.1 2281.6 2074.1 1574.4 1247.4 1161.6 730.6 706.1 546.5 457.4 321.5 191.2 171.4 24.4 21.1 82.9 54.6 31.9 3.8 6.8
i64974.2 32643.6 31726.3 23765.0 8597.8 8158.2 6258.1 5560.h 5213.9 2368.5 2157.9 162a.6 1295.6 1305.4 766.5 740.6 573.9 482.5 337.3 203.6 182.5 30.5 26.8 89.3 59.7 34.6 4.5 7.2
169097.2 33503.7 32678.1 24297 ,a 8877.9 8429.9 6425.4 5717.3 5355.1 2460.6 2244.0 1684.5 1345.3 1250.5 803.7 776.4 602.8 509.0 354.0 216.8 194.4 37.3 33.3 96.3 65.4 37.7 5.5 4.0 7.6
173312.1 34590.4 33658.0 24837.0 9163.9 8709.7 6595.4 5876.3 5498.2 2554.5 2334.9 1741.3 1396.0 1296.4 841.7 812.9 632.6 536.5 371.0 230.4 206.5 44.4 39.9 103.6 71.3 40.8 6.5 4.b 8.1
177621.7 35604.9 34667.1 25382.6 9458.0 8997.9 6767.9 6037.9 5643.3 2651.2 2427.5 1799.2 1447.6 1343.2
1079942
1107844
1136306
1165342
1194968
eao.5 850.1
663.4 564.9 388.4 244.2 218.9 51.7 46.8 111.1 77.3 43.8 7.4 5.3 a.5
Z-110
z-111
z=112
Z-113
2=114
z-115
Z=116
z=117
z=lle
21119
C17.621 Ts2.2
C17.649 1=2.2
C=7.676 T=2*2
c=7.704 T=2.2
c=7.731 T+2.2
cE7.758 Tt2.2
C=7.786 1=2.2
c17.813 T=2.2
c=7.840 Tn2.2
C=7.867 1x2.2
ie2029.4 36648.2 35706.9 25934.7 9760.4 9294.9 6943.0 6202.1 5790.4 2750.7 2523.2 1858.2 1500.4 1390.8 920.1
186538.3 37721.4 36778.9 26493.2 10071.6 9h00.9 7120.7 6368.6 5939.3 2853.3 2622.0 19la.2 1554.0 1439.1 960.4 926.7 728.3 625.1 424.4 273.0 244.5 67.1 61.4 126.7 90.1 49.8 9.4 6.6 9.4
i9iisi.e 38825.9 37884.6 27058.2 10391.7 991b.6 7301.0 6537.9 6090.3 2959.0 2724.0 1979.3 1608.7 1488.4 1OOl.b
195276.6 39965.7 39028.6 27632.5 10724.1 10245.1 7486.8 6712.3 6245.9 3070.8 2832.3 2044.3 1667.3 1541.3 1046.4 1009.2 800.6 692.7 464.7 306.1 274.0 80.6 79.8 146.4 106.9 58.6 13.8 10.1 11.6 4.9
200713.8 41139.6 40210.3 28213.5 11066.4 10584.3 7675.4 6889.6 6403.9 3186.2 2944.3 2110.6 1727.2 1595.3 1092.3 1053.3 e40.9 730.0 487.2 324.9 291.0 98.4 91.1 158.3 117.4 64.6 17.3 13.0 13.5 5.7
205b69.4 42350.7 41433.2 28803.0 ii420.e 10936.4 7868.7 7071.5 6565.8 3307.1 3062.0 2ieo.o 1790.1 1652.0 1141.0 1100.0 883.1 770.6 511.9 345.9 310.0 112.4 104.5 172.6 130.1 72.4 22.7 17.7 16.9 7.8 3.8
210745.9 43598.9 42697.9 29399.2 11786.0 11300.2 eo64.R 7256.1 6729.8 3431.7 3183.8 2250.7 la54.2 1709.9 1190.7 1147.7 927.5 812.7 537.3 367.6 329.6 126.9 lie.4 187.4 143.4 80.5 28.2 22.6 20.3 10.1 4.4
215947.7 44ea5.5 44006.6 30002.0 12162.1 11676.2 8263.7 7443.4 6895.8 3560.2 3309.7 2322.5 1919.5 1768.6 1241.3 1196.2 973.3 856.4 563.2 389.6 349.6 141.7 132.7 202.6 157.1 ea.6 33.7 27.5 23.7 12.4 5.2
221279.4 46212.4 45362.0 30611.4 12549.6 12065.1 8465.3 7633.4 7063.8 3692.7 3439.9 2395.6 1985.9 1828.3 i292.e 1245.5 1020.5 901.7 589.5 4lp.2 369.9 157.0 147.2 214.3 171.4 96.8 39.4 32.4 27.2 14.9 h.0
226748.8 47583.6 46769.2 31229.9 12951.5 12470.0 8672.2 7828.5 7236.4 3831.8 3577.2 2472.3 2056.0 1891.3 1347.6 1298.2 1072.0 951.2 618.9 437.7 393.1 175.1 lb4.6 237.1 lee.7 107.5 47.6 39.9 33.1 19.7 a.4 3.6
1256051
1287542
1319687
1352505 1386015
1420239
1455201
1490925
1527433
eea. i
695.4 594.5 406.2 258.5 231.6 59.3 54.0 lie.7 83.6 46.8 a.4
5.9 a.9
1225199
966.2
762.4 656.8 442.9 287.9 257.7 75.3 69.0 134.9 96.9 52.8 10.4 7.3 9.8
lS1/2 2s1/2 2P1/2 2P3/2 351/i? 3Pl/P 3P3/2 3D3/2 305/P 4s1/2 4P1/2 4P3/2 4D3/2 4D5/2 4F5/2 4F7/2 551/P 5P1/2 5P3/2 503/2 SDS/Z 5F5/2 5F7/2 6Sl/E bPl/Z 6P3/2 6D3/2 605/2 ISl/P 7Pl/2 7P3/2 asl/z ET
See page 89 for Explanation of Tables
91
Atomic Dota and Nuclear
DD+D Tables, Vol. 19, No. 1, Jonuory
1977
B. FRICKE and G. SOFF
TABLE
151/2 2s1/2 2P1/2 2PW2 35112 3P1/2 JP3/2 303/E 3D5/2 4-9112 4P1/2 4P3/2 403/E 405/i! 4F5/2 4f7/2 5S1/2 5Pl/P 5P3/2 503/2 5DS/P 5F5/2 5F7/2 65112 6P1/2 6P3/2 603/2 605/2 7s1/2 ?Pl/2 7P3/2 as1/2 0P1/2 703/2 6F5/2
15112 251/2 PP1/2 2P3/2 351/2 3P1/2 3?3/2 30312 305/2 451/2 4P1/2 4P3/2 403/2 405/2 4F5/2 4F7/2 5S1/2 5P1/2 5P3/2 50312 50512 5F5/2 5F7/2 5G7/2 651/2 6Pl/2 6P3/2 60312 60512 6F5/2 7S1/2 7P1/2 7P3/2 85112 0P1/2 ET
and Total Energies, Z = 100 to Z = 173 (in eV)
2.120
z--121
Z=l22
2=123
21124
z=125
21126
Z=127
z=120
Z=129
Cx7.094 TI2.2
Cl7.921 1=2.2
c17.940 T=2.2
C37.975 1-2.2
c=0.002 r12.2
C18.029 Tr2.2
C~E.056 1=2.2
c=a.082 1=2.2
c=a.109 112.2
C10.136 1=2.2
244024.3 51971.2 51321.9 33127.6 14236.2 13775.9 9312.2 0432.0 7766.7 4270.0 4021.3 2712.4 2275.9 2008.7 1520.3 1463.7 1238.7 1113.0 712.4 519.6 467.6 234.1 221.5 299.2 246.7 142.9 75.3 64.9 53.4 36.7 17.7 6.2 3.3 3.3
250086.7 53526.8 52957.0 3377n.o 14607.1 14239.2 952K.7 0635.2 7945.6 4431.6 4175.7 2790.5 2347.1 2151.9 1575.2 1516.1 1293.4 1166.5 740.2 543.5 400.7 250.1 236.7 316.9 213.0 150.7 80.6 69.4 56.9 39.4 18.4 6.4 3.4 3.4 4.7
256309.9 55130.9 5465b.2 34413.2 15148.6 14716.4 9739.9 0036.3 0120.5 4506.1 4331.9 2865.7 2415.4 2212.0 1626.9 1565.2 1346.1 1218.2 764.6 563.Y 506.4 262.6 240.4 331.3 276.2 154.9 82.5 70.5 57.6 39.7 17.4 b.l 3.3
262670.4 56777.2 56413.2 35053.6 15618.1 15205.1 9950.0 9033.9 0291.4 4741.2 4409.6 2938.1 2480.9 2269.1 1675.6 1611.3 1398.1 1269.b 788.3 583.8 523.8 275.4 260.5 8.6 340.6 292.6 163.9 90.1 77.5 a.9 65.4 47.0 23.1 10.6 6.8
289270.9 58499.0 58271.0 35714.0 16100.6 15720.4 10165.2 9237.7 8467.0 4098.6 4651.3 3006.7 2542.a 2321.9 1720.4 1653.2 1444.3 1315.6 803.9 595.h 532.0 279.7 264.0 6.1 357.6 300.9 164.3 89.1 76.1 5.9 64.0 45.9 20.2 7.4 3.9 3.6
276024.4 b0268.7 60198.3 36371.2 16609.8 16250.7 10378.9 9439.3 0639.9 5059.0 4810.0 3075.9 2605.0 2374.9 1765.3 1695.1 1493.4 1364.9 821.4 609.2 543.7 205.8 269.4 5.6 369.0 311.6 166.7 90.1 76.6 5.4 66.5 47.3 20.2 7.5 3.9
282971.4 62100.6 62215.4 37034.5 17127.5 16803.3 10594.9 9643.1 8814.3 5226.2 4991.5 3145.6 2667.0 2420.3 1810.4 1737.2 1544.1 1416.2 038.9 622.9 554.5 291.9 274.7 5.0 300.9 322.9 169.1 91.1 77.2 4.9 68.4 48.8 20.2 7.6 4.0
290120.5 63997.7 64329.5 37703.7 17662.5 17379.7 10813.1 9049.1 8989.9 5398.0 5172.2 3216.0 2731.2 2481.9 1855.0 1779.5 1596.5 1469.0 856.4 636.6 565.2 297.8 279.9
1681088
1722777 1764622
1007556
1851536
la96636
1942905
232359.0 4P999.4 46229.4 31855.6 13366.4 12809.7 8882.5 0027.0 7411.6 3975.0 3719.9 2550.9 2127.9 1955.9 1404.0 1352.3 1125.6 1003.0 649.3 464.2 417.3 194.1 183.0 257.0 207.1 119.0 56.5 47.9 39.6 25.1 11.3 4.2
ET
II. Energy Eigenvalues
DFS Energy Eigenvalues 100 2 Z 5 173
1564753
238116.4 50462.0 49746.5 32408.9 13795.2 13325.5 9096.h 8229.2 7509.7 4125.2 3860.6 2631.7 2201.9 2022.5 1462.4 1400.2 1181.9 1057.7 601.2 492.3 442.9 214.5 202.7 270.4 227.2 131.5 66.5 57.0 47.1 31.4 15.1 5.4 3.0
1602913
1642191
lS1/2 ES1/2 2P1/2 2P3/2 35112 3Pl/P 3P3/2 303/2 30512 451/2 4P1/2 4P3/2 40312 405/2 4F5/2 4f7/2 5.5112 5P1/2 5P3/2 503/2 505/P 5F5/2 5f7/2 5G7/2 6S1/2 bPl/Z bP3/2 603/2 685/2 6F5/2 7S1/2 7P1/2 7P3/2 asi/ BPI/E 70312
3.4
ET
393:: 334.7 171.5 92.1 77.b 4.4 70.2 50.3 20.2 7.7 4.0
21130
25131
2.132
Z=133
21134
z-135
Z=136
z=137
21138
z=139
Cr0.162 TI2.2
CI0.189 Tl2.2
C38.215 r=2.2
C10.242 1=2.2
C=8.268 T=2.2
C=8.295 T=2.2
C=8.321 TE2.2
csa.347 T=2.2
c=a.374 1x2.2
e-a.400 1.2.2
337800.4 76937.4 79564.3 41862.0 21292.7 21453.7 12188.7 11149.2 10090.1 6575.8 6457.5 3673.7 3145.7 2831.8 2155.2 2058.4 1972.5 1869.0 903.6 739.6 648.2 351.1 327.7 13.5 9.4 492.3 435.4 195.1 105.4 86.8 3.6 87.8 66.0 21.1
346b37.3 79379.8 82620.4 42574.1 21969.9 22249.5 12423.7 11371.4 10275.7 6792.6 6704.6 3749.5 3214.2 2888.3 2203.3 2102.6 2039.7 1944.0 1002.3 754.2 b59.P 357.1 332.8 12.5 a.2 500.7 453.1 197.7 106.5 87.2 3.0 90.5 68.R 21.1
365183.9 84546.2 89339.3 44019.8 23398.7 23967.5 12904.3 11826.2 10654.4 7252.1 7230.7 390fJ.7 3356.6 3005.0 2303.9 2195.4 2184.0 2110.0 1043.6 787.1 604.6 372.6 346.3 13.7 9.0 546.8 495.1 206.2
8.0 4.6
9.0 4.7
355762.4 81917.7 85883.6 43296.1 22b74.4 23089.4 12665.0 11599.9 10466.6 7020.7 6967.5 3029.0 3287.2 2940.9 2255.5 2151.0 2113.1 2027.4 1025.9 772.6 673.9 366.9 341.6 15.1 10.6 529.4 475.5 203.9 111.1 91.1 4.9 96.6 74.8 22.9 3.3 10.1 5.3 2362114
2421754
297400.6 65962.9 b6548.2 30379.1 18215.4 17981.5 11033.6 10057.4 9167.0 5575.5 5360.7 3287.1 2795.2 2536.0 1901.5 1822.0 1650.7 1525.9 074.2 650.4 576.0 303.8 285.1 3.6 405.9 347.2 173.9 93.1 78.1 3.9 72.2 52.0 20.2 7.9 4.1
305061.0 67999.3 60800.4 39060.5 18787.1 10610.6 11256.5 10267.9 9345.5 5758.9 5557.5 3359.0 2060.0 2590.4 1947.6 1064.8 1706.9 1584.6 092.0 664.3 506.9 309.8 290.3 2.8 419.1 360.3 176.3 94.1 78.4 3.5 74.3 53.8 20.2 8.0 4.1
312871.4 70110.1 71335.6 39748.0 19378.3 19268.6 11481.7 10480.6 9525.4 5940.6 5763.1 3431.6 2925.5 2645.2 1994.1 1908.0 1765.1 1646.3 910.1 670.5 597.8 315.9 295.5 2.0 433.0 374.3 178.8 95.2 79.1 3.0 76.5 55.8 20.2 a.2 4.3
320928.7 72305.8 73931.2 40440.8 19997.6 19965.5 11717.5 10703.7 9714.7 6153.7 5987.2 3514.5 3001.1 2710.0 2050.4 1960.7 1035.0 1720.4 937.3 701.4 617.2 330.2 300.8 8.0 454.3 395.9 185.6 99.7 82.7 3.6 80.7 59.5 20.6 a.4 4.3
329237.0 74583.0 76672.4 41156.1 20638.3 20695.9 11956.2 10929.5 9906.0 6366.2 6221.8 3598.0 3078.1 2775.0 2107.6 2014.5 1907.8 1790.b 965.1 725.2 637.3 345.1 322.6 14.5 476.6 418.8 192.7 104.4 86.3 4.1 85.1 63.5 21.1 8.6 4.4
1990396
2039193
2009267
2140769
2193732
lSl/Z PSI/P 2P1/2 2P3/2 351/2 3P1/2 3P3/2 303/E 3D5/2 4Sl/E 4P1/2 4P3/2 4D3/2 40512 4F5/2 4F7/2 55112 5P1/2 5P3/2 50312 505/2 5F5/2 5F7/2 50712 50412 6S1/2 6Pl/2 6P3/2 603/P 605/2 6F5j.2 75112 7P1/2 7P3/2 70312 as112 8P1/2 ET
See page 89 for Explanation
2240236
2304354
'2.: . 4.2 99.5 77.7 22.0 3.1 10.3 5.4
374916.4 07274.1 93019.0 44750.4 24140.5 24891.8 13146.7 12055.4 10844.2 7491.8 7523.8 3984.9 3427.4 3063.5 2353.1 2240.5 2259.6 2197.4 1062.0 802.2 695.7 378.7 351.4 12.5 7.6 565.3 516.2 208.7 113.0 91.7 10::: 01.1 22.0 3.0 10.5 5.6 2483211
of Tables
92
Atomic
Data and Nuclwr
Da+o TobIer, Vol. 19, No. 1, Jmuary
1977
DFS Energy Eigenvalues 100 5 Z < 173
B. FRICKE and G. SOFF
TABLE
ISI/ 251/2 2P1/2 2P3/2 351/P 3P1/2 3P3/2 303/2 305/C 451/2 4P1/2 4P3/2 403/2 40512 4F5/2 4F?/2 ss1/2 5P112 5P3/2 5D3/2 505/P 5FS/E SF712 56712 509/i? 65112 6P1/2 6P3/2 6D3/2 6DS/E 6FW2 751/t 7Pl/2 7P3/2 70312 851/2 BP]/2 ET
lSl/Z 2Sl/E 2P1/2 2P3/2 351/2 3P1/2 3P3/2 3D3/2 30512 4S1/2 4P1/2 4P3/2 4D3/2 4D5/2 4FW2 4F7/2 551/z 5P1/2 5P3/2 5D3/2 505/2 5F5/2 5F7/2 SG7/2 50912 65112 6P1/2 6P3/2 6D3/2 6D5/2 6F5/2 6F7/2 75112 7Pl/2 7P3/2 703/2 BSl/E 8P1/2 ET
See
page
II. Energy Eigenvalues
and Total Energies, Z = 100 to Z = 173 (in eV)
2=140
25141
21142
z=143
Z=144
Z=145
Z=146
z--147
Z.=l48
z=149
C18.426 Tr2.2
C=8.452 T12.2
c-8.476 T=2.2
CEB.504 T=2.2
we.530 T12.2
C18.556 712.2
C=8.582 T=2.2
C=8.60R T-2.2
GE.634 T-2.2
c=8.660 T=2.2
440669.5 105918.2 121067.2 49278.6 29225.7 31548.7 14666.7 13494.5 12023.9 9120.6 9563.2 4485.5 3881.9 3431.9 2669.8 2530.3 2781.9 2838.8 1195.5 908.7 776.0 427.9 393.6 15.7 9.2 704.7 604.2 232.8 126.7 100.6 3.5 130.9 112.8 25.0 3.0 13.7 8.1
453003.5 109438.7 126990.7 50062.3 30178.R 32869.6 14936.0 13749.7 12232.1 9430.7 9967.9 4579.9 3968.3 3502.7 2731.6 2587.3 21387.5 2972.6 1225.8 934.6 796.7 443.1 407.5 22.1 15.1 737.4 724.4 240.4 131.8 104.2 4.1 138.1 121.2 25.5
465773.5 113083.8 133351.6 50853.3 31162.6 34254.7 15208.5 14007.9 12442.1 9750.7 10390.6 4675.8 4056.1 3574.4 2794.4 2645.1 2996.9 3112.7 1256.8 960.9 817.9 458.7 421.7 28.9 21.4 771.5 766.9 248.1 136.9 107.9
478997.2 116855.5 140183.9 51651.8 32177.6 35705.1 15484.3 14269.3 12654.0 10080.7 10831.3 4773.1 4145.2 3647.0 2858.0 2703.6 3109.9 3259.0 1288.5 987.9 839.4 474.7 436.2 35.9 LB.0 806.9 811.5 255.9 142.1 111.6 5.2 153.4 139.5 26.4 2.8 15.5 9.9
492696.0 120759.7 147526.4 52461.6 33228.1 37225.3 15767.4 14537.8 12871.8 10424.6 11294.1 4875.7 4239.6 3724.4 2926.4 2766.7 3230.6 3415.5 1324.6 1019.3 865.3 495.0 454.9 47.1 38.7 847.5 862.3 267.6 151.2 118.9 8.3 165.1 153.1 28.6 3.3 17.2 11.5
2896743
2974135
3054251
3137210
3223127
386752.9 90713.3 97819.9 45768.9 25147.5 26142.7 13515.2 12416.8 11150.1 7833.0 7932.1 4118.0 3553.7 3170.4 2451.4 2332.2 2374.8 2331.8 1106.4 840.3 127.9 403.2 374.1 23.6 18.1 601.7 557.0 221.1 122.4 99.7 7.3 112.8 91.5 26.0 4.6 13.0 7.6
397219.3 93673.4 102063.1 46518.1 25959.4 27180.4 13767.4 12655.A 11347.1 8095.0 8253.1 4201.9 3630.1 3232.8 2505.3 2381.7 2459.6 2433.6 1129.9 859.6 743.0 413.2 383.0 26.2 20.5 625.9 585.1 227.6 127.2 103.7 9.2 119.8 98.8 27.7 5.3 14.2 6.5
408040.0 96739.7 106597.1 47269.8 26794.9 28268.0 14018.1 12893.2 11541.5 8361.6 8585.6 4282.7 3703.3 3291.7 2555.7 2427.6 2543.3 2536.4 1149.7 875.0 754.1 419.2 387.9 24.7 18.8 646.9 610.7 230.1 128.2 103.9 8.5 123.4 103.1 27.7 5.1 14.6 a.9
419234.0 99919.4 111451.9 48028.1 27658.5 29412.1 14271.5 13133.3 11737.4 8637.1 8934.3 4364.5 3777.4 3351.1 2606.5 2473.8 2630.1 2644.6 1169.7 890.7 765.3 425.3 392.8 23.2 17.0 660.8 637.8 232.6 129.2 104.2 7.8 127.3 107.6 27.6 4.9 15.0 9.2
430821.0 103219.4 116659.4 48796.8 28555.1 30619.0 14531.7 13379.9 11938.8 8925.6 9303.6 4451.2 3856.4 3415.0 2661.7 2524.3 2723.9 2762.3 1193.9 910.6 780.6 435.4 401.7 25.7 19.3 695.7 670.6 239.3 134.1 108.2 9.7 134.9 116.0 29.4 5.5 16.4 10.4
2546574
2612051
2679692
2749602
2821893
Z=150
z=151
Z-152
z-153
z-154
z.155
Z=156
21157
Z'15R
21159
c=8.686 Tr2.2
csu.711 T=2.2
C18.737 T=2.2
C10.763 T=2.?
C=8.780 T=2.2
C=0.814 T=2.2
C18.839 T=2.2
C18.865 T=2.2
cIa.890 T=2.2
C18.916 712.2
585797.1 146938.4 204200.2 57465.3 40188.0 47703.0 17512.2 16191.8 14193.1 12677.5 14415.2 5495.6 4808.6 4180.9 3327.5 3133.8 4007.8 4456.0 1526.9 1192.3 1000.7 596.0 545.5 93.0 81.1 1093.8 1187.0 313.2 180.3 137.0 7.9 2.5 217.5 222.7 28.1 2.0 20.2 15.4
603310.9 151773.6 216080.9 58333.8 41468.5 49676.4 17820.6 16484.5 14425.2 13094.3 14999.1 5609.0 4913.2 4265.0 3402.1 3202.2 4155.6 4654.6 1567.4 1227.8 1029.2 618.7 566.3 106.2 93.8 1144.6 1253.5 325.9 190.1 144.6 11.5 5.b 232.2 241.3 30.5 2.4 22.8 18.1
621441.6 156741.7 228740.9 59211.6 42782.6 51710.1 18133.3 16781.2 14659.7 13521.9 15599.0 5724.3 5019.6 4350.2 3477.9 3271.7 4307.5 4859.0 1608.8 1264.1 1058.3 641.9 587.5 119.9 106.8 1197.1 1322.3 338.9 200.1 152.3 15.2 8.6 247.5 260.7 32.8 2.9 25.1 20.8
640205.8 161841.7 242207.2 60098.A 44130.3 53802.7 18450.1 17081.9 14996.7 13960.3 16214.5 5R41.6
659621.6 167078.2 256513.7 61003.2 45519.4 55960.5 18778.6 17394.2 15143.6 14416.6 16852.6 5967.2 5244.4 4530.8 3639.6 3420.1 4630.2 5291.0 1700.3 1345.1 1124.2 695.8 637.3 154.6 140.1 1313.1 1472.8 371.6 226.6 173.9 28.5 20.5 285.6 308.0 42.3 7.9 34.9 31.7 4.0
3807237
3917011
4030583
506885.0 124794.6 155411.6 53279.6 34311.1 38812.3 16054.1 14809.8 13091.9 10779.1 11775.3 4980.1 4335.7 3803.0 2995.9 2831.0 3355.4 3578.6 1361.6 1051.6 891.8 515.9 474.2 58.9 50.0 889.9 915.6 279.8 160.5 126.4 11.7 177.4 167.6 30.7 3.7 18.9 13.1
521579.0 128958.2 163472.1 54102.1 35422.8 40462.3 16340.R 15081.6 13310.3 11140.2 12270.8 5082.4 4429.7 3879.0 3062.8 2892.4 3480.5 3744.3 1395.7 1080.9 915.1 533.5 490.2 67.5 58.0 930.1 967.7 288.5 166.5 130.6 12.6 8.0 186.7 179.4 31.2 3.6 19.R 14.1
536796.7 133251.6 172943.9 54929.4 36563.7 42174.8 16627.2 15353.0 13527.0 11507.9 lPTR0.3 5182.5 4521.3 3952.2 3126.7 2950.7 3605.6 3912.4 1426.7 1107.0 935.1 547.8 502.7 72.6 62.5 968.0 10!8.3 293.6 168.9 131.4 10.9 6.2 193.1 188.4 30.2 3.1 19.8 14.3
552562.7 137682.0 182669.0 55768.4 37741.0 43956.0 16920.9 15631.5 13749.4 11B89.8 13310.8 5287.7 4618.1 4030.0 3195.2 3013.5 3738.3 4090.2 1461.9 1137.3 959.1 566.0 519.2 81.6 70.9 1010.9 1074.8 302.4 175.0 135.6 11.8 h.7 203.1 201.6 30.7 3.0 20.8 15.5
568823.9 142223.2 193032.9 56606.4 38941.6 45789.1 17212.2 15907.2 13967.9 12276.2 13851.7 5390.1 4711.7 4104.3 3260.2 3072.6 3870.5 4269.3 1493.9 1164.4 979.6 580.8 532.2 87.2 75.9 1051.5 1129.6 307.6 177.4 136.1 9.0 4.6 209.9 211.6 29.7
3404311
3499814
3598731
3701115
3312120
lSl/2 PS1/2 2P1/2 2P3/2 3S1/2 3P1/2 3P3/2 303/2 3D5/2 4.51/2 4P1/2 4P3/2 40312 4DW2 4F5/2 4F7/2 551/2 SP1/2 SP3/2 503/E 5D5/2 5F5/2 5F7/2 507/P 5G9/2 65112 6P1/2 bP3/2 6D3/2 6DW2 6FS/2 751/2 7Pl/2 7P3/2 7D3/2 851/2 8P1/2 ET
15112 251/2 2Pl/2 2P3/2 3Sl/2 3P1/2 3P3/2 3D3/2 3D5/2 451/2 4P1/2 4P3/2 403/2 405/i! 4F5/2 4F7/2 551/2 5P1/2 5P3/2 50312 SDS/2 5F5/2 5F7/2 507/P 509/Z 6S1/2 6Pl/P bP3/2 6D3/2 6D5/2 bF5/2 6F7/2 75112 7P1/2 7P3/2 7D3/2 851/E 8P1/2 95112
2::: 15.9
ET
89 for
Explanation
1::: 8.7
14::: 130.0 26.0 2.9 14.9 9.3
XT . 3554.9 3342.2 4463.7 5069.1 1651.1 1301.1 1087.9 665.6 609.1 134.1 120.3 1251.2 1393.4 352.2 210.4 160.2 19.1 11.9 263.4 281.1 35.0 3.3 27.5 23.7
4148031
4269367
of Tables
93
Atomic Dota and Nuclear
Dota Tables, Vol. 19, No. 1, Jonuory
1977
B. FRICKE and G. SOFF
TABLE
lS1/2 PSl/2 2Pl/E 2P3/2 3S1/2 3P1/2 3P3/2 303/2 30512 451/2 4Pl/P 4P3/2 403/Z 4D5/2 4F5/2 4F7/2 5S1/2 5P1/2 5P3/2 5[33/2 5D5/2 5F5/2 5F7/2 5G7/2 50912 LSl/P 6P1/2 6P3/2 bD3/2 bD5/2 6F5/2 6F7/2 7S1/2 7Pl/2 7P3/2 7D3/2 7D5/2 BSl/E 8Pl/P 9S1/2 ET
II. Energy Eigenvalues
DFS Energy Eigenvalues 100 < 2 5 173
and Total Energies, Z = 100 to Z = 173 (in eV)
21160
21161
Z-162
Z=l63
Z=164
21165
21166
Z=167
Z=l68
Z=169
C=8.941 1=2.2
C18.966 Tat.2
C18.992 TE2.2
c19.017 TI2.2
C19.042 TSP.2
C=9.068 7-2.2
co9.093 1=2.2
Ci9.118 T12.2
c19.143 1=2.2
C19.168 112.2
679704.4 172439.7 271668.2 61912.4 46931.0 50169.4 19105.9 17705.1 15387.2 14878.4 17500.1 6090.0 5358.0 4621.4 3720.4 3494.1 4796.3 5513.7 1745.9 1385.4 1156.5 722.2 661.4 171.3 156.0 1372.3 1550.1 387.0 239.0 183.6 34.0 25.4 304.3 331.6 45.7 9.3 5.0 38.6 36.0 4.1
700462.9 177927.3 287696.7 62830.2 48386.5 60431.9 19437.1 18019.4 15632.7 15350.4 18161.7 6214.1 5472.9 4712.6 3802.0 3568.7 4966.1 5741.1 1791.9 1426.1 1189.1 748.6 685.6 188.0 171.9 1432.8 1629.1 402.5 251.3 193.2 39.5 30.1 323.4 355.8 49.0 10.6 5.6 42.3 40.5 4.3
721909.6 183529.8 304608.6 63750.0 49862.2 62740.3 19766.2 18331.3 15874.2 15827.0 18831.1 6334.7 5584.1 4799.5 3879.1 3638.7 5134.7 5968.2 1834.1 1462.9 1217.4 771.0 705.7 200.6 183.8 1490.4 1705.6 414.1 259.8 198.9 41.1 31.1 338.9 376.7 48.5 8.6 3.5 42.4 41.5
744064.2 189261.7 322430.9 64687.6 5137R.6 65110.3 20106.2 18654.2 16124.6 16320.4 19521.1 6462.8 5702.6 4893.1 3962.9 3715.2 5312.6 6205.9 1881.9 1505.2 1251.1 796.5 730.8 218.1 200.5 1554.4 1788.9 430.2 272.7 20H.9 46.9 36.1 359.3 402.7 51.7 9.8 3.9 46.3 46.3
766933.7 195112.3 341169.2 65635.4 52928.2 67533.5 20450.9 18981.4 16377.5 16824.6 20225.2 6592.9 5823.1 4987.9 4047.8 3792.6 5494.0 6448.8 1930.5 1548.3 1285.2 826.5 756.4 236.1 217.7 1620.0 1874.4 446.7 285.9 219.0 52.8 41.2 380.3 429.6 54.9 11.1 4.4 50.3 51.4
4394763
4524233
4657079
4795616
4937547
15112 2.5112 PPl/P 2P3/2 3S1/2 3P1/2 3P3/2 3D312 3D5/2 4S1/2 4P1/2 4P3/2 4D3/2 4DW2 4F5/2 4F7/2 5S1/2 5P1/2 5P3/2 5D3/2 5D5/2 5F5/2 5F7/2 5G7/2 5G9/2 6S1/2 6Pl/2 6P3/2 60312 6D5/2 6F5/2 6F7/2 7S1/2 7P1/2 7P3/2 7D3/2 7D5/2 8S1/2 8P1/2 9S1/2 9Pl/P 8P3/2 ET
lS1/2 2s1/2 2Pl/E 2P3/2 35112 3P1/2 3P3/2 3D3/2 3D5/2 45112 4P1/2 4P3/2 403/2 405/2 4F5/2 4F7/2 5s1/2 5P1/2 5P3/2
790530.3 201081.6 360834.6 66596.1 54513.6 70012.3 20802.7 19315.5 16635.4 17342.1 20945.9 6727.5 5948.0 5086.3 4136.3 3873.4 5683.6 6699.3 1982.6 1594.8 1322.4 G57.5 784.9 257.0 237.7 1689.9 1964.6 466.0 301.9 231.8 61.4 49.0 404.6 459.8 60.6 14.6 6.8 56.9 59.3 4.5
814861.0 207165.0 3131431.9 67568.2 56132.9 72545.2 21160.2 19655.1 16896.8 17871.3 21681.5 6865.2 6075.6 5187.0 4227.0 3956.2 5877.5 6955.9 2036.5 1643.1 1361.2 990.0 a14.8 279.3 259.1 1762.5 2057.8 406.6 319.1 245.8 71.1 57.8 430.5 492.0 67.3 19.0 10.0 64.6 68.4 5.2
839932.1 213359.4 402964.8 68551.3 57785.9 75132.2 21522.9 19999.8 17161.2 18411.7 22431.8 7005.4 6206.1 5289.4 4319.3 4040.5 6076.1 7218.1 2091.8 1692.7 1400.9 923.5 845.6 302.5 281.5 1837.4 2153.8 507.9 337.1 260.4 81.4 67.3 457.6 525.5 74.4 23.8 13.5 72.8 78.2 6.1 4.5
865749.2 219661.4 425434.8 69545.0 59471.6 77773.5 21890.4 2034R.9 17428.0 18962.9 23196.2 7147.6 6338.2 5392.8 4412.7 4125.6 6278.7 7485.4 2148.0 1743.0 1441.1 957.4 676.8 326.0 304.0 1913.8 2251.7 529.6 355.3 275.0 91.8 76.7 485.2 559.8 81.4 28.4 16.8 81.1 88.1 7.0 5.4
892316.7 226068.5 440642.2 70549.7 61190.7 80470.1 22262.9 20702.8 17697.6 19525.0 23975.2 7292.2 6472.6 5497.7 4507.4 4211.9 6485.7 7758.1 2205.3 1794.5 1482.1 992.0 908.6 350.2 327.2 1992.3 2352.1 551.7 374.1 290.0 102.5 86.5 513.8 595.2 80.6 33.2 20.2 89.8 98.6 8.0 6.5 5.6
5083690
5234064
5388684
5547557
5710683
z=170
z=171
Zr172
z=173
11170
21171
Z=172
z=173
c19.193 Tr2.2
W9.463 b2.2
Cs9.243 T=2.2
C19.268 Tr2.2
cr9.193 T=P.P
C19.463 Tr2.2
09.243 T=2.2
C19.268 Tr2.2
919638.3 232578.3 473186.8 71566..0 62943.6 83223.8 22641.4 21062.4 17970.5 20098.8 24769.6 7439.9 6609.9 5604.7 4604.2 4300.1 6697.9 8037.0 2264.4
938807.3 237306.9 490782.6 72617.0 64299.3 85410.8 23032.7 21434.1 18251.3 20558.9 25420.1 7591.9 6751.3 5714.2 4703.1 4389.9 6871.6 8269.6 2324.5
967112.1 243942.1 516427.1 73655.4 66100.2 8G252.7 23420.9 21802.9 18528.9 21149.0 26237.5 7743.5 bG92.3 5823.2 4801.8 4479.5 7090.0 8556.7 2385.0
1006175.0 252712.6 551833.0 74685.2 68406.9 91842.9 23810.7 22173.5 18808.5 21890.2 27247.8 7899.8 7038.2 5937.0 4905.5 4574.1 7363.8 8910.2 2451.4
5D3/2 5D5/2 5F5/2 5F7/2 5G7/2 5G9/2 651/P 6Pl/2 6Pi/E 6D3/2 6D5/2 6F5/2 6F7/2 75112 7P1/2 7P3/2 7D3/2 7D5/2 8S1/2 8P1/2 8P3/2 9S1/2 9P1/2 6G7/2 ET
See page 89 for Explanation
1847.7 1524.5 1028.0 941.7 375.6 351.7 2073.4 2455.6 575.2 394.0 306.1 114.3 97.3 544.0 632.5 96.7 38.9 24.5 99.5 110.2 6.6 9.4
1901.7 1567.1 1064.0 974.6 400.7 375.7 2140.9 2543.0 598.0 413.2 321.3 125.1 107.0 569.1 664.2 103.5 43.3 27.4 106.9 119.5 1::: 8.7
6006887
1956.2 1610.1 1100.5 1008.1 426.5 400.5 2224.4 2649.8 621.6 433.2 337.2 136.6 117.5 600.0 702.5 111.1 48.5 31.1 116.4 131.2 7.6 11.2 10.1
6180167
2016.5 1658.9 1143.0 1047.5 458.4 431.3 2331.4 2783.6 651.4 459.4 359.2 154.4 134.2 642.8 753.9 124.9 60.0 41.1 133.7 151.0 13.9 18.4 17.7 n.5 6405743
of Tables
94
Atomic Doto and Nuclwr
Data Tables, Vol. 19, No. 1, January
1977
B. FRICKE
TABLE
DFS
and G. SOFF
lSl/2
143028
2s1/2
27803
2Pl/2
26868
2P3/2
Corrections
21017
56::: 516.2 200.7 113.0 91.7 3.6 102.6 81.1 22.0
-91 -153 -92
+41 +8
-457
+155
-96
+13
-9
+11
+3
100 5 Z 5 173
+26 +4 0
SUP?
Experiment
DFS Result
-99
141953
141963
-69
27581
27573
27410
-77
26646
26664
26555
-70
20869
20868
20715
142050
+6
-42
7213
7200
7096
+1
-49
6783
6779
6695
0 -46
5411
5408
5320
4814
4746
4685
3D5/2
4540
4484
4421
451/2
1993
1940
1889
4P1/2
1793
1743
1702
4P3/2
1411
1371
1328
4D3/2
1099
1059
1031
4D5/2
1031
989
965
7292
-19
+1
3Pl/2
6864
-33
+3
-3
3P3/2
5474
-20
+2
+1
3D3/2
21139
374916.4 07274.2 93019.1 44750.4 24148.5 24891.8 13146.7 12055.4 10844.2 7491.8 7523.0 3984.9 3427.4 3063.5 2353.1 2240.5 2259.6 2197.4 1062.8 802.2 695.7 378.7 351.4 12.5
-715
3S1/2
TABLE
lSl/2 2s1/2 2Pl/2 2P3/2 351/2 w1/2 3P3/2 303/2 305/2 4Sl/2 4Pl/2 4P3/2 403/2 4DW2 4f5/2 4f7/2 5Sl/2 SPllP 5P3/2 5D3/2 SDS/2 5f5/2 5f7/2 507/2 5G9/2 6Sl/P bPl/Z 6P3/2 6D3/2 6DW2 6fW2 751/2 7Pl/2 7P3/2 703/2 i351/2 8P1/2
Eigenvalues
III. Energy Eigenvalues (in eV) for Z = 100 from DF and DFS Calculations and Binding Energies from Experiment DF Result
NEUTRAL
Energy
IV. Energy-- Eigenvalues (in eV) for Z = 139 and Z = 170 in Vkious States of Ionization
c-e.4
.s*
-25
1=2.2 17*
2=170
29+
3s*
375016.1 87373.9 93118.7 44850.3 24248.6 24991.0 13246.6 12155.4 10944.2 7591.3 7623.4 4Q04.2 3526.7 3162.7 2452.5 2339.9 2356.7 2296.5 1161.9 901.3 794.9 477.8 450.5 111.3 106.4 664.5 615.4 307.4 211.0 189.1
375254.5 07b14.7 93350.6 45092.3 24494.1 25236.2 13494.9 12402.2 11191.7 7844.1 7875.4 4339.3 3701.3 3417.7 2706.9 2594.5 2613.1 2551.1 1409.9 1148.4 1039.8 720.9 692.5 317.0
375734.0 88093.7 93837.0 45572.7 24982.2 25722.0 13989.0 12892.6 11684.0 8340.0 8377.6 4845.5 4207.0 3923.4 3212.4 3100.3 3110.0 3049.5 1882.3 1618.5 1503.1 1180.6 1148.9
375974.5 RO335.3 94070.4 45813.8 25219.1 25960.1 14223.3 13128.6 11919.2 8578.5 8608.8 5072.6 4514.9 4150.3 3440.4 3327.9 3331.9 3272.0 2098.0 1833.9 1717.0 1393.8 1361.4
898.4 849.6 517.9 414.0 387.0
1281.9 893.8 777.2 739.9
1535.5 1488.7 1084.2 963.8
198.6 176.5 109.5
385.1 361.1
NEUTRAL lSl/2 251/2 2Pl/P 2P3/2 351/2 3P112 3P3/2 3D3/2 305/2 451/2 4Pl/2 4P3/2 603/2 4D5/2 4f5/2 4f7/2 551/2 5Pl/2 5P3/2 5D3/2 SDS/2 5fW2 5f7/2 SG7/2 5G9/2 651/P 6Pl/2 6P3/2 6D3/2 6D5/2 6f5/2 6f7/2 751/2 7Pl/2 7P3/2 7D3/2 7D5/2 BSl/2 BPl/2 EP3/2 951/2
1::: 5.6
See page 89 for Explanation of Tables
95
919638.3 232578.8 473186.0 71566.1 62943.6 83223.8 22641.4 21062.4 17970.5 20098.9 24769.7 7439.9 6609.9 5604.8 4604.3 4300.1 6697.9 8037.0 2264.4 1847.7 1524.5 1020.0 941.7 375.6 351.7 2073.4 2455.6 575.2 394.0 306.1 114.3 97.3 544.0 632.5 96.7 38.9 24.5 99.5 110.2 6.6 9.4
c19.193 36* 920676.6 233594.2 474222.2 72568.5 63943.1 84229.3 23630.1 22053.8 18959.3 21084.2 25759.0 0412.2 7503.9 6576.1 5570.4 5272.9 7667.4 9010.5 3219.1 ERO2.3 2475.1 1978.2 1889.9 1322.4 1297.2 3024.5 3411.7 1481.4 1291.6 1187.9 972.9
112.2 701
1oa*
14e*
923114.4 235966.5 476654.1 74096.4 66257.1 86367.8 25903.7 24337.1 21232.4 23346.7 28037.5 10620.4 9800.4 8776.8 7794.9 7453.2 9855.9 11225.0 5245.6 4830.0 4458.3 3967.2 3319.0
927970.4 240711.2 4815OO.n 79535.7 70846.5 91232.4 30311.4 28806.0 25650.7 27683.7 32466.9 14632.8 13863.5 12761.5 11877.6 11531.5 13770.0
940986.6 253012.2 494454.2 91190.1 82149.7 103050.0 40218.8 39230.0