J. Electromagnetic Analysis & Applications, 2010, 2: 205-243
doi:10.4236/jemaa.2010.24029 Published Online April 2010 (http://www.SciRP.org/journal/jemaa)
Copyright © 2010 SciRes. JEMAA
205
Intra-Atomic Electric Field Radial Potentials in
Step-Like Presentation
Levan Chkhartishvili, Tamar Berberashvili
Department of Physics, Georgian Technical University, Tbilisi, Georgia.
Email: chkharti2003@yahoo.com
Received December 27th, 2009; revised February 8th, 2010; accepted February 15th, 2010.
ABSTRACT
Within the frames of semiclassical approach, intra-atomic electric field potentials are parameterized in form of radial
step-like functions. Corresponding parameters for 80 chemical elements are tabulated by fitting of the semiclassical
energy levels of atomic electrons to their first principle values. In substance binding energy and electronic structure
calculations, superposition of the semiclassically parameterized constituent-atomic potentials can serve as a good ini-
tial approximation of its inner potential: the estimated errors of the determined structural and energy parameters make
up a few percent.
Keywords: Electric Field Potential, Atoms, Step-Like Radial Functions
1. Introduction
Because the electron mass is negligible in comparison
with masses of atomic nuclei, substances, i.e. atoms and
polyatomic bound systems – molecules or condensed
matters – can be considered as one-electron systems in
almost stationary self-consistent electric field generated
by nuclei fixed at their equilibrium positions and space-
averaged electron charge density. For this reason, elec-
tronic structure, which includes both electron energy
spectrum and electron density space distribution, deter-
mines practically all principal physical properties of a
substance. From its part, theoretical prediction of the
substance electronic structure should be primarily based
on the inner electric field potential, so that appropriate
choice of the initial potential for such kind calculations
greatly increases their accuracy.
When isolated atoms associate forming molecular or
condensed forms of substance only part of electrons
(called as valence electrons) redistributes. And what is
more, corresponding changes in the electron density dis-
tribution are so weak that usually a simple superposition
of the free atom’s radial potentials centered at the corre-
sponding sites of the atomic structure serves as a good
initial approximation of the inner potential in any polya-
tomic system. At the worst, initial inner electric field
potentials can be presented by superposition of the atom-
ic-like radial potentials with different centers. Thus, in
this line the key problem consists in construction of the
effective atomic potentials in relevant functional form.
Relatively recently, with that end in view we have
proposed piece-wise analytical and, in particular, step-
like radial atomic potentials obtained within initial quasi-
classical, i.e., semiclassical approximation. They have
been successfully used in binding energy and electronic
structure calculations carried out for some polyatomic
systems like the sodium diatomic molecule and crystals
[1], boron-containing diatomic molecules [2,3], and
mainly for boron nitride molecular, crystalline, and nano-
structures [3-16]. In addition, semiclassical interatomic
boron-boron pair potentials have explained some ground-
state parameters of the boron nanotubes [17-19], as well
as main features of the isotopic effects in boron-rich sol-
ids [20-23].
But, above cited studies exploited semiclassical poten-
tials only of certain, namely, some light atoms, whereas
full-scale calculations performed for any wide class of
materials need a quantity of appropriate effective atomic
potentials. Present work aims to build up semiclassical
atomic potentials for the stable chemical elements in
most convenient form of radial step-like functions.
The paper is organized as follows. At first, sense of the
semiclassicality for the substance-electron-system is cla-
rified. Then, a semiclassical parameterization scheme is
introduced for charge distributions in atoms and atomic
potentials as well. Next section presents results and brief
discussion of the performed numerical calculations based
on fitting of the semiclassical electron-energy spectra
with these obtained from first principles. And finally,
accuracies of the constructed step-like radial atomic po-
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
Copyright © 2010 SciRes. JEMAA
206
tentials are estimated for energy and expansion parame-
ters of a material.
2. Substance as a Semiclassical Electron
System
Beginning from Bohr’s fundamental work [24] semi-
classically describing electronic spectrum of the one-
electron hydrogen-like atom with Coulomb potential up
to nowadays, similar analysis is widely used for light
atoms. Due to exact quantum-mechanical solvability of
the Coulomb potential, exact wave functions of electron-
states in a hydrogen-like atom can be obtained directly
from the corresponding classical orbits [25]. And there-
fore, quantum dynamics of the electron in a hydro-
gen-like atom is wholly expressed by its classical dy-
namics.
Classically a two-electron helium-like atom can be
represented as a pair of electrons placed at the opposite
ends of the straight line with nucleus at the midpoint (see
e.g. [26]). This classical model added with quantization
condition for electron orbital moment leads to the almost
hydrogen-like electron energy spectra, where atomic
number Z is substituted for the reduced value Z–1/4 (it
means that another electron effectively screens nuclear
electric charge). Ground state energies calculated from
the obtained relation for some helium-like systems differ
from the experimental ones only by 3-6% [27]. Even
entirely classical model of helium atom can be success-
fully explored numerically to obtain its possible configu-
rations [28]: most of the orbits are found to cause auto-
ionization via chaotic transients. As for the modern se-
miclassical approach based on the conception of periodic
classical orbits, it allow visually interpret physical
meaning of special quantum numbers inherent to this
three-particle system between ground and fragmented
states [29].
For many-electron atoms, a reasonable accuracy can
be achieved in terms of the self-consistent-field ap-
proximation, within which a minimum of the total energy
is sought in the class of quasi-classical wave functions
[30]. As is well known, many-electron systems such as
heavy atoms are characterized by some quantum proper-
ties like the electron-shell effects, fluctuations in pa-
rameters’ values, discrete electron energy spectrum etc,
which are averaged and, therefore, invisible in semi-
classical atomic models. However, it was demonstrated
that semiclassical treatment of the atomic many-electron
system, when it is combined with information-theory-
method, reveals resources to describe such kind effects as
well [31].
It was demonstrated how based on purely classical no-
tions it is possible to reproduce general trends in inelastic
scattering atomic form-factors dependences upon quan-
tum numbers [32]. Besides, starting from classical rela-
tions together with energy conservation law and classi-
cal-quantum correspondence principle, it was found ex-
pressions of intensity-distribution and line-width of the
electron–ion recombination X-ray spectrum, which is in
unexpectedly good agreement with these resulted from
the accurate quantum-mechanical calculations [33].
Semiclassical quantization rule leading to the exact
electron energies in a hydrogen-like atom with Coulomb
potential at the same time provides good accuracy of the
valence electron energy value in a many-electron atom
with model potential in form of sum of the nucleus Cou-
lomb potential and a screening term [34]. Substitutions of
the electron quantum numbers for their analogues in
Thomas–Fermi semiclassical statistical model of atom
can be applied for investigation of the excited and ion-
ized electron states [35]. Semiclassical electron energy
spectrum of Thomas–Fermi atom, which was described
in terms of an effective kinetic energy obtained from the
corresponding quantization rule formulated in momen-
tum space, was found to agree essentially with that in the
standard formalism employing an effective potential en-
ergy [36].
Semiclassical evaluation of sums over quantum num-
bers of electron states in many-electron atoms is known
to be an effective tool of obtaining of the integrated
atomic characteristics (see e.g. [37]) like the shell and
subshell electron densities [38] or averaged electron
momentum density [39] in atoms etc. Introducing of the
semiclassical self-consistent intra-atomic electric field
yields the relative error not more than 22
/1~ n
in de-
termining of the electronic energies, where n is the prin-
cipal quantum number of the highest occupied electron
state [40]. Then, accuracy of the semiclassical approxi-
mation should quite satisfactory even for light atoms.
Effectiveness of the Bohr-type analytical models to the
description of the periodic motion of electrons in small-
sized molecules also was demonstrated [41]. For a long
time, semiclassical asymptotic form was known to pro-
vide a fundamental device for studying quantum systems
in which non-perturbative effects play an essential role.
But, the crucial step was advanced for the bound-state
quantization of fermions few-body systems such as mo-
lecules. Semiclassical quantization rules were success-
fully applied to describe elastic interatomic scattering [42]
in spectroscopy of diatomic molecules [43]. Using path
integration as a relevant mathematical tool for semi-
classical asymptotic form it was obtained semiclassical
quantization rule for the periodic mean-field solutions
[44]. Therm energies of diatomic K2 molecule calculated
by the semiclassical method showed absolute deviations
of only ~ 0.05 cm1 from the quantum-mechanical results
[45]. Same approach was found to be a strong method for
generating the interatomic potential energy curve for
diatomic molecules. It was provided a semiclassical de-
scription of the shell-structure in fermions-system: level
densities and shell-corrections were obtained from the
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
Copyright © 2010 SciRes. JEMAA
207
periodic orbit theory [46]. The semiclassical quantifica-
tion method has raised increasing interest in relation to
approximated method in various physical systems such
as not only atoms, but molecules etc. It would serve as a
general device for evaluating the bound-state spectra,
once the exact or approximate solutions for the mean-
field equation are known. Usually, different methods all
use only periodic and/or non-closed quasi-periodic clas-
sical orbitals as basis for the quantization. Contrary to
them, in [47] it was introduced an adapted version of the
semiclassical quantization method applied to molecular
orbitals into path integrals formalism, and it also gives an
alternative procedure for the calculation of the electronic
correlation energy of a molecular system.
Primitive semiclassical treatment even reveals exis-
tence of a classical contribution to the chemical bond in
small molecules: ground state electron is found to be
exchanged classically between two nuclei [48]. Proceed-
ing classical limit for a one-electron orbital model of
such many-electron systems with electron periodic mo-
tion leads to visualization of its quantum description [49].
Quantum description also can be introduced starting from
the formal correspondence between classical harmonics
of an electron periodic motion and its quantum jumps, i.e.
Fourier-analysis added by the simple quantization condi-
tion directly yields steady-state electron energies [50].
Even formation of the electron spin, which is considered
as essentially quantum characteristic, can be explained
within a classical model [51].
In case of multidimensional systems, the globally uni-
form semiclassical approximation for energy eigenstates
can be derived explicitly [52]. This is a true semiclassical
approximation producing almost accurate wave functions
providing with considerable degree of overlap (more than
0.98) between semiclassical and exact quantum eigen-
states. Semiclassical method of calculation was used to
describe electronic super-shells in metallic clusters [53].
Later, it was supposed a general method of the quasi-
classical spectral analysis useful for central potentials
with Coulomb singularity or finite value at the center
which are characteristic for isolated atoms and spherical
clusters, respectively [54]. Atomic clusters and con-
densed phases can be calculated in framework of the
density-functional theory (DFT) using a quasi-classical
expansion of the energy functional [55].
However, as substance is considered as a non-relativ-
istic electron system affected by the external field of nu-
clei fixed at their sites in structure, its inner potential do
not satisfy the standard Wentzel-Kramers-Brillouin
(WKB) quasi-classical condition on spatial smoothness
due to singularities at nuclear sites and electron shell
effects. The success of the above approaches can be ex-
plained on the basis of the quasi-classical expressions
obtained by Maslov [56] for the energies of bound elec-
tronic states. It follows from these expressions that the
exact and quasi-classical spectra are similar to each other
irrespective of the potential smoothness at 12 2
00  R,
where 0
and 0
R are the characteristic values of the
potential and its effective range, respectively (hereafter,
all relationships will be given in the atomic system of
units (a.u.)).
3. Semiclassical Parameterization of the
Electric Charge Density and Electric Field
Potential Distributions in an Atom
The semiclassical parameterization of the atomic electric
charge density and electric field potential distributions
(see e.g. [57]) can be performed in analytical form if the
effective fields acting on any ith electron in a neutral
atom (i.e., Zi ,...,3,2,1
with Z as the nucleus charge)
are represented by Coulomb-like potentials
r
Z
ri
i )( (1)
where
||2 iii EnZ (2)
is the effective charge of the nucleus screened by other
electrons’ cloud dependent on the electron-state principal
quantum number i
n and its energy 0
i
E.
Electron charge equals to 1. Therefore, classical
turning points radii i
r
and i
r (ii rr 
) of the i th
electron with orbital quantum number i
l can be found
as the roots of the equation
2
2
)1(
)( r
ll
rE ii
ii
 (3)
As a result, we obtain
||2
)1(
2
i
iiii
iE
llnn
r
(4)
||2
)1(
2
i
iiii
iE
llnn
r
 (5)
Let )(
~r
i
be the potential of the effective electric
field induced by the i th electron. Then, potential )(
~
r
of the electric field induced by the whole electron cloud
can be written as the sum of the potentials )(
~
r
i
:
 Zi
iirr 1)(
~
)(
~
(6)
Potential of the electric field acting on an arbitrary i th
electron of the atom is equal to the sum of the potentials
of the nucleus Coulomb field and the field induced by all
the electrons, except for the potential of the electron un-
der consideration:
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
Copyright © 2010 SciRes. JEMAA
208
)(
~
)(
~rr
r
Z
r
Z
i
i (7)
Now, we sum up such potentials over electrons. As a
result, the terms independent of the electron number on
the right-hand sides are multiplied by the total number Z
of electrons in the atom and the sum of the potentials
)(
~r
i
gives )(
~r. The solution of the obtained equa-
tion with respect to )(
~
r has the form
r
Z
ZZ
r
Zi
ii1
1
)(
~1
2

(8)
i.e. in this case, effective field of the interaction between
nucleus and electron cloud also turns out to be a Cou-
lomb-like field.
Nucleus charge equals to
Z
and in the ground state
its relative (to the electron cloud) motion corresponds to
a zero orbital quantum number. Therefore, the radius of
one classical turning point for nucleus is equal to 0 and
the radius
r
~
of another turning point is a root of the
equation
)(
~
~rZE  (9)
where
E
~
is the eigenvalue of the energy associated
with the relative motion electron cloud and nucleus. Un-
der the assumption that the nucleus has an infinite mass
the reduced mass of the system nucleus – electron cloud
with Z electrons equals to the cloud total mass Z. There-
fore, energy and, consequently, turning point radius for
the nucleus motion with respect to the electron cloud are
given by the formulas
2
2
1
23
)1(2
)(
~

Z
ZZZ
E
Zi
ii (10)
)(
)1(2
~
1
22
Zi
ii
ZZZ
Z
r (11)
The semiclassical, i.e., initial quasi-classical approxi-
mation implies that exponentially decaying partial elec-
tron densities are disregarded in the classically forbidden
regions and that oscillations of these densities are ig-
nored in classically allowed regions. As a result, the ra-
dial dependence of the direction-averaged partial charge
density of the ith electron state in atom is represented
by a piecewise constant function:
33
() 0
3
4()
0
ii
ii
ii
i
rrr
rrr
rr
rr


 
 


(12)
A similar averaging for the nucleus motion with re-
spect to the electron cloud nucleus is equivalent to aver-
aging the nuclear charge over a sphere of radius
r
~
:
3
3
() 0
4
0
Z
rrr
r
rr


(13)
Summation of similar contributions gives the distribu-
tion of the total density of the electric charge in the atom
in the form of a step radial function
k
Zi
iirrr


1)()(
~
)(
kk RrR
1qk,...,3,2,1 (14)
where ρk are constants determined from the radii of the
classical turning points and Rk coincide with these radii.
Here,  1210
0qq RRRRR and Zq 2
is the number of layers with uniform charge densities.
Parameter q
R plays the role of the quasi-classical atomi-
ic radius (the charge density is equal to zero at q
Rr ).
Mathematically, this representation is equivalent to the
volume averaging in layers kk RrR 
1.
Next, we calculate the fields induced by the charged
layers with densities k
on the basis of the Gauss
theorem and sum these fields. Then, the atomic potential
can be written in the form of the continuously differenti-
able piecewise analytical function
2
1
133 3
11
1
22 2
1
1
()1, 2, 3,...,
44
()
33
2
3
2()2
k
kk kk
ik
kiiikk
i
kk
iq
kiiikk
ik
a
rbrcRrRk q
r
aRRR
b
cRRR


 



 



(15)
However, since the energy of the electronic system is a
single-valued functional of the electron density, it is ex-
pedient to approximate the above potential by a step
function too. Averaging over the volume can adequately
perform this:
kk
kk
kkk
kk
kkk c
RR
RRb
RR
RRa
r


)(5
)(3
)(2
)(3
)( 3
1
3
5
1
5
3
1
3
2
1
2
kk RrR
1 qk,...,3,2,1 (16)
4. Tables
The numerical values of parameters k
R, k
, and k
can be found by fitting quasi-classical energetic levels
i
E to the Hartree–Fock (HF) ab initio ones [58]. Results
of calculation are presented in Table 1 below for each
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
Copyright © 2010 SciRes. JEMAA
209
chemical element taken separately. Origin of a radial
layer radius is identified in parenthesis after the layer
number: is it a classical turning point radius of nucleus or
an electron-state? Note that inner turning points of nu-
cleus and s-electron states coincide with effective atomic elec-
tric field center, i.e. corresponding radii equal to 0. Radii of
inner and outer classical turning points for rest electron-states
are distinguished by single and double priming.
Values are shown with seven significant digits in ac-
cordance with the input data (HF energies) accuracy.
Such high accuracy is useful in interim calculations. As
for the final results, they should be expressed in round
numbers to the three or four significant digits because the
relative errors of the semiclassical calculations aiming to
found structural and energy parameters for polyatomic
systems usually make up a few percent.
Table 1. Calculated semiclassical parameters of the atoms
k 1 (1 H) 1 (1s)
k
R 1.000000 E + 00 2.000000 E + 00
k
2.088909 E + 01 2.984155 E – 02
k
4.875000 E 01 5.892857 E 02
k 1 (2 He) 2 (1s)
k
R 3.875716 E 01 1.476061 E + 00
k
8.052884 E + 00 1.484666 E 01
k
4.187991 E + 00 3.082284 E 01
k 1 (3 Li) 2 (1s) 3 (2s)
k
R 1.349014 E 01 8.984357 E 01 6.383510 E + 00
k
2.910724 E + 02 6.593034 E 01 9.177675 E 04
k
2.312713 E + 01 2.009273 E + 00 4.311415 E 02
k 1 (4 Be) 2 (1s) 3 (2s)
k
R 5.596220 E 02 6.500727 E 01 5.086001 E + 00
k
5.446885 E + 03 1.741653 E + 00 3.629210 E 03
k
8.057431 E + 01 4.887950 E + 00 1.097914 E 01
k 1 (5 B) 2 (1s) 3 (2p') 4 (2s) 5 (2p'')
k
R 2.758476 E 02 5.098016 E 017.441219 E 01 4.021346 E + 00 4.337060 E + 00
k
5.686514 E + 04 3.610951 E + 00 7.342212 E 03 1.028341 E 02 2.941197 E 03
k
2.105468 E + 02 8.882329 E + 003.652920 E + 00 2.060720 E 01 6.135348 E 04
k 1 (6 C) 2 (1s) 3 (2p') 4 (2s) 5 (2p'')
k
R 1.542721 E 02 4.202289 E 01 6.292303 E 01 3.367110 E + 00 3.667423 E + 00
k
3.901153 E + 05 6.446545 E + 00 1.250747 E 02 2.223623 E 02 9.728757 E 03
k
578818 E + 02 1.399183 E + 01 5.842260 E + 00 3.410756 E 01 1.835877 E03
k 1 (7 N) 2 (1s) 3 (2p') 4 (2s) 5 (2p'')
k
R 9.446222 E 03 3.577244 E 01 5.498034 E 01 2.909074 E + 00 3.204489 E + 00
k
1.982589 E + 06 1.044967 E + 01 1.939444 E 02 4.126981 E 02 2.187537 E 02
k
8.784581 E + 02 2.022523 E + 01 8.464698 E + 00 5.096684 E 01 3.993358 E 03
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
Copyright © 2010 SciRes. JEMAA
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k 1 (8 O) 2 (1s) 3 (2p') 4 (2s) 5 (2p'')
k
R 6.103946 E 03 3.110705 E 01 5.210723 E 01 2.535595 E + 00 3.037032 E + 00
k
8.397857 E + 06 1.589154 E + 01 2.928881 E 02 6.355156 E 02 3.426275 E 02
k
1.559999 E + 03 2.773984 E + 01 1.102222 E + 01 7.898878 E 01 1.796550 E 02
k 1 (9 F) 2 (1s) 3 (2p') 4 (2s) 5 (2p'')
k
R 4.176561 E 03 2.753309 E 01 4.847945 E 01 2.255511 E + 00 2.825589 E + 00
k
2.949151 E + 07 2.291743 E + 01 4.161086 E 02 9.479146 E 02 5.318060 E 02
k
2.571045 E + 03 3.638866 E + 01 1.405815 E + 01 1.114922 E + 00 3.595575 E 02
k 1 (10 Ne) 2 (1s) 3 (2p') 4 (2s) 5 (2p'')
k
R 2.985142 E 03 2.470362 E 01 4.491695 E 01 2.035740 E + 00 2.617951 E + 00
k
8.974622 E + 07 3.172744 E + 01 5.659451 E 02 1.368319 E 01 8.023741 E 02
k
4.002938 E + 03 4.617305 E + 01 1.754276 E + 01 1.481199 E + 00 5.649046 E 02
k 1 (11 Na) 2 (1s) 3 (2p')
k
R 2.333813 E 03 2.222812 E 01 3.361773 E 01
k
2.065883 E + 08 4.357330 E + 01 9.895069 E 02
k
5.636078 E + 03 5.702576 E + 01 2.540262 E + 01
4 (2s) 5 (2p'') 6 (3s)
1.691207 E + 00 1.959385 E + 00 9.942100 E + 00
2.903333 E 01 1.916255 E 01 2.429277 E 04
2.264005 E + 00 4.264542 E 01 2.565704 E 02
k 1 (12 Mg) 2 (1s) 3 (2p')
k
R 1.833883 E 03 2.019651 E 01 2.741860 E 01
k
4.644914 E + 08 5.811295 E + 01 1.551165 E 01
k
7.829429 E + 03 6.933347 E + 01 3.379468 E + 01
4 (2s) 5 (2p'') 6 (3s)
1.457155 E + 00 1.598073 E + 00 8.433944 E + 00
5.078705 E 01 3.535498 E 01 7.958830 E 04
3.315594 E + 00 9.711561 E 01 6.118891 E 02
k 1 (13 Al) 2 (1s) 3 (2p') 4 (3p')
k
R 1.462229 E 03 1.848984 E 01 2.308930 E 01 5.466816 E 01
k
9.926781 E + 08 7.576501 E + 01 2.311670 E 01 8.218780 E 01
k
1.064293 E + 04 8.299728 E + 01 4.322824 E + 01 1.753508 E + 01
5 (2s) 6 (2p'') 7 (3s) 8 (3p'')
1.276364 E + 00 1.345743 E + 00 6.764067 E + 00 8.712604 E + 00
8.222391 E 01 5.926148 E 01 1.903885 E 03 3.610562 E 04
3.600567 E + 00 1.684978 E + 00 1.386415 E 01 2.846971 E 03
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
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k 1 (14 Si) 2 (1s) 3 (2p') 4 (3p')
k
R 1.177767 E 03 1.704832 E 01 2.007802 E 01 4.595484 E 01
k
2.045794 E + 09 9.668486 E + 01 3.248175 E 01 1.223166 E + 00
k
1.423563 E + 04 9.804605 E + 01 5.346299 E + 01 2.372269 E + 01
5 (2s) 6 (2p'') 7 (3s) 8 (3p'')
1.139926 E + 00 1.170233 E + 00 5.774354 E + 00 7.323940 E + 00
1.224381 E + 00 9.020437 E 01 3.695549 E 03 1.215666 E 03
5.013770 E + 00 2.545996 E + 00 2.317236 E 01 6.068273 E 03
k 1 (15 P) 2 (1s) 3 (2p') 4 (3p')
k
R 9.593563 E 04 1.581438 E 01 1.782334 E 01 4.002321 E 01
k
4.055672 E + 09 1.211595 E + 02 4.380049 E 01 1.722228 E + 00
k
1.873096 E + 04 1.144569 E + 02 6.457731 E + 01 3.040964 E + 01
5 (2s) 6 (2p'') 7 (3s) 8 (3p'')
1.032033 E + 00 1.038820 E + 00 5.083961 E + 00 6.378601 E + 00
1.724988 E + 00 1.290617 E + 00 6.393927 E 03 2.760347 E 03
6.608240 E + 00 3.548359 E + 00 3.396463 E 01 9.624267 E 03
k 1 (16 S) 2 (1s) 3 (2p') 4 (3p')
k
R 7.873147 E 04 1.474384 E 01 1.602340 E 01 3.787647 E 01
k
7.826836 E + 09 1.495490 E + 02 5.752957 E 01 2.342732 E + 00
k
2.435211 E + 04 1.322761 E + 02 7.674520 E + 01 3.528555 E + 01
5 (2p'') 6 (2s) 7 (3s) 8 (3p'')
9.339120 E 01 9.425845 E 01 4.523887 E + 00 6.036469 E + 00
2.347074 E + 00 5.796381 E 01 9.499509 E 03 4.342400 E 03
8.375741 E + 00 4.756158 E + 00 5.098488 E 01 2.058169 E 02
k 1 (17 Cl) 2 (1s) 3 (2p') 4 (3p')
k
R 6.532226 E 04 1.380891 E 01 1.457901 E 01 3.520031 E 01
k
1.456052 E + 10 1.820631 E + 02 7.359436 E 01 3.082461 E + 00
k
3.119221 E + 04 1.514459 E + 02 8.983302 E + 01 4.146700 E + 01
5 (2p'') 6 (2s) 7 (3s) 8 (3p'')
8.497267 E 01 8.684381 E 01 4.095949 E + 00 5.609963 E + 00
3.089224 E + 00 7.427061 E 01 1.371081 E 02 6.762524 E 03
1.047479 E + 01 6.101408 E + 00 6.943084 E 01 3.204793 E 02
k 1 (18 Ar) 2 (1s) 3 (2p') 4 (3p')
k
R 5.474781 E 04 1.298535 E 01 1.338860 E 01 3.258315 E 01
k
2.618688 E + 10 2.189839 E + 02 9.217434 E 01 3.951462 E + 00
k
3.941303 E + 04 1.719603 E + 02 1.038562 E + 02 4.862917 E + 01
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5 (2p'') 6 (2s) 7 (3s) 8 (3p'')
7.803446 E 01 8.057526 E 01 3.753883 E + 00 5.192860 E + 00
3.961694 E + 00 9.319752 E 01 1.925783 E 02 1.023175 E 02
1.282209 E + 01 7.582522 E + 00 8.919572 E 01 4.376578 E 02
k 1 (19 K) 2 (2p') 3 (1s) 4 (3p') 5 (2p'')
k
R 4.727958 E 04 1.220427 E 01 1.223829 E 01 2.564030 E 01 7.113169 E 01
k
4.291847 E + 10 2.616615 E +
02
2.656616 E +
02
5.178522 E +
00
5.199519 E +
00
k
4.817966 E + 04 1.942944 E + 02 1.195273 E + 02 6.680192 E + 01 1.623827 E + 01
6 (2s) 7 (3s) 8 (3p'') 9 (4s)
7.430389 E 01 3.208255 E + 00 4.086360 E + 00 1.473043 E + 01
1.199407 E + 00 3.553070 E 02 2.107182 E 02 7.469050 E 05
9.178612 E + 00 1.258072 E + 00 2.068058 E 01 1.499003 E 02
k 1 (20 Ca) 2 (2p') 3 (1s) 4 (3p') 5 (2p'')
k
R 4.088020 E 04 1.121988 E 01 1.157157 E 01 2.163349 E 01 6.539423 E 01
k
6.988798 E + 10 3.096286 E +
02
3.147766 E +
02
6.625287 E +
00
6.660246 E +
00
k
5.866054 E + 04 2.246811 E + 02 1.363192 E + 02 8.373755 E + 01 1.982931 E + 01
6 (2s) 7 (3s) 8 (3p'') 9 (4s)
6.895990 E 01 2.831339 E + 00 3.447784 E + 00 1.279289 E + 01
1.512189 E + 00 5.622245 E 02 3.518632 E 02 2.280529 E 04
1.103673 E + 01 1.726474 E + 00 4.329498 E 01 3.507845 E 02
k 1 (21 Sc) 2 (2p') 3 (1s) 4 (3p')
k
R 3.495658 E 04 1.046439 E 01 1.097974 E 01 1.996252 E 01
k
1.173664 E + 11 3.625008 E + 02 3.688463 E + 02 8.130180 E + 00
k
7.203863 E + 04 2.552117 E + 02 1.537630 E + 02 9.620138 E + 01
5 (2p'') 6 (2s) 7 (3d') 8 (3s)
6.099095 E 01 6.475133 E 01 1.529288 E + 00 2.647865 E + 00
8.174672 E + 00 1.829179 E + 00 7.046518 E 02 7.177448 E 02
2.333772 E + 01 1.310249 E + 01 5.350410 E + 00 1.412970 E + 00
9 (3p'') 10 (4s) 11 (3d'')
3.181477 E + 00 5.707379 E + 00 1.234108 E + 01
4.605550 E 02 1.563323 E 03 2.540280 E 04
5.766749 E 01 2.237779 E 01 2.179856 E 02
k 1 (22 Ti) 2 (2p') 3 (1s) 4 (3p')
k
R 3.013518 E 04 9.820236 E 02 1.044639 E 01 1.869609 E 01
k
1.919167 E + 11 4.209588 E + 02 4.286367 E + 02 9.801412 E + 00
k
8.755133 E + 04 2.872142 E + 02 1.721800 E + 02 1.087104 E + 02
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
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5 (2p'') 6 (2s) 7 (3d') 8 (3s)
5.723653 E 01 6.110909 E 01 1.908091 E + 00 2.502871 E + 00
9.855572 E + 00 2.177684 E + 00 8.538408 E 02 8.673223 E 02
2.709414 E + 01 1.537353 E + 01 4.186494 E + 00 1.335356 E + 00
9 (3p'') 10 (3d'') 11 (4s)
2.979643 E + 00 7.121092 E + 00 8.521671 E + 00
5.627954 E 02 2.119704 E 03 7.715554 E 04
7.476607 E 01 1.196428 E 01 3.156347 E 03
k 1 (23 V) 2 (2p') 3 (1s) 4 (3p')
k
R 2.601095 E 04 9.256893 E 02 9.962640 E 02 1.762791 E 01
k
3.120117 E + 11 4.853546 E + 02 4.945213 E + 02 1.166471 E + 01
k
1.060522 E + 05 3.209083 E + 02 1.916313 E + 02 1.217554 E + 02
5 (2p'') 6 (2s) 7 (3d') 8 (3s)
5.395313 E 01 5.788639 E 01 1.867140 E + 00 2.377964 E + 00
1.172932 E + 01 2.562651 E + 00 1.010817 E 01 1.032399 E 01
3.114340 E + 01 1.785930 E + 01 4.730460 E + 00 1.618205 E + 00
9 (3p'') 10 (3d'') 11 (4s)
2.809404 E + 00 6.968261 E + 00 7.924130 E + 00
6.773191 E 02 3.117812 E 03 9.595919 E 04
9.784493 E 01 1.402956 E 01 1.832263 E 03
k 1 (24 Cr) 2 (2p') 3 (1s) 4 (3p')
k
R 2.257520 E 04 8.758647 E 02 9.521818 E 02 1.670378 E 01
k
4.979986 E + 11 5.559828 E + 02 5.668046 E + 02 1.373243 E + 01
k
1.275136 E + 05 3.562990E + 02 2.121004E + 02 1.353698E + 02
5 (2p'') 6 (2s) 7 (3d') 8 (3s)
5.104914 E 01 5.500740 E 01 1.831115 E + 00 2.268075 E + 00
1.380838 E + 01 2.986651 E + 00 1.179983 E 01 1.210491 E 01
3.546478 E + 01 2.053528 E + 01 5.299796 E + 00 1.929230 E + 00
9 (3p'') 10 (3d'') 11 (4s)
2.662124 E + 00 6.833814 E + 00 7.498190 E + 00
8.012597 E 02 4.183420 E 03 1.132588 E 03
1.243684 E + 00 1.661301 E 01 1.045829 E 03
k 1 (25 Mn) 2 (2p') 3 (1s) 4 (3p')
k
R 1.970173 E 04 8.315498 E 02 9.118571 E 02 1.590773 E 01
k
7.804374 E + 11 6.331017 E + 02 6.457474 E + 02 1.600771 E + 01
k
1.522077 E + 05 3.933287 E + 02 2.335698 E + 02 1.494468 E + 02
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5 (2p'') 6 (2s) 7 (3d') 8 (3s)
4.846627 E 01 5.242371 E 01 1.800835 E + 00 2.171677 E + 00
1.609563 E + 01 3.449931 E + 00 1.358885 E 01 1.398977 E 01
4.004232 E + 01 2.339427 E + 01 5.880152 E + 00 2.258767 E + 00
9 (3p'') 10 (3d'') 11 (4s)
2.535256 E + 00 6.720807 E + 00 7.077436 E + 00
9.327942 E 02 5.355993 E 03 1.346833 E 03
1.535328 E + 00 1.929413 E 01 3.586332 E 04
k 1 (26 Fe) 2 (2p') 3 (1s) 4 (3p')
k
R 1.728400 E 04 7.911165 E 02 8.747507 E 02 1.512669 E 01
k
1.202131 E + 12 7.171896 E + 02 7.318750 E + 02 1.854820 E + 01
k
1.804475 E + 05 4.323994 E + 02 2.561417 E + 02 1.647530 E + 02
5 (2p'') 6 (2s) 7 (3d') 8 (3s)
4.610965 E 01 5.005045 E 01 1.764513 E + 00 2.077770 E + 00
1.865046 E + 01 3.965039 E + 00 1.568596 E 01 1.619738 E 01
4.495410 E + 01 2.645283 E + 01 6.529329 E + 00 2.639717 E + 00
9 (3p'') 10 (3d'') 11 (4s)
2.410779 E + 00 6.585254 E + 00 7.033322 E + 00
1.087447 E 01 6.486578 E 03 1.372334 E 03
1.883139 E + 00 2.331049 E 01 5.767085 E 04
k 1 (27 Co) 2 (2p') 3 (1s) 4 (3p')
k
R 1.524057 E 04 7.547369 E 02 8.405654 E 02 1.444711 E 01
k
1.820837 E + 12 8.083521 E + 02 8.252652 E + 02 2.131927 E + 01
k
2.125211 E + 05 4.731134 E + 02 2.797123 E + 02 1.805247 E + 02
5 (2p'') 6 (2s) 7 (3d') 8 (3s)
4.398929 E 01 4.789933 E 01 1.733761 E + 00 1.994624 E + 00
2.143665 E + 01 4.523643 E + 00 1.790090 E 01 1.852988 E 01
5.011827 E + 01 2.969002 E + 01 7.183303 E + 00 3.034107 E + 00
9 (3p'') 10 (3d'') 11 (4s)
2.302473 E + 00 6.470483 E + 00 6.883165 E + 00
1.251318 E 01 7.753902 E 03 1.464120 E 03
2.253930 E + 00 2.716290 E 01 5.219691 E 04
k 1 (28 Ni) 2 (2p') 3 (1s) 4 (3p')
k
R 1.350222 E 04 7.216906 E 02 8.089558 E 02 1.383599 E 01
k
2.715524 E + 12 9.069139 E + 02 9.262582 E + 02 2.434036 E + 01
k
2.487756 E + 05 5.155529 E + 02 3.043036 E + 02 1.969151 E + 02
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
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5 (2p'') 6 (2s) 7 (3d') 8 (3s)
4.206321 E 01 4.593284 E 01 1.705828 E + 00 1.919013 E + 00
2.447399 E + 01 5.129635 E + 00 2.027591 E 01 2.103064 E 01
5.555121 E + 01 3.311022 E + 01 7.853485 E + 00 3.448915 E + 00
9 (3p'') 10 (3d'') 11 (4s)
2.205076 E + 00 6.366238 E + 00 6.728001 E + 00
1.427436 E 01 9.115030 E 03 1.567773 E 03
2.654621 E + 00 3.114798 E 01 4.295498 E 04
k 1 (29 Cu) 2 (2p') 3 (1s) 4 (3p')
k
R 1.220837 E 04 6.915185 E 02 7.796404 E 02 1.328183 E 01
k
3.804836 E + 12 1.013164 E + 03 1.035152 E + 03 2.762119 E + 01
k
2.849738 E + 05 5.586503 E + 02 3.288432 E + 02 2.128615 E + 02
5 (2p'') 6 (2s) 7 (3d') 8 (3s)
4.030465 E 01 4.412704 E 01 1.042111 E + 00 1.849776 E + 00
2.777226 E + 01 5.783729 E + 00 2.269000 E 01 2.641396 E 01
6.017921 E + 01 3.563878 E + 01 1.517850 E + 01 4.534901 E + 00
9 (3p'') 10 (3d'') 11 (4s)
2.116759 E + 00 3.889212 E + 00 1.060109 E + 01
1.887026 E 01 3.764039 E 02 4.007654 E 04
2.139620 E + 00 6.068395 E 01 3.377457 E 02
k 1 (30 Zn) 2 (2p') 3 (1s) 4 (3p')
k
R 1.093014 E 04 6.639125 E 02 7.523854 E 02 1.278388 E 01
k
5.484732 E + 12 1.127357 E + 03 1.152204 E + 03 3.116592 E + 01
k
3.292847 E + 05 6.042967 E + 02 3.552648 E + 02 2.302047 E + 02
5 (2p'') 6 (2s) 7 (3d') 8 (3s)
3.869566 E 01 4.246594 E 01 1.013522 E + 00 1.786819 E + 00
3.133533 E + 01 6.488273 E + 00 2.535231 E 01 2.985017 E 01
6.593855 E + 01 3.922154 E + 01 1.655417 E + 01 5.018828 E + 00
9 (3p'') 10 (3d'') 11 (4s)
2.037400 E + 00 3.782514 E + 00 1.045940 E + 01
2.148067 E 01 4.539589 E 02 4.172736 E 04
2.411364 E + 00 6.624929 E 01 3.470547 E 02
k 1 (31 Ga) 2 (2p') 3 (1s) 4 (3p') 5 (2p'')
k
R 9.999056 E 05 6.354192 E 02 7.266068 E 02 1.183149 E 01 3.703495 E 01
k
7.402800 E + 12 1.251794 E + 03 1.280136 E + 03 3.549781 E + 01 3.571151 E + 01
k
3.719511 E + 05 6.541462 E + 02 3.827763 E + 02 2.556463 E + 02 7.203164 E + 01
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6 (4p') 7 (2s) 8 (3d') 9 (3s)
4.000629 E 01 4.075339 E 01 8.207280 E 01 1.677752 E + 00
7.369772 E + 00 7.369910 E + 00 3.156732 E 01 4.003778 E 01
4.294966 E + 01 4.044939 E + 01 2.158163 E + 01 5.860955 E + 00
10 (3p'') 11 (3d'') 12 (4s) 13 (4p'')
1.885615 E + 00 3.062999 E + 00 8.681390 E + 00 1.198854 E + 01
2.992761 E 01 8.557296 E 02 8.683064 E 04 1.385572 E 04
2.525737 E + 00 9.701396 E 01 8.953004 E 02 3.130941 E 03
k 1 (32 Ge) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 9.152975 E 05 6.091629 E 02 7.025164 E 02 1.102557 E 01 3.407788 E 01
k
9.962644 E + 12 1.385189 E + 03 1.417356 E + 03 4.023520 E + 01 4.049928 E + 01
k
4.194475 E + 05 7.062215 E + 02 4.114887 E + 02 2.818673 E + 02 8.232897 E + 01
6 (2p'') 7 (2s) 8 (3d') 9 (3s)
3.550461 E 01 3.916665 E 01 7.011994 E 01 1.582128 E + 00
4.049972 E + 01 8.332968 E + 00 3.861721 E 01 5.219974 E 01
5.031343 E + 01 4.588502 E + 01 2.635623 E + 01 6.739995 E + 00
10 (3p'') 11 (3d'') 12 (4s) 13 (4p'')
1.757173 E + 00 2.616912 E + 00 7.604480 E + 00 1.021199 E + 01
4.014337 E 01 1.373594 E 01 1.534117 E 03 4.483593 E 04
2.784645 E + 00 1.339787 E + 00 1.525060 E 01 6.312235 E 03
k 1 (33 As) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 8.390709 E 05 5.848880 E 026.799527 E 021.032950 E 013.005274 E 01
k
1.333612 E + 13 1.527877 E + 03 1.564217 E + 03 4.540040 E + 01 4.572154 E + 01
k
4.718582 E + 05 7.604931 E + 024.413606 E + 023.089537 E + 029.868202 E + 01
6 (2p'') 7 (2s) 8 (3d') 9 (3s)
3.408977 E 01 3.769232 E 01 6.168400 E 01 1.497231 E + 00
4.572252 E + 01 9.382132 E + 00 4.658747 E 01 6.653952 E 01
5.747501 E + 01 4.960630 E + 01 3.109604 E + 01 7.683508 E + 00
10 (3p'') 11 (3d'') 12 (4s) 13 (4p'')
1.646238 E + 00 2.302078 E + 00 6.830392 E + 00 9.005793 E + 00
5.231378 E 01 2.019994 E 01 2.478899 E 03 9.805796 E 04
3.142610 E + 00 1.769067 E + 00 2.236234 E 01 9.621769 E 03
k 1 (34 Se) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 7.701127 E 05 5.622750 E 02 6.587597 E 02 9.705244 E 02 2.878107 E 01
k
1.777164 E + 13 1.680309 E + 03 1.721213 E + 03 5.104387 E + 01 5.143105 E + 01
k
5.296960 E + 05 8.171156 E + 02 4.724217 E + 02 3.373356 E + 02 1.075189 E + 02
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
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217
6 (2p'') 7 (2s) 8 (3d') 9 (3s)
3.277179 E 01 3.631299 E 01 5.508007 E 01 1.419578 E + 00
5.143254 E + 01 1.052897 E + 01 5.575898 E 01 8.378243 E 01
6.232486 E + 01 5.356944 E + 01 3.603637 E + 01 8.745636 E + 00
10 (3p'') 11 (3d'') 12 (4s) 13 (4p'')
1.546749 E + 00 2.055616 E + 00 6.181776 E + 00 8.624716 E + 00
6.709217 E 01 2.837442 E 01 3.509678 E 03 1.488515 E 03
3.616572 E + 00 2.303229 E + 00 3.376347 E 01 1.833763 E 02
k 1 (35 Br) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 7.079964 E 05 5.413089 E 02 6.388372 E 02 9.159978 E 02 2.701979 E 01
k
2.354433 E + 13 1.842653 E + 03 1.888496 E + 03 5.714848 E + 01 5.760900 E + 01
k
5.931226 E + 05 8.758716 E + 02 5.046158 E + 02 3.665159 E + 02 1.196651 E + 02
6 (2p'') 7 (2s) 8 (3d') 9 (3s)
3.154980 E 01 3.502848 E 01 4.996283 E 01 1.350318 E + 00
5.761125 E + 01 1.176836 E + 01 6.593011 E 01 1.034761 E + 00
6.833061 E + 01 5.776175 E + 01 4.103985 E + 01 9.882824 E + 00
10 (3p'') 11 (3d'') 12 (4s) 13 (4p'')
1.459849 E + 00 1.864638 E + 00 5.676813 E + 00 8.096922 E + 00
8.408365 E 01 3.803189 E 01 4.858655 E 03 2.248732 E 03
4.163553 E + 00 2.892445 E + 00 4.591730 E 01 2.713501 E 02
k 1 (36 Kr) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 6.520398 E 05 5.218195 E 02 6.200750 E 02 8.678239 E 02 2.523121 E 01
k
3.100213 E + 13 2.015226 E + 03 2.066399 E + 03 6.373287 E + 01 6.427441 E + 01
k
6.624313 E + 05 9.367502 E + 02 5.379329 E + 02 3.965350 E + 02 1.337821 E + 02
6 (2p'') 7 (2s) 8 (3d') 9 (3s)
3.041387 E 01 3.382960 E 01 4.584139 E 01 1.288048 E + 00
6.427773 E + 01 1.310405 E + 01 7.715564 E 01 1.257663 E + 00
7.503190 E + 01 6.217318 E + 01 4.615233 E + 01 1.109493 E + 01
10 (3p'') 11 (3d'') 12 (4s) 13 (4p'')
1.383073 E + 00 1.710824 E + 00 5.268325 E + 00 7.560943 E + 00
1.034231 E + 00 4.926861 E 01 6.579293 E 03 3.313988 E 03
4.773982 E + 00 3.534833 E + 00 5.868131 E 01 3.586672 E 02
k 1 (37 Rb) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 6.070802 E 05 5.026544 E 02 6.022254 E 02 8.132292 E 02 2.029644 E 01
k
3.947980 E + 13 2.200059 E + 03 2.257313 E + 03 7.124147 E + 01 7.189957 E + 01
k
7.312598 E + 05 1.001329 E + 03 5.724190 E + 02 4.312196 E + 02 1.753015 E + 02
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
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218
6 (2p'') 7 (2s) 8 (3d') 9 (3s) 10 (3p'')
2.929685E 01 3.264912 E 01 4.121461 E 01 1.218004 E + 00 1.296064 E + 00
7.190594E + 01 1.465283 E + 01 9.336976 E 01 1.602583 E + 00 1.338345 E + 00
8.859241E + 01 6.646259 E + 01 5.220725 E + 01 1.238409 E + 01 5.373080 E + 00
11 (3d'') 12 (4s) 13 (4p'') 14 (5s)
1.538150 E + 00 4.582967 E + 00 6.082158 E + 00 1.904387 E + 01
6.802465 E 01 1.136136 E 02 6.401139 E 03 3.456575 E 05
4.252708 E + 00 8.138172 E 01 1.393163 E 01 1.057707 E 02
k 1 (38 Sr) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 5.649045 E 05 4.848135 E 02 5.853622 E 02 7.657762 E 02 1.743202 E 01
k
5.032339 E + 13 2.396022 E + 03 2.459831 E + 03 7.933502 E + 01 8.012319 E + 01
k
8.071016 E + 05 1.068257 E + 03 6.081450 E + 02 4.667447 E + 02 2.124328 E + 02
6 (2p'') 7 (2s) 8 (3d') 9 (3s) 10 (3p'')
2.825700 E 01 3.154582 E 01 3.757189 E 01 1.155770 E + 00 1.220437 E + 00
8.013324 E + 01 1.632401 E + 01 1.114481 E + 00 1.997390 E + 00 1.688127 E + 00
1.001483 E + 02 7.106794 E + 01 5.837499 E + 01 1.384092 E + 01 6.125594 E + 00
11 (3d'') 12 (4s) 13 (4p'') 14 (5s)
1.402202 E + 00 4.107361 E + 00 5.223789 E + 00 1.673859 E + 01
8.999501 E 01 1.704132 E 02 1.015079 E 02 1.018086 E 04
5.104113 E + 00 1.102047 E + 00 2.781945 E 01 2.447504 E 02
k 1 (39 Y) 2 (2p') 3 (1s) 4 (3p')
k
R 5.236921 E 05 4.685108 E 02 5.694566 E 02 7.275406 E 02
k
6.482580 E + 13 2.602725 E + 03 2.673430 E + 03 8.784124 E + 01
k
8.935358 E + 05 1.136812 E + 03 6.450321 E + 02 5.017009 E + 02
5 (4p') 6 (2p'') 7 (2s) 8 (3d')
1.601441 E 01 2.730681 E 01 3.053329 E 01 3.490053 E 01
8.876033 E + 01 8.877329 E + 01 1.806852 E + 01 1.295142 E + 00
2.395223 E + 02 1.095471 E + 02 7.606533 E + 01 6.442781 E + 01
9 (3s) 10 (3p'') 11 (3d'') 12 (4d')
1.104356 E + 00 1.159500 E + 00 1.302505 E + 00 1.337515 E + 00
2.396705 E + 00 2.042206 E + 00 1.123117 E + 00 2.155444 E 02
1.542110 E + 01 7.004576 E + 00 6.043694 E + 00 5.413486 E + 00
13 (4s) 14 (4p'') 15 (4d'') 16 (5s)
3.841116 E + 00 4.798980 E + 00 1.143536 E + 01 1.414640 E + 01
2.171434 E 02 1.328936 E 02 3.285598 E 04 1.686566 E 04
1.360085 E + 00 3.863704 E 01 6.436441 E 02 2.580686 E 03
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k 1 (40 Zr) 2 (2p') 3 (1s) 4 (3p')
k
R 4.854586 E 05 4.533534 E 02 5.543996 E 02 6.942112 E 02
k
8.346702 E + 13 2.820873 E + 03 2.898909 E + 03 9.688049 E + 01
k
9.886325 E + 05 1.207368 E + 03 6.830739 E + 02 5.371539 E + 02
5 (4p') 6 (2p'') 7 (2s) 8 (3d')
1.497748 E 01 2.642337 E 01 2.958863 E 01 3.270379 E 01
9.793841 E + 01 9.795425 E + 01 1.991792 E + 01 1.486163 E + 00
2.648215 E + 02 1.187383 E + 02 8.135216 E + 01 7.060441 E + 01
9 (3s) 10 (3p'') 11 (3d'') 12 (4d')
1.058841 E + 00 1.106382 E + 00 1.220522 E + 00 1.301045 E + 00
2.824948 E + 00 2.422741 E + 00 1.364817 E + 00 2.603216 E 02
1.711908 E + 01 7.983580 E + 00 7.073825 E + 00 6.258831 E + 00
13 (4s) 14 (4p'') 15 (4d'') 16 (5s)
3.636969 E + 00 4.488245 E + 00 1.112355 E + 01 1.218499 E + 01
2.637962 E 02 1.645480 E 02 6.113773 E 04 2.639161 E 04
1.634497 E + 00 5.108769 E 01 6.803978 E 02 6.220605 E 04
k 1 (41 Nb) 2 (2p') 3 (1s) 4 (3p')
k
R 4.501991 E 05 4.391736 E 02 5.401178 E 02 6.643865 E 02
k
1.072707 E + 14 3.050890 E + 03 3.136732 E + 03 1.064995 E + 02
k
1.092722 E + 06 1.280030 E + 03 7.222732 E + 02 5.733900 E + 02
5 (4p') 6 (2p'') 7 (2s) 8 (3d')
1.412630 E 01 2.559691 E 01 2.870219 E 01 3.082248 E 01
1.077064 E + 02 1.077253 E + 02 2.188346 E + 01 1.690672 E + 00
2.899560 E + 02 1.280690 E + 02 8.690561 E + 01 7.697269 E + 01
9 (3s) 10 (3p'') 11 (3d'') 12 (4d')
1.017632 E + 00 1.058850 E + 00 1.150311 E + 00 1.272790 E + 00
3.289871 E + 00 2.836797 E + 00 1.629909 E + 00 3.070995 E 02
1.893695 E + 01 9.059018 E + 00 8.198586 E + 00 7.145154 E + 00
13 (4s) 14 (4p'') 15 (4d'') 16 (5s)
3.464973 E + 00 4.233175 E + 00 1.088198 E + 01 1.109917 E + 01
3.126663 E 02 1.978928 E 02 9.058751 E 04 3.491964 E 04
1.940829 E + 00 6.632702 E 01 7.957632 E 02 3.449854 E 05
k 1 (42 Mo) 2 (2p') 3 (1s) 4 (3p')
k
R 4.178552 E 05 4.258720 E 02 5.265520 E 02 6.374337 E 02
k
1.374305 E + 14 3.293107 E + 03 3.387246 E + 03 1.167202 E + 02
k
1.206027 E + 06 1.354802 E + 03 7.626188 E + 02 6.104650 E + 02
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
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5 (4p') 6 (2p'') 7 (2s) 8 (3d')
1.340394 E 01 2.482164 E 01 2.786829 E 01 2.918330 E 01
1.180867 E + 02 1.181088 E + 02 2.396970 E + 01 1.909450 E + 00
3.152121 E + 02 1.376027 E + 02 9.271058 E + 01 8.354308 E + 01
9 (3s) 10 (3p'') 11 (3d'') 12 (4d')
9.800179 E 01 1.015894 E + 00 1.089135 E + 00 1.249745 E + 00
3.793542 E + 00 3.286271 E + 00 1.919725 E + 00 3.563374 E 02
2.086513 E + 01 1.021983 E + 01 9.409282 E + 00 8.064772 E + 00
13 (4s) 14 (4p'') 15 (5s) 16 (4d'')
3.316004 E + 00 4.016708 E + 00 1.031409 E + 01 1.068495 E + 01
3.641780 E 02 2.332308 E 02 1.219220 E 03 7.840598 E 04
2.272332 E + 00 8.374436 E 01 1.059247 E 01 2.258214 E 04
k 1 (43 Tc) 2 (2p') 3 (1s) 4 (3p')
k
R 3.882324 E 05 4.133751 E 02 5.136509 E 02 6.129718 E 02
k
1.754303 E + 14 3.547815 E + 03 3.650753 E + 03 1.275539 E + 02
k
1.328965 E + 06 1.431661 E + 03 8.041074 E + 02 6.483741 E + 02
5 (4p') 6 (2p'') 7 (2s) 8 (3d')
1.278604 E 01 2.409326 E 01 2.708275 E 01 2.774215 E 01
1.290906 E + 02 1.291161 E + 02 2.617834 E + 01 2.142288 E + 00
3.405277 E + 02 1.473462 E + 02 9.876592 E + 01 9.031936 E + 01
9 (3s) 10 (3p'') 11 (3d'') 12 (4d')
9.455719 E 01 9.769087 E 01 1.035351 E + 00 1.231746 E + 00
4.335521 E + 00 3.770769 E + 00 2.234002 E + 00 4.076921 E 02
2.289872 E + 01 1.146057 E + 01 1.070110 E + 01 9.005113 E + 00
13 (4s) 14 (4p'') 15 (5s) 16 (4d'')
3.186168 E + 00 3.831546 E + 00 9.587477 E + 00 1.053106 E + 01
4.179288 E 02 2.703122 E 02 1.565457 E 03 1.023670 E 03
2.622872 E + 00 1.028803 E + 00 1.492681 E 01 2.032708 E 03
k 1 (44 Ru) 2 (2p') 3 (1s) 4 (3p')
k
R 3.611369 E 05 4.015578 E 02 5.013584 E 02 5.902079 E 02
k
2.230224 E + 14 3.815532 E + 03 3.927828 E + 03 1.390723 E + 02
k
1.461909 E + 06 1.510763 E + 03 8.467422 E + 02 6.874083 E + 02
5 (4p') 6 (2p'') 7 (2s) 8 (3d')
1.220143 E 01 2.340450 E 01 2.633820 E 01 2.643215 E 01
1.407939 E + 02 1.408232 E + 02 2.852738 E + 01 2.394761 E + 00
3.673248 E + 02 1.575063 E + 02 1.050439 E + 02 9.734860 E + 01
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9 (3s) 10 (3p'') 11 (3d'') 12 (4d')
9.133153 E 01 9.406294 E 01 9.864613 E 01 1.209399 E + 00
4.930517 E + 00 4.303789 E + 00 2.582260 E + 00 4.650346 E 02
2.504522 E + 01 1.278456 E + 01 1.208312 E + 01 1.002162 E + 01
13 (4s) 14 (4p'') 15 (5s) 16 (4d'')
3.062729 E + 00 3.656358 E + 00 9.373947 E + 00 1.034000 E + 01
4.780123 E 02 3.118181 E 02 1.877428 E 03 1.297767 E 03
3.014346 E + 00 1.252608 E + 00 1.818008 E 01 2.533380 E 03
k 1 (45 Rh) 2 (2p') 3 (1s) 4 (3p')
k
R 3.363296 E 05 3.904164 E 02 4.896407 E 02 5.693585 E 02
k
2.823766 E + 14 4.096380 E + 03 4.218567 E + 03 1.512420 E + 02
k
1.605423 E + 06 1.591948 E + 03 8.905132 E + 02 7.273057 E + 02
5 (4p') 6 (2p'') 7 (3d') 8 (2s)
1.169241 E 01 2.275514 E 01 2.526218 E 01 2.563458 E 01
1.531597 E + 02 1.531930 E + 02 3.100646 E + 01 3.391110 E + 01
3.942567 E + 02 1.678941 E + 02 1.127274 E + 02 1.045915 E + 02
9 (3s) 10 (3p'') 11 (3d'') 12 (4d')
8.835513 E 01 9.074011 E 01 9.427974 E 01 1.191622 E + 00
5.567006 E + 00 4.874783 E + 00 2.957121 E + 00 5.247938 E 02
2.720889 E + 01 1.418261 E + 01 1.354179 E + 01 1.105142 E + 01
13 (4s) 14 (4p'') 15 (5s) 16 (4d'')
2.953454 E + 00 3.503823 E + 00 9.043605 E + 00 1.018801 E + 01
5.406222 E 02 3.552900 E 02 2.228368 E 03 1.582837 E 03
3.420811 E + 00 1.490568 E + 00 2.257527 E 01 4.333491 E 03
k 1 (46 Pd) 2 (2p') 3 (1s) 4 (3p')
k
R 3.135993 E 05 3.798848 E 02 4.784571 E 02 5.501025 E 02
k
3.560771 E + 14 4.390715 E + 03 4.523348 E + 03 1.640911 E + 02
k
1.760059 E + 06 1.675240 E + 03 9.354178 E + 02 7.681297 E + 02
5 (4p') 6 (2p'') 7 (3d') 8 (2s)
1.123683 E 01 2.214131 E 01 2.420456 E 01 2.496803 E 01
1.662173 E + 02 1.662548 E + 02 3.362176 E + 01 3.692404 E + 01
4.216182 E + 02 1.785547 E + 02 1.209265 E + 02 1.120601 E + 02
9 (3s) 10 (3p'') 11 (3d'') 12 (4d')
8.558870 E 01 8.767124 E 01 9.033265 E 01 1.176168 E + 00
6.248755 E + 00 5.487216 E + 00 3.361044 E + 00 5.876710 E 02
2.945320 E + 01 1.565481 E + 01 1.507872 E + 01 1.210346 E + 01
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13 (4s) 14 (4p'') 15 (5s) 16 (4d'')
2.854421 E + 00 3.367301 E + 00 8.721407 E + 00 1.005589 E + 01
6.064830 E 02 4.011839 E 02 2.600952 E 03 1.881202 E 03
3.846500 E + 00 1.746075 E + 00 2.771911 E 01 6.997619 E 03
k 1 (47 Ag) 2 (2p') 3 (1s) 4 (3p')
k
R 2.952782 E 05 3.699131 E 02 4.677718 E 02 5.322435 E 02
k
4.358279 E + 14 4.698854 E + 03 4.842505 E + 03 1.776379 E + 02
k
1.909909 E + 06 1.759912 E + 03 9.807244 E + 02 8.091657 E + 02
5 (4p') 6 (2p'') 7 (3d') 8 (2s)
1.082510 E 01 2.156012 E 01 2.324222 E 01 2.433561 E 01
1.799854 E + 02 1.800274 E + 02 3.637649 E + 01 4.010617 E + 01
4.487302 E + 02 1.887680 E + 02 1.286466 E + 02 1.190270 E + 02
9 (4d') 10 (3s) 11 (3p'') 12 (3d'')
7.049601 E 01 8.300820 E 01 8.482500 E 01 8.674116 E 01
6.976692 E + 00 6.986521 E + 00 6.151728 E + 00 3.804267 E + 00
3.908188 E + 01 1.891337 E + 01 1.646990 E + 01 1.596332 E + 01
13 (4s) 14 (4p'') 15 (4d'') 16 (5s)
2.763928 E + 00 3.243917 E + 00 6.027200 E + 00 1.387693 E + 01
7.458398 E 02 5.197082 E 02 1.000752 E 02 1.786739 E 04
4.016741 E + 00 1.410594 E + 00 3.639316 E 01 2.123996 E 02
k 1 (48 Cd) 2 (2p') 3 (1s) 4 (3p')
k
R 2.764401 E 05 3.604624 E 02 4.575532 E 02 5.156591 E 02
k
5.424374 E + 14 5.022756 E + 03 5.176336 E + 03 1.918938 E + 02
k
2.083482 E + 06 1.853729 E + 03 1.034221 E + 03 8.581836 E + 02
5 (4p') 6 (2p'') 7 (3d') 8 (2s)
1.045398 E 01 2.100929 E 01 2.236414 E 01 2.373506 E 01
1.944751 E + 02 1.945217 E + 02 3.927316 E + 01 4.345964 E + 01
4.832583 E + 02 2.063170 E + 02 1.436819 E + 02 1.332878 E + 02
9 (4d') 10 (3s) 11 (3p'') 12 (3d'')
6.778536 E 01 8.059884 E 01 8.218190 E 01 8.346412 E 01
5.182215 E + 00 7.763532 E + 00 6.851616 E + 00 4.270299 E + 00
4.795679 E + 01 2.494971 E + 01 2.186001 E + 01 2.135897 E + 01
13 (4s) 14 (4p'') 15 (4d'') 16 (5s)
2.681445 E + 00 3.132706 E + 00 5.795447 E + 00 1.373979 E + 01
8.382595 E 02 5.906115 E 02 1.246825 E 02 1.840775 E 04
6.073621 E + 00 2.658194 E + 00 1.097410 E + 00 3.335212 E 01
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k 1 (49 In) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 2.611485 E 05 3.511143 E 02 4.477062 E 02 4.972748 E 02 9.754386 E 02
k
6.568177 E + 14 5.360185 E + 03 5.528167 E + 03 2.075506 E + 02 2.104289 E + 02
k
2.251429 E + 06 1.938178 E + 03 1.075775 E + 03 8.976829 E + 02 5.220315 E + 02
6 (2p'') 7 (3d') 8 (2s) 9 (5p') 10 (4d')
2.046444 E 01 2.137762 E 01 2.314069 E 01 3.250338 E 01 5.745003 E 01
2.104863 E + 02 4.250458 E + 01 4.729780 E + 01 8.766608 E + 00 8.766671 E + 00
2.130830 E + 02 1.462519 E + 02 1.349310 E + 02 9.904672 E + 01 4.714387 E + 01
11 (3s) 12 (3p'') 13 (3d'') 14 (4s)
7.794883 E 01 7.925194 E 01 7.978237 E 01 2.535737 E + 00
8.786849 E + 00 7.778728 E + 00 4.900401 E + 00 1.071865 E 01
2.418580 E + 01 1.920578 E + 01 1.889586 E + 01 4.776507 E + 00
15 (4p'') 16 (4d'') 17 (5s) 18 (5p'')
2.923061 E + 00 4.911808 E + 00 1.158315 E + 01 1.559485 E + 01
7.790259 E 02 2.054839 E 02 3.701749 E 04 6.294652 E 05
1.688160 E + 00 5.692079 E 01 5.639479 E 02 2.097238 E 03
k 1 (50 Sn) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 2.467213 E 05 3.422326 E 02 4.382713 E 02 4.802160 E 02 9.169330 E 02
k
7.948065 E + 14 5.714333 E + 03 5.895736 E + 03 2.240491 E + 02 2.272451 E + 02
k
2.431725 E + 06 2.031427 E + 03 1.125036 E + 03 9.447684 E + 02 5.671729 E + 02
6 (2p'') 7 (3d') 8 (2s) 9 (5p') 10 (4d')
1.994678 E 01 2.048100 E 01 2.257492 E 01 2.804256 E 01 5.062632 E 01
2.273142 E + 02 4.591169 E + 01 5.136238 E + 01 9.860977 E + 00 9.861173 E + 00
2.264465 E + 02 1.556454 E + 02 1.433694 E + 02 1.153567 E + 02 5.888310 E + 01
11 (3s) 12 (3d'') 13 (3p'') 14 (4s)
7.547442 E 01 7.643613 E 01 7.653325 E 01 2.409355 E + 00
9.890659 E + 00 8.780099 E + 00 3.329406 E + 00 1.333130 E 01
2.747505 E + 01 2.064088 E + 01 2.044099 E + 01 5.225673 E + 00
15 (4p'') 16 (4d'') 17 (5s) 18 (5p'')
2.747739 E + 00 4.328401 E + 00 1.024433 E + 01 1.345458 E + 01
9.917492 E 02 3.012673 E 02 6.401462 E 04 1.960355 E 04
1.880047 E + 00 7.646722 E 01 9.464658 E 02 4.190133 E 03
k 1 (51 Sb) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 2.332088 E 05 3.337787 E 02 4.292223 E 02 4.643023 E 02 8.664807 E 02
k
9.599455 E + 14 6.083905 E + 03 6.279443 E + 03 2.414227 E + 02 2.449588 E + 02
k
2.624084 E + 06 2.126981 E + 03 1.175481 E + 03 9.929617 E + 02 6.127320 E + 02
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6 (2p'') 7 (3d') 8 (2s) 9 (5p') 10 (4d')
1.945405 E 01 1.965963 E 01 2.203544 E 01 2.495391 E 01 4.559489 E 01
2.450406 E + 02 4.950237 E + 01 5.566519 E + 01 1.104041 E + 01 1.104083 E + 01
2.399941 E + 02 1.653418 E + 02 1.520799 E + 02 1.300246 E + 02 7.044826 E + 01
11 (3s) 12 (3d'') 13 (3p'') 14 (4s)
7.315308 E 01 7.337072 E 01 7.399704 E 01 2.297336 E + 00
1.108120 E + 01 9.861523 E + 00 3.698705 E + 00 1.625863 E 01
3.066017 E + 01 2.227480 E + 01 2.209584 E + 01 5.720609 E + 00
15 (4p'') 16 (4d'') 17 (5s) 18 (5p'')
2.596551 E + 00 3.898228 E + 00 9.270607 E + 00 1.197267 E + 01
1.232070 E 01 4.138160 E 02 1.016576 E 03 4.173142 E 04
2.112967 E + 00 9.840578 E 01 1.370464 E 01 6.326601 E 03
k 1 (52 Te) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 2.205345 E 05 3.257040 E 02 4.205326 E 02 4.492876 E 02 8.208538 E 02
k
1.157405 E + 15 6.469406 E + 03 6.679851 E + 03 2.597405 E + 02 2.636431 E + 02
k
2.829311 E + 06 2.224939 E + 03 1.227111 E + 03 1.042414 E + 03 6.598953 E + 02
6 (3d') 7 (2p'') 8 (2s) 9 (5p') 10 (4d')
1.889628 E 01 1.898342 E 01 2.151935 E 01 2.406710 E 01 4.149085 E 01
2.637394 E + 02 2.776199 E + 02 6.023488 E + 01 1.232182 E + 01 1.232244 E + 01
2.550619 E + 02 1.753634 E + 02 1.606489 E + 02 1.377109 E + 02 8.029383 E + 01
11 (3d'') 12 (3s) 13 (3p'') 14 (4s)
7.052189 E 01 7.095263 E 01 7.160411 E 01 2.194126 E + 00
1.237601 E + 01 5.435748 E + 00 4.099042 E + 00 1.964236 E 01
3.412204 E + 01 2.401900 E + 01 2.376272 E + 01 6.286788 E + 00
15 (4p'') 16 (4d'') 17 (5s) 18 (5p'')
2.459822 E + 00 3.547345 E + 00 8.448161 E + 00 1.154719 E + 01
1.512217 E 01 5.497902 E 02 1.412092 E 03 6.202203 E 04
2.405228 E + 00 1.258944 E + 00 2.074935 E 01 1.204640 E 02
k 1 (53 I) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 2.086803 E 05 3.180051 E 02 4.121852 E 02 4.352442 E 02 7.808259 E 02
k
1.392332 E + 15 6.870988 E + 03 7.097090 E + 03 2.789775 E + 02 2.832702 E + 02
k
3.047541 E + 06 2.325207 E + 03 1.279941 E + 03 1.092975 E + 03 7.075875 E + 02
6 (3d') 7 (2p'') 8 (2s) 9 (5p') 10 (4d')
1.819331 E 01 1.853470 E 01 2.102648 E 01 2.273653 E 01 3.822704 E 01
2.833820 E + 02 2.911583 E + 02 6.505592 E + 01 1.369398 E + 01 1.369489 E + 01
2.731331 E + 02 1.857106 E + 02 1.685551 E + 02 1.479557 E + 02 9.094124 E + 01
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
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11 (3d'') 12 (3s) 13 (3p'') 14 (4s)
6.789834 E 01 6.888415 E 01 6.936597 E 01 2.101721 E + 00
1.376339 E + 01 5.987138 E + 00 4.526363 E + 00 2.336622 E 01
3.772690 E + 01 2.586681 E + 01 2.548103 E + 01 6.899952 E + 00
15 (4p'') 16 (4d'') 17 (5s) 18 (5p'')
2.339872 E + 00 3.268298 E + 00 7.803381 E + 00 1.090880 E + 01
1.822322 E 01 7.041664 E 02 1.924337 E 03 9.195065 E 04
2.730047 E + 00 1.556790 E + 00 2.824270 E 01 1.830144 E 02
k 1 (54 Xe) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 1.976032 E 05 3.106561 E 02 4.041604 E 02 4.220737 E 02 7.452533 E 02
k
1.670796 E + 15 7.288990 E + 03 7.531521 E + 03 2.991585 E + 02 3.038657 E + 02
k
3.279111 E + 06 2.427739 E + 03 1.333923 E + 03 1.144606 E + 03 7.559227 E + 02
6 (3d') 7 (2p'') 8 (2s) 9 (5p') 10 (4d')
1.754323 E 01 1.810636 E 01 2.055529 E 01 2.134902 E 01 3.554090 E 01
3.039943 E + 02 3.126674 E + 02 7.013605 E + 01 1.516040 E + 01 1.516174 E + 01
2.916489 E + 02 1.963378 E + 02 1.766887 E + 02 1.594076 E + 02 1.021463 E + 02
11 (3d'') 12 (3s) 13 (3p'') 14 (4s)
6.547224 E 01 6.693523 E 01 6.726696 E 01 2.018208 E + 00
1.524696 E + 01 6.573828 E + 00 4.981703 E + 00 2.744835 E 01
4.139147 E + 01 2.780050 E + 01 2.727882 E + 01 7.550129 E + 00
15 (4p'') 16 (4d'') 17 (5s) 18 (5p'')
2.233273 E + 00 3.038641 E + 00 7.276186 E + 00 1.024308 E + 01
2.164013 E 01 8.779759 E 02 2.572283 E 03 1.332830 E 03
3.079605 E + 00 1.873818 E + 00 3.598366 E 01 2.419956 E 02
k 1 (55 Cs) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 1.882567 E 05 3.034583 E 02 3.964060 E 02 4.085289 E 02 7.021561 E 02
k
1.967990 E + 15 7.725818 E + 03 7.986020 E + 03 3.208696 E + 02 3.260607 E + 02
k
3.505658 E + 06 2.533596 E + 03 1.388984 E + 03 1.198794 E + 03 8.156654 E + 02
6 (3d') 7 (5p') 8 (2p'') 9 (2s) 10 (4d')
1.687565 E 01 1.746273 E 01 1.768685 E 01 2.009346 E 01 3.222227 E 01
3.262145 E + 02 3.359582 E + 02 3.359606 E + 02 7.575875 E + 01 1.690460 E + 01
3.125647 E + 02 2.091124 E + 02 2.029666 E + 02 1.847288 E + 02 1.168266 E + 02
11 (3d'') 12 (3s) 13 (3p'') 14 (4s) 15 (4p'')
6.298078 E 01 6.493185 E 01 6.510829 E 01 1.918350 E + 00 2.104125 E + 00
1.701896 E + 01 7.275268 E + 00 5.531181 E + 00 3.400614 E 01 2.724285 E 01
4.560922 E + 01 2.963468 E + 01 2.894976 E + 01 8.178919 E + 00 3.407417 E + 00
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16 (4d'') 17 (5s) 18 (5p'') 19 (6s)
2.754908 E + 00 6.371605 E + 00 8.378469 E + 00 2.412889 E + 01
1.186612 E 01 4.298250 E 03 2.452407 E 03 1.699414 E 05
2.230443 E + 00 5.019411 E 01 9.493183 E 02 7.804349 E 03
k 1 (56 Ba) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 1.792580 E 05 2.965819 E 02 3.889412 E 02 3.958653 E 02 6.648555 E 02
k
2.320937 E + 15 8.179920 E + 03 8.458643 E + 03 3.436230 E + 02 3.493284 E + 02
k
3.748586 E + 06 2.641857 E + 03 1.445293 E + 03 1.254123 E + 03 8.757556 E + 02
6 (5p') 7 (3d') 8 (2p'') 9 (2s) 10 (4d')
1.518527 E 01 1.626049 E 01 1.728606 E 01 1.965160 E 01 2.961243 E 01
3.495095 E + 02 3.495132 E + 02 3.604051 E + 02 8.168176 E + 01 1.876769 E + 01
3.578978 E + 02 2.377281 E + 02 2.187389 E + 02 1.930848 E + 02 1.294398 E + 02
11 (3d'') 12 (3s) 13 (3p'') 14 (4s) 15 (4p'')
6.068497 E 01 6.304911 E 01 6.309005 E 01 1.829902 E + 00 1.992348 E + 00
1.891503 E + 01 8.023115 E + 00 6.118073 E + 00 4.126575 E 01 3.347359 E 01
4.988457 E + 01 3.163095 E + 01 3.077654 E + 01 8.913591 E + 00 3.824103 E + 00
16 (4d'') 17 (5s) 18 (5p'') 19 (6s)
2.531775 E + 00 5.749176 E + 00 7.285766 E + 00 2.137902 E + 01
1.536089 E 01 6.265215 E 03 3.752607 E 03 4.886279 E 05
2.660332 E + 00 6.818691 E 01 1.877558 E 01 1.790125 E 02
k 1 (57 La) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 1.692451 E 05 2.902829 E 02 3.818004 E 02 3.859718 E 02 6.475144 E 02
k
2.806973 E + 15 8.648024 E + 03 8.945288 E + 03 3.663737 E + 02 3.725292 E + 02
k
4.041273 E + 06 2.750477 E + 03 1.502852 E + 03 1.307546 E + 03 9.178818 E + 02
6 (5p') 7 (3d') 8 (2p'') 9 (2s)
1.492569 E 01 1.579506 E 01 1.691893 E 01 1.924604 E 01
3.727252 E + 02 3.727291 E + 02 3.846125 E + 02 8.734805 E + 01
3.729340 E + 02 2.494777 E + 02 2.300989 E + 02 2.021814 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.863917 E 01 5.894798 E 01 6.151331 E 01 6.155785 E 01
2.037232 E + 01 2.053520 E + 01 8.651790 E + 00 2.496299 E + 00
1.372805 E + 02 5.348854 E + 01 3.393667 E + 01 3.292557 E + 01
14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.785570 E + 00 1.940382 E + 00 2.298301 E + 00 2.448564 E + 00
4.494250 E 01 3.655542 E 01 1.694816 E 01 1.702380 E 01
9.680064 E + 00 4.253781 E + 00 3.240094 E + 00 2.588716 E + 00
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18 (5s) 19 (4f'') 20 (5p'') 21 (6s)
5.648357 E + 00 6.894903 E + 00 7.161220 E + 00 2.121609 E + 01
7.356273 E 03 4.706705 E 03 3.950365 E 03 4.999715 E 05
7.526164 E 01 2.064493 E 01 1.488919 E 01 1.818341 E 02
k 1 (58 Ce) 2 (2p') 3 (1s) 4 (3p') 5 (4p')
k
R 1.599118 E 05 2.842692 E 02 3.749201 E 02 3.767547 E 02 6.322577 E 02
k
3.386083 E + 15 9.133412 E + 03 9.449945 E + 03 3.900092 E + 02 3.966276 E + 02
k
4.352190 E + 06 2.861066 E + 03 1.561513 E + 03 1.361690 E + 03 9.593886 E + 02
6 (5p') 7 (3d') 8 (2p'') 9 (2s)
1.472617 E 01 1.536583 E 01 1.656842 E 01 1.885836 E 01
3.968383 E + 02 3.968423 E + 02 4.097497 E + 02 9.321721 E + 01
3.867739 E + 02 2.608374 E + 02 2.416580 E + 02 2.115025 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.781337 E 01 5.734605 E 01 6.004435 E 01 6.016325 E 01
2.202548 E + 01 2.220331 E + 01 9.295950 E + 00 2.677542 E + 00
1.449479 E + 02 5.710741 E + 01 3.630382 E + 01 3.511709 E + 01
14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.746119 E + 00 1.894663 E + 00 2.055460 E + 00 2.377961 E + 00
4.850018 E 01 3.953169 E 01 1.847051 E 01 1.868198 E 01
1.043088 E + 01 4.660491 E + 00 3.931914 E + 00 3.110304 E + 00
18 (5s) 19 (4f'') 20 (5p'') 21 (6s)
5.566603 E + 00 6.166379 E + 00 7.065490 E + 00 2.108081 E + 01
8.994719 E 03 6.226691 E 03 4.112028 E 03 5.096590 E 05
7.995669 E 01 2.456582 E 01 1.710934 E 01 1.840633 E 02
k 1 (59 Pr) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 1.512190 E 05 2.785126 E 02 3.680808 E 02 3.682849 E 02 6.183397 E 02
k
4.073279 E + 15 9.636514 E + 03 9.973082 E + 03 9.980179 E + 03 4.216776 E + 02
k
4.681737 E + 06 2.973704 E + 03 1.621891 E + 03 1.416684 E + 03 1.000719 E + 03
.
6 (5p') 7 (3d') 8 (2p'') 9 (2s)
1.455508 E 01 1.496529 E 01 1.623291 E 01 1.848684 E 01
4.219028 E + 02 4.219070 E + 02 4.358787 E + 02 9.931069 E + 01
4.001429 E + 02 2.720948 E + 02 2.534467 E + 02 2.210478 E + 02
10 (4d') 11 (3p'') 12 (3d'') 13 (3s)
2.707756 E 01 5.585121 E 01 5.866197 E 01 5.884677 E 01
2.373995 E + 01 2.393267 E + 01 9.960942 E + 00 2.863529 E + 00
1.526084 E + 02 6.078199 E + 01 3.872898 E + 01 3.736104 E + 01
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14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.709870 E + 00 1.852956 E + 00 1.908274 E + 00 2.315051 E + 00
5.205225 E 01 4.250118 E 01 1.998558 E 01 2.038198 E 01
1.118484 E + 01 5.061475 E + 00 4.525381 E + 00 3.569309 E + 00
18 (5s) 19 (4f'') 20 (5p'') 21 (6s)
5.494347 E + 00 5.724821 E + 00 6.983402 E + 00 2.095775 E + 01
1.110054 E 02 8.221864 E 03 4.257831 E 03 5.186893 E 05
8.379122 E 01 2.752646 E 01 1.889244 E 01 1.860202 E 02
k 1 (60 Nd) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 1.429845 E 05 2.729903 E 02 3.598534 E 02 3.618805 E 02 6.052815 E 02
k
4.899993 E + 15 1.015774 E + 04 1.051515 E + 04 1.052275 E + 04 4.477293 E + 02
k
5.035292 E + 06 3.088887 E + 03 1.688947 E + 03 1.473064 E + 03 1.041376 E + 03
6 (5p') 7 (3d') 8 (2p'') 9 (2s)
1.439487 E 01 1.458807 E 01 1.591104 E 01 1.813003 E 01
4.479693 E + 02 4.479737 E + 02 4.630575 E + 02 1.056481 E + 02
4.139305 E + 02 2.838705 E + 02 2.659183 E + 02 2.312467 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.639634 E 01 5.444343 E 01 5.735075 E 01 5.759484 E 01
2.552730 E + 01 2.573532 E + 01 1.065151 E + 01 3.056072 E + 00
1.608111 E + 02 6.497240 E + 01 4.165075 E + 01 4.009460 E + 01
14 (4s) 15 (4p'') 16 (4d'') 17 (4f')
1.675726 E + 00 1.813825 E + 00 1.832209 E + 00 2.256809 E + 00
5.569315 E 01 3.168863 E 01 2.154176 E 01 2.213890 E 01
1.238404 E + 01 5.893310 E + 00 5.410196 E + 00 4.318720 E + 00
18 (5s) 19 (5p'') 20 (4f'') 21 (6s)
5.426173 E + 00 5.496626 E + 00 6.906539 E + 00 2.083995 E + 01
1.336062 E 02 1.037207 E 02 4.400710 E 03 5.275352 E 05
1.059656 E + 00 4.268438 E 01 3.170839 E 01 6.749257 E 02
k 1 (61 Pm) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 1.355498 E 05 2.676874 E 02 3.520315 E 02 3.556952 E 02 5.929694 E 02
k
5.847159 E + 15 1.069743 E + 04 1.107650 E + 04 1.108461 E + 04 4.748046 E + 02
k
5.400008 E + 06 3.205363 E + 03 1.756347 E + 03 1.529583 E + 03 1.081710 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.423181 E 01 1.424408 E 01 1.560196 E 01 1.778704 E 01
4.750599 E + 02 4.913051 E + 02 4.913096 E + 02 1.122356 E + 02
4.272666 E + 02 2.949123 E + 02 2.776764 E + 02 2.408401 E + 02
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10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.576158 E 01 5.311385 E 01 5.610415 E 01 5.640176 E 01
2.738987 E + 01 2.761365 E + 01 1.136849 E + 01 3.255421 E + 00
1.683087 E + 02 6.842279 E + 01 4.381140 E + 01 4.205992 E + 01
14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.643422 E + 00 1.776930 E + 00 1.784150 E + 00 2.202538 E + 00
5.943078 E 01 4.867371 E 01 2.314269 E 01 2.395107 E 01
1.277106 E + 01 5.915201 E + 00 5.450483 E + 00 4.332152 E + 00
18 (4f'') 19 (5s) 20 (5p'') 21 (6s)
5.352450 E + 00 5.361529 E + 00 6.834191 E + 00 2.072706 E + 01
1.572286 E 02 7.639086 E 03 4.541128 E 03 5.362020 E 05
9.264694 E 01 3.046666 E 01 2.061615 E 01 1.896759 E 02
k 1 (62 Sm) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 1.284936 E 05 2.625936 E 02 3.446021 E 02 3.497183 E 02 5.814608 E 02
k
6.976837 E + 15 1.125583 E + 04 1.165740 E + 04 1.166605 E + 04 5.029050 E + 02
k
5.789945 E + 06 3.324344 E + 03 1.825273 E + 03 1.587449 E + 03 1.122785 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.389563 E 01 1.410812 E 01 1.530507 E 01 1.745725 E 01
5.031758 E + 02 5.206288 E + 02 5.206335 E + 02 1.190690 E + 02
4.468028 E + 02 3.063691 E + 02 2.878084 E + 02 2.510747 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.517731 E 01 5.185918 E 01 5.492012 E 01 5.526584 E 01
2.932322 E + 01 2.956295 E + 01 1.210992 E + 01 3.460731 E + 00
1.762967 E + 02 7.236629 E + 01 4.645429 E + 01 4.450105 E + 01
14 (4s) 15 (4f') 16 (4p'') 17 (4d'')
1.613085 E + 00 1.732378 E + 00 1.742442 E + 00 2.152586 E + 00
6.321350 E 01 5.183802 E 01 5.289767 E 01 2.582047 E 01
1.358776 E + 01 6.391937 E + 00 5.920541 E + 00 4.697597 E + 00
18 (4f'') 19 (5s) 20 (5p'') 21 (6s)
5.197135 E + 00 5.301955 E + 00 6.768956 E + 00 2.062113 E + 01
1.847299 E - 02 7.876521 E 03 4.672957 E 03 5.445075 E 05
1.005250 E + 00 3.186345 E 01 2.091799 E 01 1.913206 E 02
k 1 (63 Eu) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 1.219082 E 05 2.576970 E 02 3.375364 E 02 3.439396 E 02 5.706899 E 02
k
8.301428 E + 15 1.183327 E + 04 1.225816 E + 04 1.226736 E + 04 5.320452 E + 02
k
6.201154 E + 06 3.445400E + 03 1.895290 E + 03 1.646235 E + 03 1.164159 E + 03
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6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.357784 E 01 1.398620 E 01 1.501968 E 01 1.713991 E 01
5.323316 E + 02 5.510390 E + 02 5.510438 E + 02 1.261507 E + 02
4.666162 E + 02 3.178006 E + 02 2.979675 E + 02 2.615256 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.463879 E 01 5.067318 E 01 5.379403 E 01 5.418307 E 01
3.132728 E + 01 3.158308 E + 01 1.287570 E + 01 3.671886 E + 00
1.843447 E + 02 7.637629 E + 01 4.915445 E + 01 4.699317 E + 01
14 (4s) 15 (4f') 16 (4p'') 17 (4d'')
1.584561 E + 00 1.676329 E + 00 1.710165 E + 00 2.106543 E + 00
6.703014 E 01 5.502921 E 01 5.639366 E 01 2.775422 E 01
1.440904 E + 01 6.931056 E + 00 6.421800 E + 00 5.042089 E + 00
18 (4f'') 19 (5s) 20 (5p'') 21 (6s)
5.028988 E + 00 5.247153 E + 00 6.710462 E + 00 2.052170 E + 01
2.174508 E 02 8.100574 E 03 4.795583 E 03 5.524607 E 05
1.093016 E + 00 3.350770 E 01 2.119955 E 01 1.928248 E 02
k 1 (64 Gd) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 1.157214 E 05 2.529679 E 02 3.306830 E 02 3.383459 E 02 5.597565 E 02
k
9.859391 E + 15 1.243045 E + 04 1.287962 E + 04 1.288941 E + 04 5.623746 E + 02
k
6.636392 E + 06 3.568843 E + 03 1.966987 E + 03 1.706333 E + 03 1.207276 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.327075 E 01 1.383863 E 01 1.474405 E 01 1.683315 E 01
5.626781 E + 02 5.827144 E + 02 5.827193 E + 02 1.335489 E + 02
4.871441 E + 02 3.299331 E + 02 3.087194 E + 02 2.722655 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.408313 E 01 4.952712 E 01 5.270179 E 01 5.313159 E 01
3.344636 E + 01 3.372027 E + 01 1.368393 E + 01 3.895931 E + 00
1.929045 E + 02 8.062657 E + 01 5.201204 E + 01 4.963145 E + 01
14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.555765 E + 00 1.677401 E + 00 1.696154 E + 00 2.059036 E + 00
7.125924 E 01 5.857953 E 01 2.822890 E 01 2.973424 E 01
1.534610 E + 01 7.325831 E + 00 6.736773 E + 00 5.441206 E + 00
18 (4f'') 19 (5s) 20 (5p'') 21 (6s)
5.088462 E + 00 5.185206 E + 00 6.639659 E + 00 2.041409 E + 01
2.342792 E 02 8.374598 E 03 4.949733 E 03 5.612436 E 05
1.110918 E + 00 3.285374 E 01 2.153353 E 01 1.946442 E 02
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k 1 (65 Tb) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 1.099388 E 05 2.484157 E 02 3.241524 E 02 3.329320 E 02 5.495105 E 02
k
1.167810 E + 16 1.304731 E + 04 1.352163 E + 04 1.353202 E + 04 5.937848 E + 02
k
7.094619 E + 06 3.694361 E + 03 2.039781 E + 03 1.767355 E + 03 1.250692 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.297977 E 01 1.370587 E 01 1.447873 E 01 1.653759 E 01
5.941056 E + 02 6.155199 E + 02 6.155250 E + 02 1.412059 E + 02
5.079517 E + 02 3.420359 E + 02 3.194925 E + 02 2.832223 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.357027 E 01 4.844117 E 01 5.166100 E 01 5.212751 E 01
3.563983 E + 01 3.593202 E + 01 1.451773 E + 01 4.126144 E + 00
2.015240 E + 02 8.494418 E + 01 5.492782 E + 01 5.232165 E + 01
14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.528655 E + 00 1.646698 E + 00 1.695881 E + 00 2.015188 E + 00
7.552868 E 01 6.216232 E 01 3.008211 E 01 3.177642 E 01
1.628864 E + 01 7.862463 E + 00 7.114606 E + 00 5.792547 E + 00
18 (4f'') 19 (5s) 20 (5p'') 21 (6s)
5.087643 E + 00 5.128200 E + 00 6.575961 E + 00 2.031322 E + 01
2.557768 E 02 8.634514 E 03 5.094160 E 03 5.696462 E 05
1.149220 E + 00 3.282643 E 01 2.184604 E 01 1.963136 E 02
k 1 (66 Dy) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 1.045269 E 05 2.440289 E 02 3.179110 E 02 3.276889 E 02 5.398232 E 02
k
1.379658 E + 16 1.368419 E + 04 1.418455 E + 04 1.419557 E + 04 6.263047 E + 02
k
7.576753 E + 06 3.821960 E + 03 2.113703 E + 03 1.829316 E + 03 1.294514 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.270311 E 01 1.358371 E 01 1.422305 E 01 1.625253 E 01
6.266431 E + 02 6.494872 E + 02 6.494924 E + 02 1.491312 E + 02
5.290553 E + 02 3.541427 E + 02 3.303080 E + 02 2.943813 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.309114 E 01 4.740864 E 01 5.066629 E 01 5.116604 E 01
3.791227 E + 01 3.822303 E + 01 1.537886 E + 01 4.363147 E + 00
2.102216 E + 02 8.932320 E + 01 5.788990 E + 01 5.505145 E + 01
14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.502929 E + 00 1.617668 E + 00 1.686402 E + 00 1.974224 E + 00
7.986697 E 01 6.580243 E 01 3.196398 E 01 3.387848 E 01
1.722567 E + 01 8.385086 E + 00 7.508497 E + 00 6.148345 E + 00
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18 (4f'') 19 (5s) 20 (5p'') 21 (6s)
5.059205 E + 00 5.074819 E + 00 6.517351 E + 00 2.021750 E + 01
2.803033 E 02 8.885350 E 03 5.232098 E 03 5.777754 E 05
1.178608 E + 00 3.118441 E 01 2.048830 E 01 1.315337 E 02
k 1 (67 Ho) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 9.945252 E 06 2.397961 E 02 3.119218 E 02 3.226082 E 02 5.305342 E 02
k
1.626068 E + 16 1.434149 E + 04 1.486882 E + 04 1.488048 E + 04 6.599750 E + 02
k
8.084010 E + 06 3.951747 E + 03 2.188906 E + 03 1.892339 E + 03 1.339029 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.243882 E 01 1.346577 E 01 1.397634 E 01 1.597724 E 01
6.603314 E + 02 6.846629 E + 02 6.846682 E + 02 1.573397 E + 02
5.505829 E + 02 3.664274 E + 02 3.413134 E + 02 3.058120 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.263474 E 01 4.642232 E 01 4.971177 E 01 5.024187 E 01
4.027217 E + 01 4.060211 E + 01 1.627070 E + 01 4.608181 E + 00
2.191267 E + 02 9.384923 E + 01 6.097224 E + 01 5.789403 E + 01
14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.478214 E + 00 1.589832 E + 00 1.680044 E + 00 1.935203 E + 00
8.433617 E 01 6.955431 E 01 3.390715 E 01 3.603710 E 01
1.823287 E + 01 8.969195 E + 00 7.941848 E + 00 6.547806 E + 00
18 (5s) 19 (4f'') 20 (5p'') 21 (6s)
5.023137 E + 00 5.040132 E + 00 6.460761 E + 00 2.012445 E + 01
3.043672 E 02 2.666954 E 02 5.370063 E 03 5.858267 E 05
1.254156 E + 00 3.325995 E 01 2.233961 E 01 1.994078 E 02
k 1 (68 Er) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 9.469073 E 06 2.357091 E 02 3.061683 E 02 3.176825 E 02 5.216126 E 02
k
1.912044 E + 16 1.501953 E + 04 1.557477 E + 04 1.558710 E + 04 6.948161 E + 02
k
8.617273 E + 06 4.083653 E + 03 2.265324 E + 03 1.956354 E + 03 1.384176 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.218603 E 01 1.335162 E 01 1.373813 E 01 1.571122 E 01
6.951912 E + 02 7.210684 E + 02 7.210739 E + 02 1.658366 E + 02
5.724670 E + 02 3.788218 E + 02 3.524393 E + 02 3.174441 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.219906 E 01 4.547890 E 01 4.879482 E 01 4.935263 E 01
4.272134 E + 01 4.307108 E + 01 1.719384 E + 01 4.861411 E + 00
2.281714 E + 02 9.845260 E + 01 6.410479 E + 01 6.077933 E + 01
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14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.454434 E + 00 1.563097 E + 00 1.676339 E + 00 1.897953 E + 00
8.894001 E 01 7.342118 E 01 3.591345 E 01 3.825247 E 01
1.924028 E + 01 9.544839 E + 00 8.344504 E + 00 6.920616 E + 00
18 (5s) 19 (4f'') 20 (5p'') 21 (6s)
4.973004 E + 00 5.029016 E + 00 6.405994 E + 00 2.003387 E + 01
3.278073 E 02 3.272135 E 02 5.508257 E 03 5.938094 E 05
1.310607 E + 00 3.202432 E 01 2.122952 E 01 1.541445 E 02
k 1 (69 Tm) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 9.022326 E 06 2.317622 E 02 3.006476 E 02 3.129052 E 02 5.131126 E 02
k
2.242874 E + 16 1.571857 E + 04 1.630266 E + 04 1.631569 E + 04 7.308296 E + 02
k
9.176975 E + 06 4.217696 E + 03 2.342943 E + 03 2.021375 E + 03 1.429839 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.194452 E 01 1.324514 E 01 1.350809 E 01 1.545411 E 01
7.312236 E + 02 7.587025 E + 02 7.587081 E + 02 1.746181 E + 02
5.947097 E + 02 3.912844 E + 02 3.636650 E + 02 3.293243 E + 02
10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.178790 E 01 4.457756 E 01 4.791497 E 01 4.849797 E 01
4.525532 E + 01 4.562524 E + 01 1.814636 E + 01 5.122005 E + 00
2.373568 E + 02 1.031677 E + 02 6.733126 E + 01 6.375168 E + 01
14 (4s) 15 (4p'') 16 (4f') 17 (4d'')
1.431713 E + 00 1.537626 E + 00 1.667520 E + 00 1.862801 E + 00
9.362794 E 01 7.735846 E 01 3.795567 E 01 4.053003 E 01
2.029026 E + 01 1.015463 E + 01 8.798674 E + 00 7.337621 E + 00
18 (5s) 19 (4f'') 20 (5p'') 21 (6s)
4.925525 E + 00 5.002560 E + 00 6.354907 E + 00 1.994718 E + 01
3.538065 E 02 3.138504 E 02 5.641505 E 03 6.015851 E 05
1.391601 E + 00 3.364342 E 01 2.255136 E 01 2.023324 E 02
k 1 (70 Yb) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 8.533454 E 06 2.279488 E 02 2.953483 E 02 3.082698 E 02 5.050267 E 02
k
2.689273 E + 16 1.643892 E + 04 1.705282 E + 04 1.706656 E + 04 7.680314 E + 02
k
9.843350 E + 06 4.356263 E + 03 2.424143 E + 03 2.089788 E + 03 1.478365 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s)
1.171367 E 01 1.314809 E 01 1.328583 E 01 1.520552 E 01
7.684410 E + 02 7.975768 E + 02 7.975825 E + 02 1.836854 E + 02
6.196960 E + 02 4.061612 E + 02 3.773473 E + 02 3.438525 E + 02
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10 (4d') 11 (3d'') 12 (3p'') 13 (3s)
2.140080 E 01 4.371600 E 01 4.707041 E 01 4.767629 E 01
4.787355 E + 01 4.826391 E + 01 1.912814 E + 01 5.390067 E + 00
2.490679 E + 02 1.103905 E + 02 7.305095 E + 01 6.921061 E + 01
14 (4s) 15 (4p'') 16 (4d'') 17 (4f')
1.410030 E + 00 1.513395 E + 00 1.652496 E + 00 1.829705 E + 00
9.841722 E 01 8.138557 E 01 4.005970 E 01 4.046665 E 01
2.378244 E + 01 1.319903 E + 01 1.171609 E + 01 1.020663 E + 01
18 (5s) 19 (5p'') 20 (6s) 21 (4f'')
4.880889 E + 00 4.957488 E + 00 6.308344 E + 00 1.986459 E + 01
1.430803 E 02 1.020179 E 02 6.132236 E 03 4.263839 E 04
3.435089 E + 00 1.892657 E + 00 1.467032 E + 00 1.425577 E 01
k 1 (71 Lu) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 8.266763 E 06 2.241482 E 02 2.895126 E 02 3.037472 E 02 4.909457 E 02
k
3.000290 E + 16 1.718498 E + 04 1.783064 E + 04 1.784522 E + 04 8.077731 E + 02
k
1.030606 E + 07 4.493213 E + 03 2.505109 E + 03 2.156018 E + 03 1.536383 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s) 10 (4d')
1.145729 E 01 1.230806 E 01 1.306431 E 01 1.495764 E 01 2.060470 E 01
8.082229 E + 02 8.393586 E + 02 8.393656 E + 02 1.937087 E + 02 5.103228 E + 01
6.427891 E + 02 4.323445 E + 02 3.989907 E + 02 3.527581 E + 02 2.592397 E + 02
11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
4.275920 E 01 4.614035 E 01 4.677554 E 01 9.189539 E 01 1.362795 E + 00
5.146966 E + 01 2.033393 E + 01 5.748237 E + 00 1.082878 E + 00 1.082977 E + 00
1.129170 E + 02 7.322243 E + 01 6.907144 E + 01 3.719560 E + 01 1.636277 E + 01
16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.374502 E + 00 1.471199 E + 00 1.761641 E + 00 4.088386 E + 00
1.133767 E + 00 9.498991 E 01 5.000522 E 01 6.267649 E 02
1.166921 E + 01 1.081014 E + 01 8.408322 E + 00 1.930121 E + 00
20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
4.645356 E + 00 5.905303 E + 00 1.341504 E + 01 1.902817 E + 01
1.188695 E 02 7.123908 E 03 1.682207 E 04 6.930276 E 05
5.542266 E 01 3.295314 E 01 6.708647 E 02 4.500897 E 03
k 1 (72 Hf) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 7.942153 E 06 2.204711 E 02 2.838944 E 02 2.993548 E 02 4.777245 E 02
k
3.431067 E + 16 1.795337 E + 04 1.863188 E + 04 1.864735 E + 04 8.488828 E + 02
k
1.087839 E + 07 4.634963 E + 03 2.590096 E + 03 2.225943 E + 03 1.597709 E + 03
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6 (3d') 7 (5p') 8 (2p'') 9 (2s) 10 (4d')
1.121167 E 01 1.166256 E 01 1.285000 E 01 1.471763 E 01 1.987707 E 01
8.493792 E + 02 8.825983 E + 02 8.826065 E + 02 2.041024 E + 02 5.433133 E + 01
6.689327 E + 02 4.589846 E + 02 4.212568 E + 02 3.644445 E + 02 2.720719 E + 02
11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
4.184252 E 01 4.524498 E 01 4.590678 E 01 7.958842 E 01 1.182512 E + 00
5.481852 E + 01 2.159127 E + 01 6.122393 E + 00 1.187123 E + 00 1.187427 E + 00
1.181039 E + 02 7.603467 E + 01 7.156347 E + 01 4.406821 E + 01 2.099441 E + 01
16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.340888 E + 00 1.431579 E + 00 1.699431 E + 00 3.547535 E + 00
1.265168 E + 00 1.067123 E + 00 5.788844 E 01 9.169640 E 02
1.329924 E + 01 1.101342 E + 01 8.611454 E + 00 2.453383 E + 00
20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
4.454872 E + 00 5.595599 E + 00 1.161845 E + 01 1.856056 E + 01
1.395547 E 02 8.554943 E 03 3.792083 E 04 7.467376 E 05
7.626280 E 01 4.153868 E 01 9.719603 E 02 7.325306 E 03
k 1 (73 Ta) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 7.631713 E 06 2.169085 E 02 2.784660 E 02 2.950866 E 02 4.651300 E 02
k
3.920741 E + 16 1.874457 E + 04 1.945706 E + 04 1.947345 E + 04 8.914216 E + 02
k
1.147814 E + 07 4.779089 E + 03 2.676727 E + 03 2.297139 E + 03 1.660270 E + 03
6 (3d') 7 (5p') 8 (2p'') 9 (2s) 10 (4d')
1.097535 E 01 1.111061 E 01 1.264236 E 01 1.448492 E 01 1.919797 E 01
8.919505 E + 02 9.273707 E + 02 9.273802 E + 02 2.148920 E + 02 5.778574 E + 01
6.957360 E + 02 4.852762 E + 02 4.430852 E + 02 3.764243 E + 02 2.852119 E + 02
11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
4.096055 E 01 4.437983 E 01 4.506598 E 01 7.279785 E 01 1.052722 E + 00
5.832648 E + 01 2.280348 E + 01 6.515035 E + 00 1.298346 E + 00 1.298943 E + 00
1.234953 E + 02 7.900383 E + 01 7.420106 E + 01 4.903137 E + 01 2.527371 E + 01
16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.308684 E + 00 1.393838 E + 00 1.641369 E + 00 3.158166 E + 00
1.409128 E + 00 1.196100 E + 00 6.671165 E 01 1.263770 E 01
1.484975 E + 01 1.131803 E + 01 8.915607 E + 00 3.000450 E + 00
20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
4.287157 E + 00 5.330777 E + 00 1.062715 E + 01 1.819478 E + 01
1.619138 E 02 1.013193 E 02 6.761963 E 04 7.926851 E 05
9.792991 E 01 5.038921 E 01 1.234208 E 01 9.712115 E 03
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k 1 (74 W) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 7.335294 E 06 2.134557 E 02 2.732218 E 02 2.909372 E 02 4.531461 E 02
k
4.476005 E + 16 1.955890 E + 04 2.030652 E + 04 2.032387 E + 04 9.354103 E + 02
k
1.210557 E + 07 4.925515 E + 03 2.764911 E + 03 2.369521 E + 03 1.723925 E + 03
6 (5p') 7 (3d') 8 (2p'') 9 (2s) 10 (4d')
1.062835 E 01 1.074799 E 01 1.244111 E 01 1.425921 E 01 1.856389 E 01
9.359824 E + 02 9.359932 E + 02 9.737090 E + 02 2.260828 E + 02 6.139738 E + 01
7.309494 E + 02 5.113910 E + 02 4.618265 E + 02 3.886275 E + 02 2.985765 E + 02
11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
4.011205 E 01 4.354405 E 01 4.425243 E 01 6.785347 E 01 9.535360 E 01
6.199545 E + 01 2.427965 E + 01 6.926302 E + 00 1.416575 E + 00 1.417558 E + 00
1.290182 E + 02 8.205992 E + 01 7.691620 E + 01 5.342073 E + 01 2.945134 E + 01
16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.277873 E + 00 1.357926 E + 00 1.587157 E + 00 2.860608 E + 00
1.565828 E + 00 1.337016 E + 00 7.649445 E 01 1.668816 E 01
1.633277 E + 01 1.168801 E + 01 9.286319 E + 00 3.565638 E + 00
20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
4.137164 E + 00 5.099395 E + 00 9.905362 E + 00 1.789615 E + 01
1.861103 E 02 1.186834 E 02 1.066182 E 03 8.330332 E 05
1.197595 E + 00 5.905312 E 01 1.466285 E 01 1.066271 E 02
k 1 (75 Re) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 7.052590 E 06 2.101090 E 02 2.681617 E 02 2.869023 E 02 4.417950 E 02
k
5.104189 E + 16 2.039662 E + 04 2.118055 E + 04 2.119890 E + 04 9.808544 E + 02
k
1.276098 E + 07 5.074261 E + 03 2.854636 E + 03 2.443103 E + 03 1.788532 E + 03
6 (5p') 7 (3d') 8 (2p'') 9 (2s) 10 (4d')
1.020708 E 01 1.052952 E 01 1.224605 E 01 1.404029 E 01 1.797421 E 01
9.814717 E + 02 9.814839 E + 02 1.021596 E + 03 2.376730 E + 02 6.516340 E + 01
7.738094 E + 02 5.373127 E + 02 4.779253 E + 02 4.011031 E + 02 3.121685 E + 02
11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
3.929669 E 01 4.273761 E 01 4.346616 E 01 6.321120 E 01 8.751885 E 01
6.582227 E + 01 2.570976 E + 01 7.355407 E + 00 1.541238 E + 00 1.542757 E + 00
1.347099 E + 02 8.524797 E + 01 7.975271 E + 01 5.819505 E + 01 3.383441 E + 01
16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.248527 E + 00 1.323911 E + 00 1.536742 E + 00 2.625565 E + 00
1.734519 E + 00 1.489190 E + 00 8.718813 E 01 2.130049 E 01
1.778149 E + 01 1.212521 E + 01 9.722206 E + 00 4.151119 E + 00
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20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
4.003368 E + 00 4.897269 E + 00 9.227675 E + 00 1.766722 E + 01
2.124345 E 02 1.380188 E 02 1.606236 E 03 8.658389 E 05
1.415530 E + 00 6.732158 E 01 1.719958 E 01 1.225940 E 02
k 1 (76 W) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 6.782561 E 06 2.068583 E 02 2.632472 E 02 2.829760 E 02 4.307877 E 02
k
5.814921 E + 16 2.125837 E + 04 2.207983 E + 04 2.209924 E + 04 1.027866 E + 03
k
1.344595 E + 07 5.225432 E + 03 2.946108 E + 03 2.517994 E + 03 1.854817 E + 03
6 (5p') 7 (3d') 8 (2p'') 9 (2s) 10 (4d')
9.799526 E 02 1.031804 E 01 1.205659 E 01 1.382751 E 01 1.740920 E 01
1.028532 E + 03 1.028545 E + 03 1.071175 E + 03 2.497110 E + 02 6.911444 E + 01
8.191251 E + 02 5.643502 E + 02 4.943785 E + 02 4.138285 E + 02 3.261744 E + 02
11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
3.850746 E 01 4.195437 E 01 4.270153 E 01 6.193245 E 01 8.085513 E 01
6.983957 E + 01 2.720979 E + 01 7.808158 E + 00 1.676031 E + 00 1.677970 E + 00
1.405995 E + 02 8.855556 E + 01 8.269640 E + 01 6.040299 E + 01 3.733654 E + 01
16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.219978 E + 00 1.290925 E + 00 1.488435 E + 00 2.425654 E + 00
1.921159 E + 00 1.658201 E + 00 9.923529 E 01 2.672200 E 01
1.927409 E + 01 1.264124 E + 01 1.024084 E + 01 4.810809 E + 00
20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
3.872806 E + 00 4.701730 E + 00 9.041002 E + 00 1.736408 E + 01
2.403135 E 02 1.581149 E 02 2.030086 E 03 9.119816 E 05
1.678574 E + 00 7.911883 E 01 1.919439 E 01 1.255294 E 02
k 1 (77 Ir) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 6.524992 E 06 2.037057 E 02 2.585066 E 02 2.791552 E 02 4.203832 E 02
k
6.617015 E + 16 2.214417 E + 04 2.300436 E + 04 2.302485 E + 04 1.076373 E + 03
k
1.416063 E + 07 5.378885 E + 03 3.039060 E + 03 2.594036 E + 03 1.921907 E + 03
6 (5p') 7 (3d') 8 (2p'') 9 (2s) 10 (4d')
9.440459 E 02 1.011485 E 01 1.187284 E 01 1.362102 E 01 1.688400 E 01
1.077089 E + 03 1.077105 E + 03 1.122356 E + 03 2.621587 E + 02 7.322356 E + 01
8.638821 E + 02 5.912136 E + 02 5.111503 E + 02 4.268041 E + 02 3.403589 E + 02
11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
3.774915 E 01 4.119886 E 01 4.196280 E 01 5.983490 E 01 7.535920 E 01
7.401849 E + 01 2.876770 E + 01 8.279000 E + 00 1.817282 E + 00 1.819790 E + 00
1.466288 E + 02 9.197084 E + 01 8.573813 E + 01 6.355893 E + 01 4.117309 E + 01
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16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.192849 E + 00 1.259747 E + 00 1.443532 E + 00 2.260776 E + 00
2.120161 E + 00 1.838851 E + 00 1.122330 E + 00 3.274016 E 01
2.075273 E + 01 1.320819 E + 01 1.080825 E + 01 5.489014 E + 00
20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
3.755672 E + 00 4.529453 E + 00 8.734797 E + 00 1.712980 E + 01
2.703104 E 02 1.801785 E 02 2.603355 E 03 9.499142 E 05
1.938918 E + 00 9.033696 E 01 2.149277 E 01 1.326012 E 02
k 1 (78 Pt) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 6.279256 E 06 2.006461 E 02 2.539271 E 02 2.754356 E 02 4.104965 E 02
k
7.521102 E + 16 2.305439 E + 04 2.395454 E + 04 2.397616 E + 04 1.126414 E + 03
k
1.490592 E + 07 5.534636 E + 03 3.133523 E + 03 2.671247 E + 03 1.989927 E + 03
6 (5p') 7 (3d') 8 (2p'') 9 (2s) 10 (4d')
9.115679 E 02 9.919285 E 02 1.169451 E 01 1.342048 E 01 1.639215 E 01
1.127184 E + 03 1.127201 E + 03 1.175181 E + 03 2.750300 E + 02 7.749827 E + 01
9.087151 E + 02 6.181979 E + 02 5.282418 E + 02 4.400267 E + 02 3.547585 E + 02
11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
3.701928 E 01 4.046900 E 01 4.124811 E 01 5.775879 E 01 7.069320 E 01
7.836692 E + 01 3.038651 E + 01 8.769163 E + 00 1.965711 E + 00 1.968898 E + 00
1.528042 E + 02 9.549197 E + 01 8.887572 E + 01 6.694126 E + 01 4.511803 E + 01
16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.166953 E + 00 1.230120 E + 00 1.401480 E + 00 2.120796 E + 00
2.332757 E + 00 2.032301 E + 00 1.262751 E + 00 3.940994 E 01
2.224029 E + 01 1.382535 E + 01 1.142476 E + 01 6.196621 E + 00
20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
3.648215 E + 00 4.373626 E + 00 8.431724 E + 00 1.692784 E + 01
3.024032 E 02 2.040700 E 02 3.285504 E 03 9.843213 E 05
2.205280 E + 00 1.017173 E + 00 2.390923 E 01 1.402244 E 02
k 1 (79 Au) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 6.044821 E 06 1.976755 E 02 2.495013 E 02 2.718132 E 02 4.010913 E 02
k
8.538629 E + 16 2.398938 E + 04 2.493072 E + 04 2.495351 E + 04 1.178013 E + 03
k
1.568253 E + 07 5.692682 E + 03 3.229489 E + 03 2.749620 E + 03 2.058871 E + 03
6 (5p') 7 (3d') 8 (2p'') 9 (2s) 10 (4d')
8.819474 E 02 9.730951 E 02 1.152137 E 01 1.322567 E 01 1.593048 E 01
1.178838 E + 03 1.178857 E + 03 1.229677 E + 03 2.883314 E + 02 8.194135 E + 01
9.537326 E + 02 6.453641 E + 02 5.456497 E + 02 4.534934 E + 02 3.693735 E + 02
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11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
3.631640 E 01 3.976366 E 01 4.055643 E 01 5.576508 E 01 6.666796 E 01
8.288773 E + 01 3.206721 E + 01 9.278955 E + 00 2.121442 E + 00 2.125426 E + 00
1.591232 E + 02 9.911578 E + 01 9.210602 E + 01 7.048931 E + 01 4.916488 E + 01
16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.142212 E + 00 1.201935 E + 00 1.362009 E + 00 2.000039 E + 00
2.559251 E + 00 2.238845 E + 00 1.413880 E + 00 4.674971 E 01
2.374419 E + 01 1.448861 E + 01 1.208641 E + 01 6.934115 E + 00
20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
3.548987 E + 00 4.231509 E + 00 8.140679 E + 00 1.675164 E + 01
3.367208 E 02 2.299068 E 02 4.085500 E 03 1.015709 E 04
2.477770 E + 00 1.132656 E + 00 2.642118 E 01 1.480553 E 02
k 1 (80 Hg) 2 (2p') 3 (3p') 4 (1s) 5 (4p')
k
R 5.821331 E 06 1.947908 E 02 2.452258 E 02 2.682846 E 02 3.921587 E 02
k
9.681318 E + 16 2.494941 E + 04 2.593320 E + 04 2.595720 E + 04 1.231179 E + 03
k
1.649075 E + 07 5.852996 E + 03 3.326914 E + 03 2.829128 E + 03 2.128635 E + 03
6 (5p') 7 (3d') 8 (2p'') 9 (2s) 10 (4d')
8.550357 E 02 9.549643 E 02 1.135324 E 01 1.303637 E 01 1.549764 E 01
1.232061 E + 03 1.232082 E + 03 1.285853 E + 03 3.020634 E + 02 8.655148 E + 01
9.986890 E + 02 6.726233 E + 02 5.633633 E + 02 4.671986 E + 02 3.841763 E + 02
11 (3d'') 12 (3p'') 13 (3s) 14 (5d') 15 (4f')
3.563975 E 01 3.908226 E 01 3.988730 E 01 5.364145 E 01 6.316740 E 01
8.757939 E + 01 3.380894 E + 01 9.807862 E + 00 2.284060 E + 00 2.289033 E + 00
1.655741 E + 02 1.028348 E + 02 9.542193 E + 01 7.446016 E + 01 5.345713 E + 01
16 (4s) 17 (4p'') 18 (4d'') 19 (4f'')
1.118616 E + 00 1.175167 E + 00 1.325003 E + 00 1.895022 E + 00
2.799053 E + 00 2.457940 E + 00 1.575308 E + 00 5.473941 E 01
2.525985 E + 01 1.518807 E + 01 1.278284 E + 01 7.692339 E + 00
20 (5s) 21 (5p'') 22 (5d'') 23 (6s)
3.457738 E + 00 4.102389 E + 00 7.830668 E + 00 1.660763 E + 01
3.737423 E 02 2.582468 E 02 5.077650 E 03 1.042362 E 04
2.748177 E + 00 1.242705 E + 00 2.904978 E 01 1.570841 E 02
From the presented results one can drew following
conclusions. In accordance with well-known ionization
potential – atomic number relationship, quasi-classical
atomic radius Rq reveals a quasi-periodic dependence
upon the parameter Z with maxima at hydrogen H and
typical metals (including all alkali elements) Li, Na, Al,
K, Ga, Rb, Ag, In, Cs, Tl corresponding to the atomic
ionization potentials’ minima.
Schematic-plots of the obtained )(r
and )( r
functions in the step-like form are shown in Figures 1
and 2, respectively. Electric-charge-density reveals sharp
and positive main maximum in the vicinity of center,
which corresponds to the nucleus vibrations’ region,
broad negative minimum, which corresponds to the elec-
tron-density main maximum located at relatively short
distance from the center, and a few extremes at relatively
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
Copyright © 2010 SciRes. JEMAA
240
r
(r)
Figure 1. Schematic-plot of the electric-charge-density step-
like radial distribution in atoms
r

(r)
Figure 2. Schematic-plot of the electron-potential-energy
step-like radial distribution in atoms
long distance, which are characteristic for the shell-
structure of atoms. As for the electron-potential-energy-
function, anywhere it is negative and monotonously rises.
Thus, it posses only minimum at the center (an additional
minimum may be revealed in effective-potential-func-
tion). Of course, behind the atomic radius both )( r
and )(r
functions in the step-like presentation are
identically zero.
5. Accuracy of Binding-Energy and
Electronic-Structure Calculations Based on
Radial Step-Like Atomic Potentials
It is not out of place to consider accuracy of the binding
energy and electronic-structure calculations carried out
within the semiclassical approximation, i.e. on the basis
of above introduced radial step-like atomic potentials. It
is most convenient to estimate the method accuracy for
Thomas-Fermi (TF) statistical semiclassical atomic mod-
el starting from the only analytical solution
F
r
r 4
2
8
81
)(
(17)
of the TF equation. Here
F
is the Fermi-energy for
intra-atomic electron gas, i.e. higher occupied electron
level. Corresponding electron charge density is expressed
by the function
6
8
243
)(
r
r
 (18)
As electron charge equals to 1 its potential energy
in atom  4
/1)()( rrrU
when 0r.
Then, inner turning point radius 0
r for any electron
bound in TF “atom”. As for the outer turning point radius
r
of the electron with energy
F
E, it can be found
as only real positive root of the equation )( rUE eff
,
where 2
2/)1()()( rllrUrUeff  is the effective po-
tential energy of the electron with orbital quantum num-
ber l, i.e.
24
2
2
)1(
8
81
r
ll
r
FE

(19)
Because differences between semiclassical electron
energies are negligible if compared with their depth, one
can suppose that approximately all of them coincide with
Fermi-energy,
F
E
. In that case, the product )1(
ll
also should be substituted for its standard semiclassical
expression 2
)2/1( l. As a result, we get
12
9
 l
r
(20)
Consequently, averaged partial charge density of a
l-electron-subshell equals to
4
3
3972
)12(
3/4
1
)(



l
r
r
l (21)
and 0, respectively, inside and outside the
r
 -sphere.
As is known, when summation over the principal and
orbital quantum numbers n and l characterizing elec-
tron motion in central-symmetric electric field is substi-
tuted for semiclassical integration the combinations
2/1
n
and 2/1
l
serve as integration vari-
ables. As 1
nl the limit of integration over
should be taken equal to
 2/11n. As for the de-
generacy factor, it equals to
4)12(2 l. Note that
partial electron charge density takes on a nonzero value
43 243/2

if
2/9
rr . Consequently,
Intra-Atomic Electric Field Radial Potentials in Step-Like Presentation
Copyright © 2010 SciRes. JEMAA
241
r2/9
. But, maxmax
and, then, the ratio
r2/9
should serve as the limit of integration over
too.
Now we can found total electron charge density by
means of semiclassical integration:
 
r
calSemiclassi r
ddr
2
9
00
6
2
4
3
80
729
243
2
4)(

(22)
It yields semiclassical atomic potential in following
form
F
r
r
calSemiclassi 4
3/122
80
)90(81
)(

(23)
Variable parts of the obtained semiclassical expres-
sions reveal same radial dependences (6
/1~ r and
6
/1~ r, respectively, for electron charge density and
potential) as corresponding exact analytical solutions, but
differ from them by the multipliers 10/3
and
3/2
)10/3(
. Therefore, semiclassically determined struc-
tural and energy parameters are expected to be dis-
tinguished from their exact values by the multipliers
of order of magnitude 1~02.1)3/10(~ 3/1
and
1~96.0)10/3(~ 3/2
, respectively. Thus the estimated
errors of the semiclassical approach make up a few per-
cent. This conclusion is actually proved by the above
cited calculations performed for some one-, two-, and
three-dimensional real polyatomic structures.
6. Conclusions
Obtained results, numerically reflected in presented ta-
bles, vividly show that an effective method of parame-
terization of the intra-atomic electric field can by based
on semiclassical approach. Such possibility follows from
the Maslov criterion, according to which the exact and
semiclassical atomic electron-energy spectra should be
similar to each other irrespective of the atomic poten-
tials’ smoothness properties. Within the semiclassical
approximation, intra-atomic eclectic charge density and
electric field potential distributions can be presented by
the step-like radial functions, where nucleus and elec-
tron-states classical turning point radii play role of the
steps’ limits, while charge density and potential inside a
step are substituted for their volume averaged values.
Superposition of the semiclassical atomic step-like radial
potentials can serve as an initial approximation for the
substance inner potential. Binding energy and electronic
structure calculations based on such potential allow de-
termining of the substance structural and energy parame-
ters with relative accuracy making up a few percent,
what is quite sufficient for materials science purposes.
7. Acknowledgment
Authors are very grateful to the Georgia National Sci-
ence Foundation (GNSF) for the financial assistance
(Grant #GNSF/ST08/4-411).
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