Cascading electron deexcitation in xenon ions after K-shell ionization

A.

404 Table

1. Electronshake-off

probabilities

ELShemi

et al.

for different subshells in xenon atoms. n,: location of the primary vacancy: n.: subshell of the vacancy created by electron shake-off

00

K

LI

L

L

M,

MI

MI

L L 4 MI M* MI M, MI N, N N, N4 NI 0, O* Oi

0.0002 0.0003 0.0006 0.0007 0.0012 0.0023 0.0023 0.0034 0.0025 0.0025 0.0079 0.0170 0.0254 0.0206 0.0410 0.0896

0.0000 0.0000 0.0001 0.0002 0.0004 0.0009 0.0017 0.0025 0.0025 0.0025 0.0052 0.0166 0.025 1 0.0189 0.037 I 0.0835

0.0000 0.0000 0.0000 o.OQo3 0.0004 0.0011 0.0015 0.0030 0.0018 0.0024 0.0052 0.0166 0.025 1 0.0189 0.0363 0.0851

0.0000 0.0000 0.0000 0.0003 0.0005 0.0009 0.0019 0.0025 0.0017 0.0027 0.0052 0.0174 0.0246 0.0188 0.0378 0.0832

0.0000 0.0000 o.OQOo 0.0000 0.0000 0.0001 0.0002 0.0003 0.0007 0.0013 0.0027 0.0111 0.0170 0.0163 0.0345 0.0783

0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0004 0.0009 0.0011 0.0030 0.0109 0.0176 0.0172 0.0328 0.0794

0.0000 0.0000 0.0000 0.0000 0.0000 O.OOGl 0.0002 0.0003 0.0008 0.0013 0.0025 0.0111 0.0167 0.0171 0.0349 0.0769

realize a Monte-Carlo selection of the actual deexcitation Channel the probabilities of al1 deexcitation channels were normalized to 1. Then a random number in the interval [O,l] selects the next deexcitation step including vacancy transfer and ionization. For each created vacancy we first determine whether electron shake-off wil1 take place or not using total shake-off probabilities for the shells considered (see Tables 1 and 2). If electron shake-off takes place, the atomic shell from which a shake-off electron is ejected is determined according to relative shake-off probabilities and the number of vacanties is increased by one. In the next step we decide from the fluorescente yield whether radiative or non-radiative transitions take place. When a radiative transition is selected, the vacancy is transformed to a higher shell. In the case of Auger or Coster-Kronig transitions two new vacanties are generated according to the relative transition probabilities of energetically allowed channels. Electron transitions in the course of Auger cascading are accompanied by shifts of the electron energy levels (Zschornack et al., 1986). Owing to this some initially allowed CosterKronig transitions may become energy-forbidden, which influences the further deexcitation process. A non-consideration of the energetic shell structure leads to a deformation of the ion charge state spectrum in comparison with experimental spectra (Carlson et al., 1966b). Thus, for each ion ground state a test is done to check the energetics of ai1 possible Coster-Kronig channels by calculating the Table 2. Electron shake-off probabilities

N, NI N N. N 0, 02 0,

0.0001 0.0002 0.0004 0.0032 0.0050 0.0126 0.0299 0.0687

0.0000 0.0001 0.0005 0.0019 0.0053 0.0137 0.0265 0.0702

MI

M,

O.oooO o.oOQO 0.0000 0.0000 0.0000 0.0000 O.OOOQ 0.0005 0.0010 0.0014 0.0032 0.0 102 0.0187 0.0175 0.0345 0.0795

O.OOC!G 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0010 0.0015 0.0030 0.0121 0.0265 0.0175 0.0351 0.0788

transition energies with the Dirac-Fock-Slater method. Shake-off probabilities are calculated using our own code (Mohammedein, 1994). Results for neutral xenon atoms are presented in Tables 1 and 2. In this way we calculate the electron shake-off probabilities according to Aberg (1967, 1969) by overlap integrals between the wave functions of the initial state Gi and the final state @( of the process considered. The wave functions @, and @, are given as Slater determinants

udrd

udrz) udr3) . ..

uI(rN)

U&J u,irJ UirJ ... UirN) with N as electron number. Thus, the probability for an electron transition from the orbital nlj to the orbital n’l’j’ yields Pn,,_n’rj

=

s

I @44&,(A)

dtl*

(2)

with u,,,(A) and u,$(A,,) being orbital wave functions for the orbital nlj in the atom A and for the orbital n’f’j’ in the ion A,,. 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

for different subshells in xenon atoms. n,: location of the primary vacancy; n,: subshell of the vacancy created by electron shake-off

0.0000 0.0003 0.0029 0.0029 0.0036 0.0135 0.0301 0.0654

0.0000 0.0000 O.oooO 0.00 16 0.0036 0.0127 0.0270 0.0665

0.0000 0.0000 0.0003 0.0022 0.0029 0.0126 0.0285 0.0644

0.0000 0.0000 0.0000 0.0000 0.0001 0.0025 0.0096 0.0246

0.0000 0.0000 0.0000 0.0000 0.0000 0.0028 0.0056 0.0243

0.0000

0.0000

o.oooo 0.0000

o.oooo 0.0027 0.0085 0.0179

Cascading

electron

deexcitation

405

in xenon ions

0 0 0 own calculatlons ??????

10

0

Fig.

nQ becomes

20

30

40

1. Shake-off probabilities

as a function of the atomic number the L,,,, M,,, and N,,, sub-shells after the production

ionized

is given by

P = 1 - (1 u,$,(A,)u,,,,(A) dsl’)” - P, s

(3)

If the electron is emitted from the orbital nlj, it is either ionized to the continuum (electron shake-olT) or populates a bound state (electron shake-up). In the calculation of the electron shake-off process the possibility that transitions occur to occupied subshells have to be excluded, since such transitions are not allowed according to the Pauli exclusion principle. The quantity Pr represents a correction for physically not allowed transitions to occupied shells and has the form

Carlson end Nestor

50

2J + , l w%(A&dA) s

W

z

Z for the emission of an electron of an inner-shell vacancy.

from

selected sub-shells after the production of a primary K-vacancy in this shell. A good agreement is observed with the values of Carlson and Nestor (1973). The vacancy cascade modeling takes into account that transition probabilities change as a result of ionization processes. Hence the transition rates were calculated according to the following scheme: at first, for the neutral atom, quantum-mechanically determined transition rates were computed. Than for al1 other configurations with additional vacanties corrected rates (A,, A, and Ac,: X-ray, Auger and Coster-Kronig rates), based on a staling procedure proposed by Larkins (1971) were calculated:

A, = n, -,v P,=xN& ,,,,

60

‘l A,

X-ray transition

rdte

(4)

with n’ # n and N’ as number of the electrons in the orbital n’Jj. As an example we show in Fig. 1 the dependence of the calculated shake-off probability on the atomic number Z for the emission of an electron from

A

,I (8 - n,)(N - n,)

= .I

A

I

=

ck

NP,

A

Auger transition

A

n (4 - n,)(N,- n, - 1) N,(N, - 1)

A

I

CK

Coster-Kronig

own calcul8tlon.s Carlson et al.

2

3

4

5

6

7

9

9

10

11 12 13 14 15 16 17 18

final ion charge state

Fig. 2. Final ion charge state distribution vacancy. Shown are our own calculation

of initial neutral xenon after deexcitation of a primary K-shell results and experimental results (Carlson and Krause. 1965).

rate

A. El-Shemi ef al.

406

K-shell vacsncy deexcitation

lr

I

0

I

I

I

10

I

I

8,

20

I

I

I

I

I

I

I

30

11

I

I

40

I

I

50

xenon ion charge state

Fig. 3. Change of the mean ion charge state in xenon ions after deexcitation

A,, A, and AcLcharacterize the corresponding rates for ionized atoms with n, vacanties in the subshell of the primary vacancy and n, vacanties in the final subshell, containing N2 electrons in the case of complete occupation. For non-radiative transitions n3 gives the number of vacanties in a further subshell, containing N, electrons in the atomic ground state. For each new vacancy the computer code goes back to the first step described above. The appearance of new vacancy configurations continues until al1 vacanties have reached the outer shell. Then the number of vacanties is recorded. After a cascade has finished, the same initial vacancy is set again in

Fig. 4. Ion charge

state distribution

following

of a primary

K-shell vacancy.

the inner shell and the simulation of the cascade process is repeated. For each case, we calculated 10’ histories to get stable results for the final charge state distributions with a given initial inner-shell vacancy.

RESULTS

In the manner described above we analyze states distributions in xenon ions after ionization. In Mohammedein et al. (1993) shown that, with the simulation code used for

initial

K-shell

ionization

of an Xe’+ ion.

charge K-shell it was neutral

Cascading electron deexcitation in xenon ions

80. 60. 40.

po %

40 .

52

4p64a2

I

II

30

I

po %

P(5) %

“0

10

20

--30

40

50

ion charge Fig. 5. Probabilities P(k) tbat the remaining ion is k-fold ionized (k = 1...5) after the deexcitation of a primary K-shell vacancy. Fully ionized subshells are indicated.

xenon, results very close to the experimental results of Short et al. (1987) and Carlson and Krause (1965) were derived. To illustrate the situation, in Fig. 2 calculated results are compared with a measured ion charge state distribution after deexcitation of an initial K-shell vacancy. Thus, we claim that calculations for ionized atoms give realistic modelling results too.

407

Figure 3 shows the average number of additional ejected electrons as a function of the primary ionization state of the xenon ions for ion charge states up to 50 (fully ionized 2p orbital). A first clear bend is seen in the curve at q = 8, where the 0-shell is completely ionized. In the region q = 8.. ,18 the xenon 4d subshells are ionized step by step and we find only smal1 differences in the mean number of ejected electrons from ions of corresponding charge states. Beginning with 4p ionization the number of ejected electrons decreases until the fully ionized N-shell is reached at q = 26. The next significant decrease in the mean ion charge states reached occurs at about q = 44 (beginning of L-shell ionization). In Fig. 4 the quantity P(k) for Xev+ ions as a function of the ion initial charge state and of the ion charge state after K-shell ionization in xenon is shown. The ion charge state distribution shows a clear simplification after full ionization of the N-shell. During the ionization of the M-shell, the ion charge state distribution shows a maximum for two additional vacanties, and beginning with L-shell ionization one additional vacancy dominates. After full ionization of the M-shell, LMM Auger channels are closed, only KLL Auger transitions take place, and the radiative vacancy transformation increases, in particular, after full ionization of the 3s-subshell (q = 44). The increasing change of the mean ion charge state at Xe’“+ occurs because the transition rate for KL,L, Auger processes is three orders of magnitude higher that for the radiative KL, transition. In Figs 5 and 6 the probabilities P(k) that the remaining ion is k-fold ionized (k = 1 18) are shown. Generally, al1 figures show a clear dependence on the actual occupation of the atomic subshells. Thus, for instance, the increasing probability P( 1) after reaching the fully ionized M-shell (q = 44) occurs because the K,, and Kg2 transition rates are one order of magnitude higher than the non-radiative KLL ones. The opening of Auger channels leads to significant bends after full N-shell ionization for P(2) and after full 0-shell ionization for P(3). Thereby, an increasing number of KLM and higher non-radiative transitions take place. For higher P(k), cascades of non-radiative transitions are necessary to reach multiply ionized ions after the deexcitation process. Thus, beginning with P(3) we see a decreasing probability P(k) after full N-shell ionization and starting with P(8) after full 0-shell ionization. Probabilities P(14) and higher are only significant for occupied 5s and Sp orbitals. (For the numerical values of the charge state distributions, see Table 3.) Analyzing the results of Figs 3 - 6 leads to the following conclusions. 1. The spectrum of the number of ejected electrons at a concrete xenon initial ion charge state forms an asymmetrie peak, e.g. a maximum probable charge

408

A. ELShemi et al.

state with decreasing probabilities for charge states at the lower and higher end of the distribution. As a

CONCLUSION

rule, double peak structures are not observed. 2. For complex spectra (low ionization degrees of xenon) we observe nearly symmetrie charge spectra. 3. The mean number of ejected electrons decreases with increasing initial ionization degree. This behavior is influenced by the decreasing number of occupied subshells, opened Auger channels and by increasing electron binding energies.

Vacancy cascades in neutral and ionized xenon are calculated as a result of deexcitation processes after primary K vacancy production. The mean ion charge distribution and the probability P(k) that the remaining ion is additionally k-fold ionized are calculated as a function of the xenon ionization degree. Electron shake-off processes and the closing of Auger channels as a result of energetically

P(6)30

?? P(7) 30

5r2

%25 20 15 10 5 n

5a2

%25

I

P(5) 25 36

4p’O

I

20

15 10

5 20 LL

-0

10

20

0

10

ion charge

ion charge

20

-0

10

ion charge

20

P(S) 20 15

I 58

?lO

10 5 %

0 LI

10

0

20

kL.Q.

P(12) 5 T

4 3 2 1 0

20

0

ion charge P(14) 285 I% 2

P(13) 5 9c

LI 5s2 I

4 LI

Sr2

5r2 I

I

3

1.5

2

1

1

0

0

10

ion charge

0

0.5 0h 0

10

10

km charge

ion charge P(17) 0.5

P(W) OB2

ü

% 0.15 0,3 0,l 0.2 0,05

O,l

0

10

Ion charge

0

ion

084 0 -1 0

00

10 bn charge

0

10

hchuge

Fig. 6. Probabilities P(k) that the remaining ion is k-fold ionized (k = 6.. .18) after the deexcitation of a primary K-shell vacancy. Fully ionized subshells are indicated.

1.6 1.0 3.1 6.0 14.0 23.6 18.4 12.2 7.7 4.3 2.9 2.0 1.2 0.7 0.5 0.2 0. I

Xe” + 21.5 67.3 5.4 5.7

1.5 0.9 3.4 3.8 7.4 10.0 22.3 18.8 12.6 1.7 4.2 2.7 2.1 1.3 0.8 0.3 0.2 0.1

Xe” + 21.4 67.4 5.3 5.7

f 2 3 4

Xe* +

Xe0 +

4

distributions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Table 3. Ion charge stak

21.3 67.4 5.3 5.9

Xe” + 13.9 74.6 5.5 5.9

Xe” + 13.7 74.6 5.5 6.1

1.4 18.0 25.9 23.4 10.7 1.6 3.1 2.7 2.1 1.6 1.o 0.4 0.1

1.9

Xel * 5.4 83.3 4.4 6.9

1.9 7.5 17.9 26.3 13.9 12.0 8.4 4.3 3.0 2.2 I .6 0.7 0.2 0.1

Xe’” + 5.4 83.3 4.4 6.8

1.8 7.4 15.3 28.6 19.9 7.3 8.3 4.3 2.7 2.3 1.4 0.6 0.2

Xe” + 6.9 83.3 4.4 5.5

2.8 7.1 16.9 15.3 20.2 15.5 10.4 5.0 3.0 2.5 1.0 0.3

21.6 71.7 6.7

XeG +

2.7 5.4 14.9 29.2 21.2 13.3 5.3 2.8 2.6 2.1 0.5

initial charged xenon ions Xe q + after deexcitation of a primary K-shell vacancy. Tabulated greater than 0.1%). q = change of the initial ion charge state in charge units Xe”’ Xe”+ Xe’ + Xe’” + Xel + Xe’ +

2.4 7.8 18.4 26.4 17.8 ll.0 6.4 3.2 2.3 1.8 1.3 0.7 0.4 0.1

for different

Xe]0 +

1.9 2.3 6.1 17.9 25.4 17.8 ll.4 6.8 3.8 2.4 1.6 1.2 0.8 0.4 0.2

Xe’ I

(in percent)

Xe” ’ 90.7 9.3

2.6 1.9 16.0 31.8 18.9 12.5 3.2 4.1 2.4 0.5

XelB+

are the additional

Xe*+ 90.7 9.3

2.5 7.9 17.0 32.1 20.5 12.2 4.2 2.3 0.6 0.1

Xem +

produced

Xeq + 92.4 7.6

1.8 9.1 24.9 42.5 13.4 4.2 2.7 0.7

Xez2 +

Xe’+ 0.3 99.1

4.8 35.6 38.0 13.8 4.5 3.4 0.1

Xez’+

ion charge states (contributions

: _. 0 2

z

[ _. D f. Jo _. z

$ rz 0 8 $ g

D w

A. El-Shemi er al.

410

forbidden channels during the cascade development are considered. The results derived for P(k) show a clear dependence on the actual atomic structure of the ion considered. Acknowledgemenrs-The

work was supported

by BMBF

under contract No. 06 DD 111. REFERENCES

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