Adv. Studies Theor. Phys., Vol. 5, 2011, no. 1, 31 - 43
De-Excitation Auger Cascade Following InnerShell Ionization in Ne, Mg Atoms and Fe14+ Ions
Y. A. Lotfy*, Adel M. Mohammedein-ElShemi, Adel A. Ghoneim
Applied Sciences Department, College of Technological Studies
P.O. Box 42325, Shuwaikh 70654, Kuwait
[email protected], [email protected]
*El-Minia University, Faculty of Science, Physics Department
61111 El-Minia, Egypt
Abstract
An inner-shell ionized atom relaxes via parallel radiative (x-ray) and nonradiative (Auger) transitions. The de-excitation decay of inner-shell vacancies gives
rise to Auger spectra and yields highly charged ions. The successive radiative and
Auger transitions lead to stable holes in the outer-shells of atoms. The radiative and
non-radiative transition probabilities obtained using Dirac-Fock-Slater
wavefunctions. The multiply charged ions yield after de-excitation decay of a hole in
K and L1-subshell of Ne , Mg atoms and Fe14+ ion are calculated using Monte Carlo
(MC) Simulation technique. The charged ions yield after K vacancy creation mainly
turns into Ne2+ and Ne3+ ions. Doubly charged ions Ne+2 are predominate, whereas
in L1 hole situation the singly charged Ne1+ ions are manly. At K hole states in Mg
atoms, the yield of Mg3+ ions are predominate. The highest intensities are Fe16+ions
in the K and L1 shell ionization. The average charged ions result after K and L1
vacancy production are calculated for Ne, Mg atoms and Fe14+ ions. The present
results of charge state distributions of ions agree well with the experimental and
theoretical data.
Keywords: Ionization processes, Auger cascades, Multiply charged ions
1. Introduction
Photoelectron emission lead to formation of core holes in atoms. These Core
holes are eliminated by relaxation that is accompanied by: (1) X-ray fluorescence (Xray fluorescence spectroscopy) (2) Auger electron emission (Auger electron
32
Y. A. Lotfy, A. M. Mohammedein-ElShemi, A. A. Ghoneim
spectroscopy). Atomic reorganization starts by filling the initially inner-shell
vacancy by a radiative transition (x-ray) or by a non-radiative transition (Auger and
Coster- Kronig processes). New vacancies created during this atomic reorganization
may in turn be filled by further radiative and non-radiative transitions until all
vacancies reach the outermost occupied shells (energetically stable final states or
metastable ones because of relevant selection rules). In the case of x-ray processes
the vacancy moves to an outer shell under emission of characteristic x-rays, while for
non-radiative transitions one electron from an outer shell fills up the inner-shell
vacancy and another electron is ejected into continuum. With exception of the K and
L shells in heavy atoms, the Auger processes are much more probable than x-rays.
The production of inner-shell vacancy in an atom and the de-excitation decays
through radiative and non-radiative transitions due to a change of the atomic
potential, this change leads to an additional electrons can be emitted to a continuum
(electron shake off processes). In each Auger processes an electron ejects into
continuum, a series of such events called vacancy cascade, gives rise to a highly
charged ions.
The charge state distributions of ions result from de-excitation decay on innershell vacancies were studied both experimentally and theoretically. The multiply
charged ions following vacancy cascades in rare gas atoms were measured at some
restricted energies of photos that could be obtained from the x-ray tubes, and the
produced ions were analyzed with a magnetic spectrometer [1-5]. The charge state
distribution of ions as a function of photon energies were measured by sweeping the
photon energy across the ionization threshold [6-12]. The initial inner-shell vacancy
produced by synchrotron radiation and the yield ions are analyzed by using the timeof flight mass spectrometer.
There are tow major approaches to calculate the vacancy cascades and
multiply charged ions following inner-shell vacancy production in atoms. The first
method is based on straightforward construction of the de-excitation decay trees for
radiative and non-radiative transitions [13-16]. The second method is based on
simulation of all possible radiative and non-radiative pathways to fill the inner- shell
vacancies in atoms [17-21].
Inner-shell ionization processes were analyzed under different points of view.
Thereby, basic investigations of atomic properties as well as investigation in
connection with other disciplines as solid state physics, plasmaphysics and
astrophysics were of interest. Here the atomic reorganization cascades following
inner-shell vacancy production and the creation of multiply ionized atoms connected
with it. The importance of this process is based on the fact, which because of atomic
reorganization cascades ionized atoms with different ion charge states are produced,
e.g. as result of a primary inner-shell vacancy ions with different charge states can be
created.
In the present work, the charge state distribution of ions and the average ion
charge, which produced from de-excitation decay of vacancies after K shell
ionization in atoms, is calculated using Monte Carlo (MC) simulation technique. The
Monte Carlo (MC) algorithms are applied to simulate all possible pathways of
radiative and non-radiative transitions to fill the K- shell vacancy in these atoms. The
radiative transitions of single ionized atoms are calculated using
De-excitation Auger cascade following inner-shell ionization
33
mulitconfiguration Dirac Fock (MCDF) wave functions from Grant et al. [22]. The
non-radiative transitions for single are calculated by using Dirac Fock Slater by
computer code written by Lorenz and Hartmann [23]. The electron shake off
processes which due to from the change of atomic potential after inner shell vacancy
production and non-radiative transitions are calculated with an code given by ElShemi [24]. The results of final charge state distributions and average number of
electrons are compared with available theoretical and experimental data.
2. Method of Calculation
The description of the de-excitation vacancy cascades resulting from inner –
shell ionization in an atoms and ground state ions is given in detail elsewhere
Abdullah et al. [21]. Therefore, only a brief description of it is given in this section.
The calculation technique is used for simulating de-excitation cascades
decays following inner-shell vacancy creation, considering fluorescence yields (
radiative branching ratios), Auger and Coster- Kronig yields ( non- radiative
branching ratios), and electron shake off processes. The radiative branching ratio is
defined as the probability that the vacancy in an atom is filled through a x-ray
transitions (photon emission), that is therefore given by
A (i → f )
ω ( f → i) = r
(1)
Γ
and Auger yield (non-radiative branching ratios), is the probability that the vacancy
filled through Auger or Coster-Kronig transitions,
A (i → f )
a( f → i) = a
(2)
Γ
where Γ is the sum of the total radiative width Γ R and non-radiative width Γ A .The
relationship between fluorescence yield ω and Auger yield a must hold
ω + a =1
(3)
The calculation of radiative transition rates were performed for single ionized atoms
using Multiconfiguration Dirac Fock (MCDF) wave functions [22]. The nonradiative transition rates were computed with a code written by Lorenz and
Hertmann [23] using Dirac Fock Slater (DFS) wave functions.
The electron shake of process, that due to from a sudden change of atomic
potential during vacancy cascade development, which can lead to the ejection of
additional electrons through monopole processes, that are calculated using own code
[24]. In this way we calculate the electron shake off probabilities according Åberg
[25] by overlapping integrals between the wave functions of initial state ϕ i and the
final state ϕ f of the considered process. The probability of an electron transition
from the orbital nlj to the orbital n′l ′j ′ is given by
p nlj →n′l ′j′ =
∫ϕ
∗
nlj
( A0 )ϕ n′l′j′ ( A)dτ
2
(4)
34
Y. A. Lotfy, A. M. Mohammedein-ElShemi, A. A. Ghoneim
with ϕ nlj ( A) and ϕ n′l′j′ ( A0 ) being orbital wave functions for the orbital nlj and for the
orbital n′l ′j ′ in the ion A0. Thereby the ion originates from the atom A during a
change in the potential in the course of the ionization processes. The probability that
at least one of N electrons located in the sub-shell nlj becomes ionized is given by
2
∗
p = 1- ( ∫ ϕ nlj
( A0 )ϕ n′l′j′ ( A)dτ )N – pf
(5)
where the quantity pf represented a correction for physically not allowed transitions
to occupied shells and has the form
2
N′
∗
pf = ∑ N
ϕ
(
A
)
ϕ
(
A
)
d
τ
(6)
′
n
lj
nlj
0
2 j +1 ∫
n′lj
with n′ ≠ n and N ′ as number of the electrons in the orbital n′lj .
The calculation technique is based on the simulating of the de-excitation
vacancy cascade originating from a configuration with a single vacancy. Each
cascade starts with the implementation of atomic data for all possible x-ray , Auger,
Coster Kronig, and shake off channels. To realize a Monte Carlo selection of the
actual de-excitation channel, the probabilities of all de-excitation channels were
normalized to one.
Let N denote the number of vacancies created in nl subshells of an atomic
configurations via radiative or non-radiative transitions. For example , The
configuration 1s 2s2 2p6 3s2 3p6 would represent a distribution with a single K-shell
vacancy (N=1);1s2 2s2 [2p5] 3s2 [3p5] would represent a distribution that could be
formed via an Coster-Kronig transition. Electron symbol in the square brackets will
be used to indicate spectator holes. After creating a new spectator vacancy in an
actual configuration, the program at first controls whether shake-off takes place or
not. If the random number generated is smaller than the sum of all normalized shake
off probabilities of the preceding vacancy configuration, then a shake-off process
tacks place, i.e. an additional electron ejected in an higher subshell. The channel
whose subshell shake –off probability value coincides with the random number
generated will be activated. After the decision about the occurrence of shake –off
processes the program selects the following de-excitation trees by generating a new
random number. Here at first a comparison of the value of random number and the
fluorescence yield proves whether radiative or non-radiative take place. The actual
de-excitation channel after this decision is chosen in analogy with the determination
of the shake-off channels. Each new configuration is analyzed to see if further decay
are possible, If they are, then the program code goes back to the first step described
above. The generation of new vacancy configurations continues until all vacancies
have reached the outer shells or no further decays are possible. If no further decays
are possible for any of the final configurations we have a complex de-excitation tree
ending up with a great number of configurations each of which is characterized by its
probability depending on its de-excitation history. The charge state degree of ions
( Z f ) in outer shells are recorded. After finishing the de-excitation tree the same
inner shell vacancy will be simulated again. The probabilities of charged ions state
De-excitation Auger cascade following inner-shell ionization
distributions p ( Z f ) and the average charged ions
Zf
35
are recorded after 105
histories.
105
p(Z f ) =
∑Z
i
f
1
n
here the subscript i is denoted to the equal produced ionization degree for
Z f and n the histories ( =105 ) in our calculation.
The mean charge state of ions is given by
Z f = ∑ p( Z if ) Z if
(7)
(8)
The change of radiative (x-ray photon ) and non- radiative (Auger and Coater
– Kronig ) transition rates is considered in the present work. This change aris from
the photons and electrons emission in course of atomic rearrangement following
inner – shell vacancy,. The calculation of transition rates for intermediate
configuration with spectator vacancies during the cascade propagation is based on
the radiative and non-radiative transition rates for single ionized atom Jacobs et al.
[26]. The radiative transition rates (x- ray transition) are given by
a r ( n1l1N1 , n 2l 2 N 2 → n1l1N1 −1 , n 2l 2 N 2 +1 ) = N1
( 4l2 + 2 − N 2 )
A r ( n1l1 → n 2l 2 )
( 4l 2 + 2)
(9)
and the non-radiative transition rates are
N
N
a a (n1l1 1 , n3 l3 3 , n 4 l 4
N1
N4
→ n1l1
N1 −1
, n3 l 3
N 3 +1
, n4 l 4
N 4 +1
)=
(4l 3 + 2 − N 3 ) (4l 4 + 2 − N 4 )
Aa (n1l1 → n3l 3 , n 4 l 4 )
(4l 3 + 2)
(4l 4 + 2)
N
a a (n1l1 1 , n3l3
N3
→ n1l1
N1 −1
, n3 l 3
N3 + 2
(10)
)=
(11)
N1 (4l3 + 2 − N 3 ) (4l3 + 1 − N 3 )
2
Aa (n1l1 → n3l3 )
2
(4l3 + 2)
(4l3 + 1)
where Ar and Aa are the radiative and non-radiative transition rates for single ionized
atom, respectively. ar and aa are the transition rates for atom with various spectator
inner shell vacancies. n1l1 is initial state and n3l3 ,n4l4 are a final state in equation (10)
(e.g. K-LM transition ), but in equation (11) the n3l3 is the final state such as
( K → MM transition).Ni is the number of vacancies in the nili sub-shell.
Because most Coster–Kronig energies are so low and the rates are so
sensitive to the transition energy, so some Coster–Kronig channels may be
energetically forbidden during the cascade de-excitation decays. The production of
various vacancies in intermediate configurations during the cascade decay due to a
closing of Coster - Kronig channels. This effect well be considered in our treatment
by using a semi empirical approaches so-called “ Z+1 rule”, which specifies that the
effect of the nl vacancy on the binding energy of the n'l ' electron can be
36
Y. A. Lotfy, A. M. Mohammedein-ElShemi, A. A. Ghoneim
approximated by taking the n'l ' binding energy in the neutral atom of next –higher
atomic number Then the kinetic energy E∞l A of the continuum electron emitted in a
radiationless transition is given by
E∞l A = En ''l '' − 1 [ Enl ( Z ) + Enl ( Z + 1) + En 'l ' ( Z ) + En 'l ' ( Z + 1)]
2
(12)
Where En ''l '' , and Enl ( Z ) are the absolute value of neutral atom binding energies,
while Enl ( Z + 1) and En 'l ' ( Z + 1) are the binding energies of the next higher atomic
number. However, Auger and Coster – Kronig transitions are energetically
impossible if
En ''l '' p 1 [ Enl ( Z ) + Enl ( Z + 1) + En 'l ' ( Z ) + Enl ( Z + 1)]
2
(13)
If Coster–Kronig transitions are energetically possible, they tend to provide the
dominant channel for inner shell vacancy decay in an atom or ion.
3. Results and discussion
The branching ratios (%) to individual channels for all possible transitions state
configurations resulting after K-shell vacancy creation in neutral Ne and Mg atoms
are listed in Tables 1. The fluoresce yields of 4.34% and 2.16% belong to the x-ray
K-L23 transitions for Ne and Mg, respectively. The radiative channels (x-ray
transitions) are generally much weaker than the non-radiative channels (Auger
transitions) for K-shell vacancy decay in neon and magnesium. Therefore, the
probability of formation ion charge through x-ray transitions in Ne and Mg are low.
For Auger channels in Ne, the dominant transitions are correspond to K-L1L1, KL1L23, and K-L23L23 with Auger yields 19.62%, 28.05% and 48.14% respectively.
From the Auger yields of the previous transitions for Ne atom, it is obvious, that the
K-L23L23 is the strongest one and the second one is K-L1L23 transition. Therefore, the
probability of filling the K- shell vacancy through these Auger channels is extremely
high. The decay of inner shell vacancy in neon through Auger transitions leads to
double ion charge. The treble charged ions are due to from Auger channels and
shake-off processes. The branching ratio for K- L1L1, -L1L23 and – L23L23 transitions
in Mg atom are 14.2%, 36.90% and 35.21% respectively. The branching ratio for KLM transitions are approximately 11.5%. The filling of inner shell hole in Mg
through Auger transitions K-LL leads to highly charged ions Mgn+ (n ≥ 2 ). The total
Auger yield after K-shell vacancy production for Ne and Mg are approximately 96%
and 98%, respectively.
37
De-excitation Auger cascade following inner-shell ionization
Final states
(Ne)
Branching
ratio (%)
Final states
(Mg)
L23
L1L1
L1L23
L 23L23
4.34
19.62
28.05
48.14
Total radiative yield
4,34
95.81
L23
L1L1
L1L23
L1M1
L 23L23
L23M1
M1M1
Total radiative yield
Total Auger yield
Total Auger yield
Branchin
g ratio
(%)
2.16
14.2
36.90
10.24
35.21
1.23
0.05
2.16
97.84
Table1: Branching ratios (%) for the decays of Ne and Mg after K- shell electron
ionization.
Fig. 1a shows the results of Nei+ ions following de-excitation decay after Kshell vacancy in Ne atom. The results obtained by performing the calculation with
considering the electron shake off processes. The results for charge state distributions
with consideration electron shake off probability demonstrates the importance of this
process in the calculation of vacancy cascades in atoms. The calculation of charge
state distributions with consideration of shake off process agree well with
experimental value. The de-excitation of a primary K -shell vacancy in neon occurs
with high probability by 1s2- 2s22p4 Auger transitions because of the small K
fluorescence yield (ω (Ne) = 0.04) and Auger yield is (a =0.96). As a result of this
KLL Auger transitions the contribution of Ne2+ ions is 79 %. New vacancies created
by this process could not further de-excite by non-radiative electron transitions. The
triple Ne3+ ions are produced by contribution of Auger and shake off processes. From
this situation, the production of vacancies in the outermost subshells occurs from
shake off processes, if non-radiative de-excitation transitions are impossible. The
contribution of Ne3+ ions in the charge state distribution (CSD) are approximately
17%. The highest final charge state from K shell hole is found to be Ne2+ ions. The
average charged ions <Zf> = 2.11.
The charge state distributions (CSD) following vacancy production in L1
subshell are presented in Figure 1b. The contribution of Auger process after L1 hole
creation is not possible. Therefore the Ne1+ (L1) is strongest, because no de-excitation
decays following L1 vacancy production in Ne atoms. The consideration of shake
process is due to formation of Ne2+ ions. The result of double ionization Ne2+ is
small. The mean charged ions <Zf> = 1.88. As shown from the Fig., the results agree
well with the experiment data.
38
Y. A. Lotfy, A. M. Mohammedein-ElShemi, A. A. Ghoneim
1
Present work
Kochur [14 ]
Omar and Hahn[15]
Exp [2]
a
0.8
Probability
Ne (K+1),
<Z>=2.11
0.6
0.4
0.2
0
0
1
2
3
Ion charge
4
5
1
Present work
Exp [2]
b
0.8
Probability
Ne(L1-1) , <Zf>=1.1
0.6
0.4
0.2
0
0
1
2
3
Ion charge
4
5
Fig. 1. The charge state distributions (CSD) with consideration of shake off
process in Ne atom after vacancy creation in K and L1 shells production
The charge state distributions following K- and L1- subshell vacancies deexcitation in Mg and another available theoretical values [15,20] are compared in
figure 2a,b. The Mg(K1+) ionization mainly produces Mg2+, Mg3+ and Mg4+ ions, the
doubly Mg2+ and triply Mg3+ charged ions appeared strongly in the distribution. The
spectrum of the number of ejected electrons after K- shell vacancy de-excitation
forms an asymmetric peak. The probabilities of charge states are decreasing at lower
and higher end of the distributions, and the maximum probable charge states appear
in the middle distribution as shown in Fig.2a. The mean charge state of ions <Zf> =
39
De-excitation Auger cascade following inner-shell ionization
2.9. The final charge state distributions following L1 hole production in Mg are
shown in Fig.2b. The doubly Mg2+ ions appeared strongly in the charge state
distributions (CSD). The formation of Mg3+ results from the contribution of L-LM
and L-MM Auger channels and shakes process. The average charge state of ions <Z>
after L1 hole creation is equal to 2.2.
1
Present work
Omar and Hahn [15]
Opendak[ 20 ]
a
0.8
Probability
Mg(K-1), <Zf>=2.9
0.6
0.4
0.2
0
0
1
2
3
4
Ion charge
5
6
7
1
Present work
Omar and Hahn [15]
Opendak[20]
b
0.8
Probability
Mg(L1-1), <Zf>=2.2
0.6
0.4
0.2
0
0
1
2
3
4
Ion charge
5
6
7
Fig.2: The charge state distributions (CSD) with consideration of shake off
process in Mg atom after vacancy creation in K and L1 shells production
Fig.3a,b shows the probability of final charge state distributions for Fe14+ ions
after de-excitation of K and L1 vacancy. The calculated results are compared with
40
Y. A. Lotfy, A. M. Mohammedein-ElShemi, A. A. Ghoneim
other calculations. The ionization in the K shell induces the multiply charged ions
from Fe15+ to Fe16+ ions. The probabilities of charge states are decreasing at lower
and higher end of the distributions, and the maximum probable charge states appear
in the middle distribution as shown in Fig.3a. The Fe16+ ions appeared strongly in the
charge state distributions (CSD) after K and L1 shell vacancies as appear in Fig. 3a,b.
The mean charge state of ions <Zf> = 2.11 for K ionization and <Zf >= 1.88 for L1
ionization, respectively.
1
Present work
Omar and Hahn[15]
Opendak [20]
a
0.8
Probability
Fe14+(K-1), <Zf>=2.11
0.6
0.4
0.2
0
13
14
15
16
17
Ion charge
1
18
19
Present work
Omar and Hahn [15]
Opendak [20]
b
0.8
Probability
Fe14+(L1-1), <Zf>=1.88
0.6
0.4
0.2
0
13
14
15
16
17
Ion charge
18
19
Fig. 3. The charge state distributions (CSD) with consideration of shake off process
in Fe14+ ion after vacancy creation in K and L1 shells production
De-excitation Auger cascade following inner-shell ionization
41
4. CONCLUSIONS
The ion charge state distribution (CSD) of single ionized Ne1+, Mg1+ atoms
and Fe
ion are computed using Monte Carlo (MC) simulation technique. All
allowed radiative, non-radiative branching ratios and electron shake off probabilities
are taken into account in the calculation of relative abundances of charged ions.
Multiconfiguration Dirac Fock Slater (MDFS) wave functions are applied to
calculate radiative (x-ray) transitions. The Auger transition rates and electron shakeoff probabilities are obtained using Dirac-Fock-Slater wavefunctions. At K hole
states in Ne and Mg atoms, the yield of Ne2+ and Mg3+ ions are predominate,
respectively. The highest intensities are Fe16+ions in the K and L1 shell ionization.
The present results of charge state distributions of ions agree well with the
experimental and theoretical data.
14+
References
[1] Carlson, T. A., Krause, M.O., 1965. Atomic readjustment to vacancies in the K
and L shells of argon. Phys. Rev. 137, A1655-1662.
[2] Carlson, T. A., Hunt, W. E., Krause, M. O., 1966. Relative abundances of ion
formed as the result of inner-shell vacancies in atoms. Phys. Rev. A151,41-47.
[3] Krause, M. O., Carlson, T. A., 1967. Vacancy Cascade in the Reorganization of
Krypton Ionized in an Inner Shell. Phys. Rev. 158, 18-24.
[4] Krause, M. O., Vestal, M. L., Johnston, W. H., Carlson, T. A., 1964.
Readjustment of the neon atom ionized in the K shell by X-ray. Phys. Rev. Lett.
65, 988-991.
[5] Krause, M. O., 1971, Rearrangement of inner shell ionized atoms. J. De physique,
C4-67.
[6] Church, D. A., Kravis, S. D., Sellin, I. A., Levin, J. C., Short, R. T., Meron M.,
Johnson, B. M., Jones, K. W., 1987. Confined thermal multicharged ions
Produced by synchrotron radiation. Phys. Rev. A, 36, 2487-2490.
[7] Cooper, J. W., Southworth, S. H., MacDonald, M. A., LeBrun, T., 1994. Cascade
effects on the Ar LMM Auger spectrum. Phys. Rev. A 50, 405-412.
[8] Jauhiainen, J., Kivimaki, A., Aksela, S., Sairanen, O-P, Aksela, H., 1995. Auger
and Coster-Kronig decay of the 3p hole states in Krypton. J. Phys. B: At. Mol.
Opt. Phys. 28, 4091-4100.
42
Y. A. Lotfy, A. M. Mohammedein-ElShemi, A. A. Ghoneim
[9] Kravis, S.D., Church, D. A., Johnson, B. M., Sellin, I. A., Azuma,Y., Mansour,
N. B., Berry, H. G., 1991. Inner-Shell Photoionization of Stored Positive Ions
Using Synchrotron Radiation. Phys. Rev. Lett. 66, 2956- 2959.
[11] Tamenori, Y., Okada, K., Tanimoto, S., Ibuki, T., Nagaoka, S., Fujii, A., Haga,
Y., Suzuki, I. H., 2004. Branching ratios of multiply charged ions formed through
photoionization of Kr 3d, 3p and 3s sub-shells using a coincidence technique. J.
Phys. B: At. Mol. Opt. Phys. 37, 117-129.
[12] von Busch, F., Doppelfeld, J., Gunther, C. and Hartmann, E., 1994. Argon L23MM Auger satellite spectrum emitted after K ionization. J. Phys. B: At. Mol.
Opt. Phys. 27, 2151-2160.
[13] Kochur, A. G. Dudenko, A. I., Sukhorukov, V. L., Petrov, I. D., 1994. Direct
Hartree-Fock calculation of multiple Xei+ ion production through inner-shell
vacancy de-excitations. J. Phys. B: At. Mol. Opt. 27, 1709-1721.
[14] Kochur, A. G., Dudenko, A. I., Sukhorukov, V. L, Petrov, I. D., 1995. Direct
Hartree-Fock calculation of the cascade decay production of multiply charged
ions following inner-shell ionization of Ne, Ar, Kr, and Xe. J. Phys. B: At. Mol.
Opt. 28, 387- 402.
[15] Omar, G., Hahn, Y., 1991a. Cascade decay of hollow ions. Phys. Rev. A 43,
4695- 4701
[16] Omar, G., Hahn, Y., 1991b. Photo-Auger - ionization and charge-state
distribution. Phys. Rev. A 44, 483-488.
[17] Mirakhmedove, M. N., Parilis, E. S. 1988. Auger and x-ray cascades following
inner- shell ionization. J. Phys. B: At. Mol. Opt. Phys.21, 795-804.
[18] Mukoyama, T., 1985. Vacnacy cascade following inner-shell ionization. Bull.
Inst. Chem. Res. Kyoto Univ. 63, 373-382.
[19] El-Shemi, A. M., Lotfy, Y. A., 2005. Ion charge state distributions following Kshell ionization in atoms. European Physical J. D 31, 1-7.
[20] Opendak, M. G., 1990 Auger Cascades in atoms and ions of astrophysically
important elements, Astrophys. Space Sci. 165, 9-25.
[21] A. H. Abdullah, A. M. El-Shemi, A. A. Ghoneim, 2003. Yields of multiply
charged ions produced from inner-shell ionization in neutral Ne, Ar and Kr atoms,
Radia. Phys. and Chem. 697-705.
De-excitation Auger cascade following inner-shell ionization
43
[22] Grant, I. P., Mckenzie, B. J., Norrington, P., Mayers, D. F., Pyper, N. C., 1980,
An atomic multiconfigurational Dirac-Fock package. Comput. Phys. Commun.
21, 207-231.
[23] M. Lorenz, E. Hartmann; Report ZFI-109, Leipzig (1985) 27.
[24] A. El- Shemi, "Self ionization probabilities in atoms and ions as result of innershell ionization" Egypt. J. Phys. 27, (1996) 231-240.
[25] T. ˚Aberg, Ann. "Multiple excitation of a many electron system by photon and
electron impact" Acad. Sci. Fenn. A VI Physica, (1967) 303.
[26] V. L. Jacobs, J. Davis, B. F. Rozsnyai, and J. W. Cooper, 1980 Multiple
ionization and x-ray emission accompanying the cascade decay of inner-shell
vacancies in Fe, Phys. Rev. A, 1917-1926.
Received: August, 2010
.
.
.