radiative properties of the WVI ion

12 avril 2013 TUNGSTEN - W VI

Hardet Aimlain NGOMA Atomic spectroscopy
aimlain@hotmail.fr
Radiative properties of the
W5+ ion
Comparison of the values gotten by the use of the code of COWAN and those
of the picture of the MCDHF-EOL calculations and RCI of ab initio for W VI.
Drawn of the presented article by:
S Enzonga Yoca, P Palmeri, P Quinet, G Jumet and E´ Biémont


Département de Physique, Faculté des Sciences, Université Marien Ngouabi, BP 69 Brazzaville,
Congo.
Astrophysique et Spectroscopie, Université de Mons—UMONS, B-7000 Mons, Belgium.
IPNAS, Université de Liège, B-4000 Liège, Belgium.
Chimie Quantique et Photophysique, Université Libre de Bruxelles, B-1000 Brussels, Belgium.
E-mail: enzosat@yahoo.fr
①Adjustment of the average Energies and spin-orbits parameters
The radiative properties of the W5+ ion is used in the survey of two theoretical
independent approaches, i.e. the method Hartree-Fock with relativistic corrections
executed by the Cowan code and the multiconfigurationnel method of Dirac-Hartree-Fock
(MCDF) executed in the GRASP2K set. The interrelationships (interactions) valence heart is
studied in detail while comparing the models of the potential of core-polarization more a
correction of the operator of the dipole considered (HFR + CPOL) in a case and on the
configurations core-excited are included explicitly in the valance interaction configuration
of the expansion of the atomic state function (Migdalek[5] showed that the interaction
corresponds to the interaction of configuration). In general, a good agreement is found
between these two theoretical methods. Remarkably, the core-polarization effects
lengthen the life spans of 15% until 35% and even by a factor of 2 for the levels 5f. The
lifetimes of these two 5f levels are instituted to be a dependent and in particular sensitive
model, excluding the core-penetration effects, clearly requiring for it of the precise
measures.
Hardet Aimlain NGOMA |tungstène W VI 1
12 avril 2013 TUNGSTEN - W VI

 Calculations
Tungsten is a heavy element of the periodic picture with z=74. The level fundamental of
the W VI is 5 with electron of valence revolving around an erbium-like of the ionic
core of its 68 electrons. Therefore, it is important to consider the effects at a time
relativistic and of interrelationship to describe this atomic structure correctly. As no
measurements are available in the literature, two independent theoretical methods that
take in consideration the two the effects have been used in this survey to calculate and to
basis the radiative parameters. These are described briefly in the following subdivisions.

 Method Hartree-Fock with the relativistic corrections
In the Hartree-Fock method with the relativistic corrections (HFR) of Cowan (1981), a whole of
orbital is gotten for every electronic configuration while solving the Hartree-Fock equations
spherically for an averaged atom. The equations result from the variational principle application to
the configuration average energy. The relativistic corrections are included in this set of equations,
i.e. the Blume-Watson spin-orbits , mass-velocity and of a part calls Darwin terms. The Blume-
Watson spin-orbit term consists of the part of the Breit interaction can be reduced to an uniform
operator [25, 26]. The multiconfiguration Hamiltonian matrix is constructed and diagonalized in the
LSJM representation in the structure of the theory of Slater-Condo. Every element of the matrix is j ∏
a sum of products of Racah angular coefficients and radial integrals (of Slaters and the spin-orbit
integrals),i.e.:
, ,
< │H │ J > = ∑ . ∏ ∏
,The radial parameters , can be adjusted to adapt the levels of available experimental energies in
,an approach of least squares; are the angular coefficients. The values and the states gotten in
this approach (ab initio or semi-empiric) are used to calculate the length of wave and the probability
of transition for every possible transition. This technique has been modified (to see for example,
Quinet and al (1999)) to include the disruptions of the core-polarization effects and is known as HFR
method + CPOL.
 HFR method and programs of computer of Cowan
Briefly, the organization of the continuation of programs used for the setting in work of the
HFR method is the following [1]:
RCN: value the radial wave-functions and the parameters of Slater.
RCNPOLB: is a RCN program including the polarization of the heart.
RCN2: calculate the integrals of configuration interaction, the electric and magnetic
multipolar integrals (E1, E2, M1 and M2).
RCN2POLB: is a RCN2 program including the polarization of the heart.
RCG: calculate the energy angular coefficients matrixes, constructs and diagonalize the
matrixes of energy while giving the vectors and clean values, calculate the oscillator
strengths and the transition probabilities.
RCE: conduct the adjustment of the clean values calculated to the experimental levels of
energy.
Hardet Aimlain NGOMA |tungstène W VI 2

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 Modeling of the core-polarization effects
Calculations retailed of atomic structures, for the atoms (or ions) heavy, must take in account the
relativistic effects and the interaction of configuration; this last induced the interrelationships of
valence-valence type and core-valence. To treat these effects, Migdaleks and Baylises [5] proposed
an approach in which biggest part of the valence-valence interrelationship is represented inside the
diagram of configuration interaction, while the interrelationship core-valence is represented
roughly by a model of type "core-polarization”. For an atom (or ion) with n electrons of valence, the
single electronic operator of this potential can write:
∑ , (1)
( )

Where:
is the dipolar polarizability of the heart and is the ray of cut. One generally takes for the
average value of calculated in the HFR approach for the orbital of the heart most external.
Besides, the interaction between the modified electric fields undergone by the valence electrons
leads to one term bielectronic:
.
= − ∑ , (2) ⁄ 〔( )( ) 〕
A supplementary correction, taking into account the core-penetration of the valence electrons, has
been proposed by Hameed and al [3, 4]; it is translated, in the setting of the present formalism, by
the addition of the term of core-penetration, to know,:
( ) ∫ ( ) (3)
To the integral ( ) (4) ∫ ⁄( )
In (2)
The inclusion of the core-polarization in the hamiltonian imposes, for the consistency in the
reasoning, of the modifications to the operator of the dipolar moment in the element of transition
matrix [39]. The radial dipolar integral
( ) ( ) (5) ∫
Must be to replace by:
( ) ( ) ( ) 〔 − 〕 ( ) − (6) ∫ ∫
These modifications, programmed in the code of Cowan [1] by Quinet and al [2], lead to the HFR+PC
approach.
 Procedure of adjustment by least squares
The HFR approach / (HFR+PC) can be used either of manner ab initio is in a semi-empiric manner
(combined with an adjustment by least squares of the calculated clean Hamiltonian values to the
Hardet Aimlain NGOMA |tungstène W VI 3

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