The atomic structure and the properties
of Ununbium (Z = 112) and Mercury
(Z = 80)
LI JiGuang1 , DONG ChenZhong1,2† , YU YouJun1 , DING XiaoBin1 , S. FRITZSCHE3 , B. FRICKE3
1
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China;
2
National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China;
3
Institut für Physik, Universität Kassel, Kassel 34132, Germany
A super heavy element Uub (Z = 112) has been studied theoretically in conjunction with relativistic effects and the effects of electron correlations. The atomic structure and the oscillator strengths of low-lying levels have been calculated, and the ground states have also been
determined for the singly and doubly charged ions. The influence of relativity and correlation effects to the atomic properties of such a super heavy element has been investigated
in detail. The results have been compared with the properties of an element Hg. Two energy levels at wave numbers 64470 and 94392 are suggested to be of good candidates for
experimental observations.
super heavy element, atomic structure, relativistic effects, electron correlation effects, MCDF method
The study of super heavy elements attracts many scientists’ interest all the time [1] , including atomic,
nuclear and nuclear chemical physicists. Especially, because a number of theoretical papers were
published suggesting the presence of nuclear stability island around the elements with Z = 114
to 126 in the 1960s [2], the investigations have been focused on the synthesis of the super heavy
elements and their physical and chemical properties [3−7] . Since a couple of new elements have
become to be actually produced, their identification has become to be a very important issue. However, the method of identifications by measuring the α-spectra of their known decay products has
some disadvantages [7]. Therefore, the chemical identification is an important alternative. Nevertheless, because of their short half-life (seconds or less) and very low production rates (one at a time)
for super heavy elements, experiments are difficult without a precise theoretical support [8,9]. In
addition, the relativistic effects are so important that the atomic structure of super heavy elements
becomes quite different from that of homogenous elements; a simple extrapolation of the trends, as
known from the periodicity of the elements, yields no longer reliable predictions [10,11]. Calculation
Received August 25, 2006; accepted January 5, 2007
doi: 10.1007/s11433-007-0073-3
†
Corresponding author (email: [email protected])
Supported by the National Natural Science Foundation of China (Grant Nos. 10376026 and 10434100), the Foundation of Theoretical Nuclear
Physics of National Laboratory of Heavy Ion Accelerator of Lanzhou, and the China/Ireland Science and Technology Collaboration Research Fund
(No. CI-2004-07)
www.scichina.com www.springerlink.com
Sci China-Phys Mech Astron | Dec. 2007 | vol. 50 | no. 6 | 707-715
of properties and trends based on the relativistic atomic structure and quantum-chemical calculations are highly desirable. So far, accurate calculation of the atomic structure for super heavy
element is really a challenge, because (i) there exists a large number of electrons, which have to be
taken into account individually in any ab-initio theory; (ii) there are strong relativistic and quantum
electrodynamic (QED) effects [12] and (iii) for existing various open d- and f- shells the electron
configurations are often degenerate with other nearby lying configurations. Furthermore, for super
heavy elements, electron correlation effects and relativistic effects are strongly coupled [13], therefore, it is necessary to use a relativistic theory which also incorporate electron correlation effects
on the same footing.
A new element Uub (Z = 112) was produced at GSI, Darmstadt in 1996 [14]. Based on earlier
Dirac-Fock calculations of Desclaux [15], it should appear in group IIB. In order to identify the element Uub and determine its physical and chemical properties, the investigation on the adsorption
properties of the element Uub were performed using gas phase chromatography techniques [16].
Evaluation of the experimental data in term of adsorption enthalpies indicates that in the given
chemical environment the element Uub behaves like Rn rather than Hg. The further study shows
that the reasons may be the strong relativistic effects in the element Uub [17] . To obtain more accurate properties of the element Uub, a straightford spectroscopic study would be desired. Recently,
Sewtz et al.[9,18] successfully measured the low-lying levels of fermium (Z = 100) using two-step
resonance ionization spectroscopy, which has stimulated the study of super heavy elements [19].
However, a sophisticated atomic spectroscopy method, even the most sensitive laser method, is
normally hampered by the fact that a broadband search for levels is limited due to the small number of atoms available for the studies. Therefore, an experimental investigation strongly depends
on the theoretical level predictions. In this couple of years, some studies have been done. Eliav et
al.[20] calculated the ground state of Uub, Uub + and Uub2+ and evalutated its first two ionization
potentials. Pershina et al.[17,21] and Sarpe-Tudoron et al. [22] have studied the chemical bonding
between Uub and Pb, Cu, Ag and Au using density function theory (DFT) method to solve the
question of adsorption of the element Uub on the transition metal surface. However, the study of
the excited state structure of neutral Uub is still scarce.
On the basis of successful prediction of low-lying levels for the element fermium [9] , bohrium[23]
and hassium[24,25], we have already calculated the low-lying level structure, absorption oscillator
strengths and determined the ground state of the first two charged states by taking into account
important relativistic, electron correlation effects and Breit interaction using the MCDF method.
In the present paper, we analyze the influence of relativistic and electron correlation effects on the
atomic structure of the element Uub by comparing with the element Hg.
1
Theoretical method
1.1 MCDF method
In the MCDF method[26,27] the no-pair Dirac-Coulomb Hamiltonian for an atom with N electrons
and nuclear charge Z, in atomic unit, is
H DC =
N
i=1
708
Hi +
N
−1
i=1
N
1
,
|r i − r j |
j=i+1
LI JiGuang et al. Sci China Ser G-Phys Mech Astron | Dec. 2007 | vol. 50 | no. 6 | 707-715
(1)
and
Hi = cα · Pi + (β − 1)c2 − Vnucl (ri ),
(2)
where c is the velocity of light, α, β are Dirac 4 × 4 matrices, P i is the momentum operator,
Vnucl (ri ) is Coulomb potential of nucleus. Correspondingly the atomic state wave function (ASF)
can be expanded by
nc
|Γ P JM =
cr |γr P JM ,
(3)
r=1
where nc is the number of the configuration state wave function (CSF) with the same parity P , total
angular momentum J and its z component of the atomic system, and c r is configuration mixing
coefficient for each single CSF |γP JM . These CSFs are further expressed by all possible Slater
determinants in each corresponding configuration, which consist of the single electron orbitals,
Pnκ (r)χκμ (θ, φ)
1
,
ψnκμ =
(4)
r
iQnκ (r)χ−κμ (θ, φ)
where Pnκ (r) and Qnκ (r) are the large and small component radial functions, which are obtained by solving a series of radial integro-differential equations in the framework of MCDF. The
χκμ (θ, φ) is a 2-component spinor function.
1.2 Breit interaction
The first important relativistic correction to the two-electron Coulomb interaction is the Breit interaction, which describes the magnetic interaction and the retardation effect between the two
electrons[26] . It can be given by
N cos(ωij rij − 1)
αi αj cos(ωij rij )
HBreit = −
+ (αi · ∇i ) × (αj · ∇j )
(5)
,
2
rij
ωij
rij
i=j
where ωij is the energy of the photons exchanged between the two electrons, and r ij is the interelectronic distance. In actual calculations, the Breit interaction is treated as a perturbation and corrections are made for the total energies and mixing coefficient but not for the orbital functions. The
atomic energies and wave functions are obtained from the atomic structure package GRASP92 [28]
and RELCI[29] .
1.3 Absorption oscillator strength
Once the initial and final state wave functions and energies have been obtained, we can further
calculate the transition probability for the electric dipole transitions from the upper state to the
lower state. According to the time-dependent perturbation theory, the Einstein spontaneous transition probability for the electric dipole transition can be given by
3
4 e2 ωik
|Γi Pi Ji Mi |O(1) |Γk Pk Jk Mk |2 ,
Aik =
(6)
3c3 (2ji + 1)
where O (1) is the electric dipole operator, j i is the total angular momentum of the upper state i,
|Γi Pi Ji Mi and |Γk Pk Jk Mk are the wave functions of the upper atomic state i and the lower
atomic state k, respectively. Then absorption oscillator strengths can be obtained from [30]
ωki
|Γk Pk Jk Mk |O(1) |Γi Pi Ji Mi |2 ,
fki =
(7)
3(2jk + 1)
LI JiGuang et al. Sci China Ser G-Phys Mech Astron | Dec. 2007 | vol. 50 | no. 6 | 707-715
709
where jk is the total angular momentum of the lower state k , ω f i is the energy of photon absorbed by an atom through the transition from the lower state k to the upper state i. In practical
calculations, we use the newest program REOS99 on the basis of GRASP92 package, which can
treat the orbital relaxation in calculation of transition probabilities for any complex atomic systems
conveniently [31].
2
Results and discussions
2.1 The properties of the valence orbitals
The valence orbitals play an important role in the chemical property of the elements [32] . As the influence of the relativistic effects on the properties of the valence orbital increases dramatically with
Z 2 , the physical and chemical properties for heavy and super heavy element would be changed so
that their behavior may not necessarily follow the trends known from lighter homologs in the chemical groups. We will analyze in detail the difference of the properties of valence orbitals between
Uub and Hg caused by the relativistic effects.
Table 1 displays the orbital average radii and the orbital energies of the elements Uub and Hg.
As can be seen from Table 1, due to the stronger relativistic effects for the element Uub compared
to the ones for Hg, 7s 1/2 of Uub is more strongly contracted than 6s 1/2 of Hg, whereas 6d3/2 and
6d5/2 of Uub are more strongly expanded than 5d 3/2 and 5d5/2 of Hg. In addition, the 6d 3/2 −6d5/2
splitting for Uub is larger than the 5d 3/2 − 5d5/2 splitting for Hg. Because of the strong relativistic
7s contraction and the relativistic 6d expansion, the 7s electrons of Uub are more deeply bound
than the 6d5/2 electrons, which results in the marked difference of the atomic structure between
Uub and Hg.
We have also compared the properties of Uub + and Uub2+ with Hg+ and Hg2+ . Table 1 shows
that the expectation values for the outer valence orbital radius become smaller, while their binding energies become deeper with the increase of charge, because the Coulomb energy increases.
Furthermore, the energy reversal between 7s 1/2 and 6d5/2 disappears in Uub + and Uub2+ . In addition, from valence orbiatl energies, we can estimate the dominant configurations of the ground
state Uub+ and Uub2+ to be 6d9 7s2 and 6d9 7s, respectively. We also find that the average orbital
radius of 6d3/2 and 6d5/2 of Uub and its first two charged state are larger than the 5d 3/2 and 5d5/2
of Hg and its first two charged state, while the 7s 1/2 is smaller. Moreover, the d − s separation
energies of Uub and Uub + are smaller than that of Hg and Hg + .
2.2 The ground state
Due to the relativistic stabilization of the 7s 1/2 orbital relative to the 6d5/2 orbital, the ground state
of Uub+ and Uub2+ are different from the ground state of Hg + and Hg2+ . We systematically
calculate the ground state of Uub + and Uub2+ . To obtain enough reliable results, we include all
CSF formed by single, double, triple and quadruple substitutions of valence electrons from the
reference configuration to {(n − 1)d, ns, np} for Uub (n = 7) and Hg (n = 6) respectively,
while [Rn]5f14 for Uub and [Xe]4f 14 for Hg were treated as the core. Breit interactions are estimated in this calculation. The QED effects are not considered because they are small for valence
electrons[33] .
Table 2 presents the dominant configuration of the ground state and its weights for neutral
710
LI JiGuang et al. Sci China Ser G-Phys Mech Astron | Dec. 2007 | vol. 50 | no. 6 | 707-715
and the first two charge states. As can be seen from this table, the ground state of Uub + is the
[Rn]5f 14 6d43/2 6d55/2 7s2 (5/2+ ), but the ground state of Hg + is [Xe]4f 14 5d10 6s(1/2+ ). These
results are consistent with the one inferred from the properties of valence electrons. The switch
is the relativistic effect. For the ground state of Uub 2+ , 6d43/2 6d45/2 7s2 (2+ ), however, is not in
agreement with the results estimated by the properties of valence orbital, which may be caused by
very strong mixing of 6d 43/2 6d45/2 7s2 (2+ ) and 6d43/2 6d55/2 7s(2+ ) configuration. In the earlier calculation of Eliave[20] , the ground state of Uub 2+ is formed by the 6d8 7s2 (4+ ), which is a marked
difference from our results. In order to confirm our results, we further included more CSF and
calculated the ground state of Uub 2+ again. Our new result also stands for above conclusions.
Meanwhile, the properties of valence orbital also support our results. Of course, the results need to
be verified by experiment.
Table 1 The expected values r and the energies of the valence orbital for Uub and Hg in the charges states 0, 1+ and 2+ (unit:
atomic unit)
r
Charge state
0
1+
2+
Orbital
Energy
Hg
Uub
Hg
Uub
d3/2
1.4345
1.6465
0.65387
0.57319
d5/2
1.5027
1.7975
0.57787
0.45101
s1/2
2.7821
2.4785
0.36058
0.48370
d3/2
1.4175
1.5964
0.97806
0.97152
d5/2
1.4786
1.7202
0.90238
0.83967
s1/2
2.5970
2.3373
0.64871
0.82343
d3/2
1.4100
1.5580
1.3170
1.3842
d5/2
1.4654
1.6675
1.2429
s1/2
1.2426
2.2267
1.1952
The dominant configurations and their weights for Uub and Hg in the charge states 0, 1+ and 2+
Table 2
Hg
Charge state
Ground state (J P )
Uub
Mixing coefficient (%)
Ground state (JP )
0
5d10 6s2 (0+ )
94.42
6d10 7s2 (0+ )
94.12
1+
5d10 6s(1/2+ )
98.55
95.38
2+
5d10 (0+ )
6d43/2 6d55/2 7s2 (5/2+ )
98.92
Mixing coefficient (%)
6d43/2 6d45/2 7s2 (2+ )
6d43/2 6d55/2 7s(2+ )
64.70
30
As already mentioned, the calculation of the atomic structure for super heavy element is so difficult that we can take into account only a limited amount of electron correlation in a real calculation.
Due to the difference of electron numbers in different charge states, which result in different electron correlations, the MCDF ionization potentials may not be precise enough under the present
calculational model. Therefore, to obtain the best ionization potentials we employ an extrapolative
method[34], and we will discuss these in another paper [35].
2.3 The low-lying level structure
The theoretical study of the low-lying level structure not only helps our understandings of the
physical and chemical properties, but also makes effective predictions needed for experiment [9,18].
LI JiGuang et al. Sci China Ser G-Phys Mech Astron | Dec. 2007 | vol. 50 | no. 6 | 707-715
711
Therefore, we calculate the low-lying level structure of the element Uub and Hg. The results are
listed in Tables 3 and 4. As can be seen from Table 3, the excited state energies of the element
Hg agree with the experimental values of the NIST database, which shows that our calculational
method is reliable. We find the low-lying level structure is markedly different between Uub and
Hg. Due to the fact that the 7s electrons of Uub are more strongly bound than the 6s electrons
of Hg, the first excited level of Uub is 6d 43/2 6d55/2 7s2 7p1/2 (2− ) in contrast to the excited state
configuration of Hg d 10 sp. In addition, because the orbital energies of the 7s 1/2 and 6d5/2 are
very close, there is a very strong configuration interaction between the 6d 9 7s2 7p and 6d10 7s7p of
Uub, for example, the mixing coefficient of the 4th, 9th and 10th level arrives at 20%–30%, but the
maximum mixing coefficient is only 10% in Hg.
Table 3 The dominant configuration of excited state with its weight and excited state energy for Hg (unit: cm−1 )
Excited state (J P )
No.
Mixing coefficient (%)
Excited energy
Ref.a)
0
5d10 6s2 (0+ )
94.42
0
0
1
5d10 6s6p1/2 (0− )
98.42
38248
37645
5d10 6s6p1/2 (1− )
77.52
38441
39412
2
5d10 6s6p3/2 (1− )
20.92
3
5d10 6s6p3/2 (2− )
93.38
49363
44043
4
5d10 6s6p
(1− )
76.17
57402
54068
5d10 6s6p1/2 (1− )
23.38
5d43/2 5d55/2 6s2 6p1/2 (2− )
80.76
70139
68887
71453
73119
5
3/2
5d43/2 5d55/2 6s2 6p3/2 (2− )
6
7
8
9
10
11
12
13
14
15
5d43/2 5d55/2 6s2 6p1/2 (3− )
5d43/2 5d55/2 6s2 6p3/2 (4− )
5d43/2 5d55/2 6s2 6p3/2 (2− )
5d43/2 5d55/2 6s2 6p1/2 (2− )
5d43/2 5d55/2 6s2 6p3/2 (1− )
5d33/2 5d65/2 6s2 6p1/2 (1− )
5d10 6s6p3/2 (1− )
4
5d3/2 5d55/2 6s2 6p3/2 (3− )
5d33/2 5d65/2 6s2 6p1/2 (2− )
5d33/2 5d65/2 6s2 6p3/2 (0− )
5d33/2 5d65/2 6s2 6p3/2 (3− )
5d33/2 5d65/2 6s2 6p3/2 (1− )
5d33/2 5d65/2 6s2 6p1/2 (1− )
5d33/2 5d65/2 6s2 6p1/2 (1− )
5d33/2 5d65/2 6s2 6p3/2 (1− )
5d43/2 5d55/2 6s2 6p3/2 (1− )
5d33/2 5d65/2 6s2 6p3/2 (2− )
16
a) NIST database.
10.77
95.40
97.06
76120
76945
80
78675
78676
79357
78813
12.05
61.05
18.32
10
95.02
80101
90.21
84926
95.69
88563
96.51
91722
55.79
92641
88761
93012
94060
39.74
34.92
32.57
16
93.50
94006
In contrast to the calculations of the ionization potentials, the number of electrons remains the
same in the calculation of excited levels, an extra systematic error arising from the difference of
electron numbers is absent in the calculation of excited state energies.
2.4 Resonance oscillator strength
Recently, in atomic spectroscopy, Resonance Ionization Spectroscopy (RIS) has been found to
712
LI JiGuang et al. Sci China Ser G-Phys Mech Astron | Dec. 2007 | vol. 50 | no. 6 | 707-715
be a powerful technique and sensitive enough to be applied to super heavy element [9,18] . However, as perviously mentioned, this experiment is hampered without theoretical level predictions.
Therefore, we further calculate the related oscillator strengths from the excited states satisfying
the selection rules of electric dipole radiation to the ground state of Uub and Hg. Our results are
presented in Table 5.
Table 4 The dominant configuration of excited state with its weight and excited state energy for Uub (unit: cm−1 )
No.
Excited state (J P )
Mixing coefficient (%)
0
6d10 7s2 (0+ )
94.12
0
1
6d43/2 6d55/2 7s2 7p1/2 (2− )
95.47
34150
6d43/2 6d55/2 7s2 7p1/2 (3− )
Excited energy
97.70
37642
3
6d10 7s7p
(0− )
96.64
48471
4
6d10 7s7p1/2 (1− )
69.35
52024
6d33/2 6d65/2 7s2 7p1/2 (1− )
22.24
2
1/2
6d43/2 6d55/2 7s2 7p3/2 (4− )
5
6d43/2 6d55/2 7s2 7p3/2 (2− )
6
6d33/2 6d65/2 7s2 7p1/2 (2− )
6d43/2 6d55/2 7s2 7p3/2 (3− )
6d33/2 6d65/2 7s2 7p1/2 (2− )
6d43/2 6d55/2 7s2 7p3/2 (2− )
6d43/2 6d55/2 7s2 7p3/2 (1− )
6d10 7s7p1/2 (1− )
3
6d3/2 6d65/2 7s2 7p1/2 (1− )
6d10 7s7p3/2 (1− )
6d10 7s7p1/2 (1− )
6d10 7s7p3/2 (2− )
3
6d3/2 6d65/2 7s2 7p3/2 (0− )
6d33/2 6d65/2 7s2 7p3/2 (3− )
6d33/2 6d65/2 7s2 7p3/2 (1− )
6d33/2 6d65/2 7s2 7p3/2 (2− )
6d10 7s7p3/2 (1− )
6d10 7s7p1/2 (1− )
3
6d3/2 6d65/2 7s2 7p1/2 (1− )
7
8
9
10
11
12
13
14
15
16
97.36
60366
62.82
60809
29.84
97.10
64017
68.62
64267
28.04
66.93
64470
28.24
55.26
73686
33.66
9
93.69
76641
92.02
82895
97.46
84871
91.28
85533
96.10
86871
55.41
94392
22.25
14.77
Table 5 Resonance energies, oscillator strengths from the ground state to the excited state satisfying the selection rules of electric dipole transition (unit: atomic unit). No. is the same as that in Tables 3 and 4
Hg
Uub
No.
Excited energy (cm−1 )
Oscillator strength
Ref.a)
No.
Excited energy (cm−1 )
Oscillator strength
2
38441
2.25 × 10−2
2.31 × 10−2
4
52024
5.94 × 10−2
4
57402
1.53
9
79357
14
92641
15
93012
9
64470
1.07 × 10−1
5.68 ×
10−1
10
73686
1.07 × 10−2
1.96 ×
10−1
14
85533
2.38 × 10−3
16
94392
3.58
2.02
a) NIST database.
As can be seen from Table 5, the result of Hg is in good agreement with the experimental results
from NIST, which indicates that the results of Uub could be reliable. In addition, it is found that
LI JiGuang et al. Sci China Ser G-Phys Mech Astron | Dec. 2007 | vol. 50 | no. 6 | 707-715
713
there are two levels, i.e., 6d 43/2 6d55/2 7s2 7p3/2 (1− ) at 64470 cm−1 and 6d10 7s7p3/2 (1− ) at 94392
cm−1 , having large absorption oscillator strengths, which could be observed by experiment.
3
Conclusion
In conclusion, based on the MCDF method, we have calculated the low-lying level structure of
atomic Uub and Hg by taking important relativistic and electron correlation effects into account.
We analyzed the influence of relativistic effects and electron correlation effects on the properties
of the valence orbitals, low-lying level structure and the ground state of ions. We found that,
due to the strong relativistic effects, the energy levels of the 6d 9 7s2 7p and 6d10 7s7p have been
reversed between Uub and Hg; the first excited state of Uub is 6d 43/2 6d55/2 7s2 7p1/2 (2− ), and the
ground state of Uub + is 6d43/2 6d55/2 7s2 (5/2+ ) rather than the 5d10 6s6p1/2 (0− ) of Hg and the
5d10 6s(1/2+ ) of Hg+ , respectively. In addition, very strong configuration interactions cause the
ground state of Uub 2+ to be 6d43/2 6d45/2 7s2 (2+ ), while the ground state of Hg 2+ is 5d10 (0+ ).
Finally, we found that the two levels, at 64470 cm −1 of 6d43/2 6d55/2 7s2 7p3/2 (1− ) and 94392 cm −1
of 6d10 7s7p3/2 (1− ) for Uub, have large absorption oscillator strengths. We hope that the two
levels will be observed by experiment.
We are grateful to Prof. F. Koike for help in preparation of this manuscript.
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