Adv. Studies Theor. Phys., Vol. 4, 2010, no. 2, 55 - 66
Shake Processes after inner Shell Ionization for
Elements with Atomic Number from 7 to 36
Adel M. Mohammedein, Adel A. Ghoneim, Jasem M. Al-Zanki,
Majida S. Altouq and Ashraf H. El-Essawy
Applied Sciences Department, College of Technological Studies
P.O. Box 42325, Shuwaikh 70654, Kuwait
[email protected], [email protected]
Abstract
The probabilities of shake processes (shake up and shake off) after inner shell
vacancy creation are computed for elements with Z=7 to 36. Multiconfiguration
Dirac Fock Slater (MDFS) wave functions are adapted to calculate the shake
processes. It's found that, the Z- dependence of shake probabilities Pnlj(1s; 2p) and
Pnlj(2s; 2p) are very well smooth. The obtained results allow one to easily estimate
the shake probabilities of any element with 1s vacancy from Z=7 to 36 and with
2s vacancy from Z= 12 to 36. Shake probabilities due to 1s and 2s vacancies
decrease generally with increasing the atomic number Z. Deviation in the results
for charge state distributions with and without consideration of the electron shake
off probability demonstrates the importance of this process in the calculation of
vacancy cascades in atoms. Taking the electron shake probabilities into
consideration in the calculation of charge state distributions leads to good
agreement with the experimental data.
Keywords: shake processes, ionization processes, Auger cascades
1. INTRODUCTION
Photoejection of an inner shell electron in an atom results in a sudden
change of atomic potential. This sudden change can excite other electron to an
unoccupied bound state (electron shake up) or eject into the continuum (electron
shake off) via monopole transition [1]. In the monopole transition, all the other
quantum numbers except the principal quantum number are not allowed to
56
Adel M. Mohammedein et al
change. The study of shake processes is important for the general area of
photoionization. For example: x-ray photoelectron need understanding the
probabilities of electron shake up and electron shake off upon the creation of inner
shell vacancy in atom.
The emission of core electron follows by a cascade of successive radiative
(x-ray) transitions and non-radiative (Auger) transitions leading to yield of ions of
various charges. In experimental, the charged ions yield are greater than the
expected results based on consideration of only radiative and non-radiative
transitions without consideration the shake processes.
Therefore, the
consideration of electron shake off processes in the study of vacancy cascades
during consecutive Auger decay play and important role in the formation of ion
charge state distributions [2,3]. The role of shake processes and inter-multiplet
Auger transitions in production of multiply charged ions upon cascade decay of
resonantly excited state of argon atom are performed by Kochur et al. [4].
Electron shake up and shake off well be termed, respectively, SU and SO
processes. There are extensive studies of shake processes (SU and SO) both
theoretically and experimentally.
The de-excitation of an inner shell vacancy in an atom via parallel
radiative and non-radiative cascades leads to the emission of several satellite
spectra. These spectra arise from the presence of various additional spectator
vacancies yield by consecutive Auger decays and by additional monopole
excitation, ionization (shake processes). The shake processes give rise to intense
satellite structures in all the inner shell spectroscopic experiments [5]. The
experimental evidence for the shake processes has been established by observing
satellite peaks or a satellite continuum on the low-energy side of the main peak in
photoelectron and conversion electron spectra. Satellite lines are created in
photoelectron spectra as the results of electron shake up.
The intensities of the main lines in photoelectron spectra are dependent on
the probability for electron shake off [6]. The calculation method of shake
processes is usually performed in the sudden approximation. Carlson et al. [7]
calculated the shake probabilities for various atoms in the case of β- decay. The
shake up and shake off probabilities result of inner shell vacancy production are
evaluated for wide variety of atoms in the sudden approximation [8-10].
Carlson and Nestor [11] have performed calculations for shake processes
of rare gases as a result of inner shell vacancy production. The calculations have
been performed using the relativistic Hartree-Fock-Slater (RHFS) wave functions.
Mukoyama et al. [12] calculated the electron shake off probabilities for Ne, Ar, Kr
and Xe atoms upon K and L ionization. The electron shake up and electron shake
off probabilities during vacancy decay cascades which start after inner shell hole
creation are calculated for Mg, Al, and S atoms by Kochur et al. [13-15]. In
sudden approximation, the electron shake off probabilities upon ionization of
atomic inner shells are calculated for outer-shell L-, M-, and N-electrons in wide
verity of atoms [16]. The electron shake up and electron shake off probabilities
during vacancy decay cascades which start after inner shell hole creation are
calculated for Mg, Al, and S atoms by Kochur et al [17-19].
Shake processes after inner shell ionization
57
In the present work, we have computed the probabilities of shake
processes for elements with Z between 6 and 36 as the result of K, L, and M
vacancy creation. The probabilities of shake off process are made for outer shell
L, M and N electrons after inner shell ionization of atoms. The calculations are
based on the sudden approximation [1]. The Multiconfiguration Dirac Fock Slater
(MDFS) are used for the calculations of shake probabilities. The calculated results
are compared with other theoretical calculations and with experimental data.
2. METHOD OF CALCULATION
Sudden change of atomic potential due to inner shell vacancy creation is
valid, when the photoionization energy is above the ionization threshold. In this
case, the production of inner shell vacancy takes less time than the outer shell
electron needs to readjusts itself in the system with a new Hamiltonian after core
hole creation. The probabilities of shake processes can be easily calculated within
the sudden approximation [SA]. Based on the sudden approximation, the
probability that an electron in the initial state i makes transition to a final state f
with the presence of an inner shell vacancy can be expressed as the overlap
integral:
pif = ∫ Ψ ∗f Ψi dτ
2
(1)
where Ψi is the electron wave function in the initial state and Ψ f is that final
state. The wave function Ψi for initial state corresponds to the ground state of the
neutral atom, while the final state is a positive ion with an inner shell vacancy and
the atomic potential is different from that for ground state. After the creation of an
inner-shell -vacancy, the atomic orbitals of the core relax whereupon a new set of
one-electron states Ψ ∗f describes an ion. The shake processes correspond to the
monopole transitions.
In this monopole transition, all the other quantum numbers except the
principal quantum number are not allowed to change. In the sudden change of
atomic potential following creation of inner shell vacancy the final state is
different from the initial state. An electron may be exist by additional monopole
transition in other orbital. The square overlap integral in Eq. (1) is unity.
Suppose that the nlj is one electron in the outer shell of an atom. In the sudden
approximation, the square of the overlap integral:
58
Adel M. Mohammedein et al
Ψ{∗n ' ,ε }lj Ψnlj
2
(2)
is the probability for the nlj electron excited into any of the discrete state n ' l
(shake up) or into continuum state εl (shake off). Thus, the probability for
another outer shell electron staying in its nlj state after the relaxation of atomic
core is given by:
∗
Ψnlj
Ψnlj
2
(3)
The calculation method of the probability of shake processes is expressed
by Carlson and Nestor [11]. Following they expression the probability that an
atomic electron staying in an orbital with the same quantum numbers in the final
state subtracts from unity. When the probability of staying electron the orbital
subtracted from unity yields the chance an electron will be removed from the
orbital. The probability of removing an electron in orbital nlj to a higher bound
state (shake up) or to continuum state (shake off) is given by
N
2
'*
p nl = 1 − ⎡ ∫ Ψnlj
( A0 )Ψnlj ( A)dr ⎤ −
⎥⎦
⎢⎣
n' = x
N'
N
∑' 2 j + 1 ∫ Ψn∗'lj ( A0 )Ψnlj ( A)dr
n
2
(4)
where Ψnlj ( A) denotes to the electron wave functions for the orbital nlj in the
neutral atom (A) and Ψnlj ( A0 ) represents orbital nlj in the ion (A0). The inner
shell vacancy is created in a given subshell of atom A. N is the number of
electrons in orbital nlj and N’ is the number of electrons in the orbital n’lj. The
second term in Eq. (4) represents the correction for physically not allowed
transitions to occupied levels. The correction for contributions to filled states is
from n’=1 to x.
The probability of shake processes is calculated using MulticonfigurationDirac Fock-Slater (MDFS) wave functions from Grant et al. [20].
The production of inner shell vacancies leads to a cascade of successive radiative
(x-ray) and non-radiative (Auger) transitions. In each Auger process ejecting
electron into the continuum, a series of such events called vacancy cascade. Since
the Auger transitions occur with ejection of electrons. This de-excitation cascades
of inner shell vacancies give rise to a multiple ionized atom. The creation of deep
vacancy and the following consecutive decays through radiative and non-radiative
transitions may result in a sudden change of atomic potential. As above mentioned
the sudden change in atomic potential may cause additional monopole excitation
(shake up) and/or ionization (shake off).
The consideration of the additional monopole excitation and ionization in
the calculation of multiple ionization of atoms leads to good agreement with
Shake processes after inner shell ionization
59
experimental data. We are calculated the formation of multiple ionization
following inner shell vacancy in Ar atom using Monte Carlo algorithms. This
method is applied to simulate all possible pathways of radiative (x-rays) and
nonradiative (Auger) and additional monopole process to fill the 1s shell hole in
argon atom. The calculation technique is based on the simulation of the deexcitation vacancy cascades originating from atomic configuration with single
inner shell vacancy. Each decay cascade starts with the implementation of atomic
data for all possible radiative and nonradiative and shake processes. To realize a
Monte Carlo (MC) selection of the actual de-excitation channel, the probabilities
of all de-excitation channels were normalized to one. Then a random number
generated in the interval [0,1] selected the next de-excitation step including
vacancy transfer and ionization.
3. RESULTS AND DISCUSSIONS
The shake processes accompanying the inner shell vacancy creation are
computed for elements between Z=7 and 36. The calculation of shake processes
are based on the sudden approximation (SA) after core hole production in an
atom. The total probabilities of shake processes, i.e. summation of shake up and
shake off from outer shell upon 1s and 2s ionization in atoms up to Kr are
calculated. The Multiconfiguration Dirac Fock Slater (MDFS) wave functions for
neutral atom and the positive ions are obtained with Grant program [20]. The
probabilities of shake processes from outer shell 2p after 1s and 2s ionization in
atoms with Z =7 to 36 are shown in Figure 1.
60
Adel M. Mohammedein et al
0.2
K---3p
Present work
Mukoyama [8]
Carlson [11]
Shakeprobability
0.15
shake process
0.1
0.05
0
5
10
15
20
25
30
35
40
Z
0.02
L1---3p
present work
Mukoyama [8]
Carlson [11]
Shakeprobability
0.015
0.01
0.005
0
5
10
15
20
25
30
35
40
Z
Fig. 1. Shake probability in 3p shell as the result of 1s and 2s vacancy
creation as function of atomic number Z
It is found that the Z- dependence of shake probabilities Pnlj(1s; 2p) and
Pnlj(2s; 2p) are very well smooth. The results in the figures allow one to easily
estimate the shake probabilities of any element with 1s vacancy from Z=7 to 36
and with 2s vacancy from Z= 12 to 36. The shake probabilities due to 1s and 2s
vacancies decrease generally with increasing the atomic number Z. The 2p
subshell becomes progressively filled beginning with boron (Z=5, ground state
configuration 1s2 2s2 2p) up to neon (Z=10, ground state configuration [He] 2s2
2p6). In fact, neon atom has maximum number of electrons allowed in the n=2 (L)
shell. Since the 2p subshell for neon atom is closed, its ionization potential
reaches the value 21.56, which is larger than any other one except He atom. The
Shake processes after inner shell ionization
61
2p subshell is the outer shell in light elements Z ≤ 10. Therefore, the probabilities
Pnlj(1s;2p) and Pnlj(2s;2p) are large for light elements up to neon. Form the figure,
it is clear that the Pnlj(1s,2p) and Pnlj(2s,2p) are decreasing for elements with
higher atomic number Z ≥ 10 . The results of shake processes from a given orbital
are compared with other calculation values performed by Mukoyama [8] and by
Carlson et al. [11]. Their calculations are made using relativistic Hartree- FockSlater wave functions.
The Z- dependence of the probabilities of shake processes from 3s
subshell upon 1s and 2s ionization are shown in Figure 2. The probabilities are
obtained for elements with Z=11 to 36. With Z=11 (sodium) the eleventh electron
must go into the 3s subshell. The ionization potential of sodium (5.14 eV) is
therefore much smaller than that of neon. Therefore, the shake probabilities in the
valence shell 3s after 1s or 2s vacancy creation in sodium are larger than any other
atoms. The 3s subshell is closed for magnesium and its ground state configuration
being [Ne] 3s2. From Z=13 (aluminum) to Z=18 (argon) the 3p subshell is
progressively filled, the ground state configuration of argon being [Ne] 3s2 3p6. It
is noted that, the 3p subshell is closed for argon and has the maximum number of
electrons allowed in L23.
As shown from the figure, the probability of shake process that one
electron from 3s ejected upon 1s and 2s ionization is decreasing gradually with
increasing the number of electrons in outer shell of atoms. The shake processes in
the valence shell are found to be nearly independent of the location of the initial
inner shell hole, increasing slightly as one goes to the lower principle quantum
number n. For example, the electron shake up and shake off from outer shell up
on 1s ionization are larger than the results up on 2s ionization in atoms.
62
Adel M. Mohammedein et al
0.2
K---3s
present work
Mukoyama [8]
Carlson [11]
Shake probability
0.16
0.12
0.08
0.04
0
10
15
20
25
30
0.2
40
L1----3s
Present work
Mukoyama [8]
Carlson [11]
0.16
Shake probability
35
Z
0.12
0.08
0.04
0
10
15
20
25
30
35
40
Z
Fig. 2. Shake probability in 3s shell as the result of 1s and 2s vacancy
creation as function of atomic number Z
Figure 3 presents the total shake probabilities
∑ P nlj
after 1s and 2s
vacancy production as function of atomic number Z= 7 to 36. The total shake
probabilities are the probabilities that at least one electron will be removed from a
various subshells by means of electron shake up and shake off upon. It is found
that the Z-dependence of shake probabilities ∑ Pnlj (1s; n ' lj ) and
Shake processes after inner shell ionization
∑P
nlj
63
(2 s; n ' lj ) are not a smooth function of Z. The results in Figure 3 allow one
to easily estimate the total shake probabilities
∑P
nlj
of any element with 1s
vacancy from Z=7 to 36 and with 2s from Z= 12 to 36. It is clear that, the shake
processes for Ne, Ar, Fe, and Kr atoms after inner shell ionization are smaller than
the shake processes from other elements.
40
Average
Present work
Mukoyama [8]
Carlson [11]
Total shake probability(%)
1s
35
30
25
20
15
10
5
10
15
20
25
30
35
40
Z
40
Average 2s
present work
Mukoyama
Carlson
2s
Total shake probability(%)
35
30
25
20
15
10
5
10
15
20
25
30
35
40
Z
Fig. 3. The total shake probabilities after 1s and 2s vacancy
productions as function of atomic number Z.
Figure 4 shows the results of Arq+ ions resulting from deexcitation decay after 1s
shell vacancy production in Ar atom. The results are obtained by performing the
calculation with and without considering the electron shake processes. The results
of shake processes from a given orbital are compared with experimental values
64
Adel M. Mohammedein et al
performed by Carlson et al.[21] The deviation in the results for charge state
distributions with and without consideration of the electron shake off probability
demonstrates the importance of this process in the calculation of vacancy cascades
in atoms. It is clear that the consideration of the electron shake probabilities in the
calculation of charge state distributions leads to good agreement with the
experimental data. However, in Ar the present value of Ar7+ ions are slightly
smaller than the experimental values.
0.8
Calc. with shake-off
Calc. without shake-off
Exp. [21]
Ar1s+
Branching ratio
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
9
q
Fig. 4. The charge state distributions with and without consideration of
Shake processes in Ar atom after K- shell vacancy production
4. CONCLUSIONS
The electron shake Probabilities due to inner shell vacancy creation are
calculated for elements with Z=7 to 36. Multiconfiguration Dirac Fock Slater
Shake processes after inner shell ionization
65
(MDFS) wave functions are applied to calculate shake processes. The shake
processes are obtained as function of atomic number Z. It's found that, the Zdependence of shake probabilities Pnlj(1s; 2p) and Pnlj(2s; 2p) are very well
smooth. The calculated results allow one to easily estimate the shake probabilities
of any element with 1s vacancy from Z=7 to 36 and with 2s vacancy from Z= 12
to 36. The probabilities of shake processes decrease generally with increasing the
atomic number Z. the consideration of the electron shake probabilities in the
calculation of charge state distributions leads to good agreement with the
experimental data.
Acknowledgement. The authors would like to thank the Public Authority for
Applied Education and Training (PAAET), Kuwait for financial support of the
present work under the project No. (TS-08-04).
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Received: August, 2009