Production of Highly Charged Ions in Neon Following Photoionization and Resonant Excitation

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1 Egypt. J. Solids, Vol. (7), No. (), (004) 0 Production o Highly Charged Ions in Neon Following Photoionization and Resonant Excitation Yehia A. Loty El-Minia University, Faculty o Science, Physics Department, 6 El-Minia, Egypt The inal charge state distributions o ions are calculated ater photoionization s, s and resonant excitation s 3p and s 3p in neon atoms. The calculation o vacancy cascades based on the simulation o radiative and non-radiative pathways to ill the inner-shell hole and spectator vacancies in atomic conigurations. The charged ions at s hole state ater photoionization mainly turns into Ne + and Ne 3+ ions. In thes hole situation, the doubly charged Ne + ollowing photoionization are predominate, while in s hole situation the singly charged Ne + ions are the most abundant one. At s hole state ater photoionization and resonant excitation, the charged Ne + predominate in the distributions. The consideration o electron shake o processes improves the results o inal charge state distribution. The results o charge state distributions o ions ater core hole production agree well with the experimental values.. Introduction: The inner-shell vacancy in ground state atom is ormed leaving an ionic state, could be transerred into ground state via a cascade o successive radiative (x-ray) and non-radiative (Auger and Coster- Kronig) transitions. The cascades o these radiative and non-radiative transitions lead to the ejection o electrons and yield highly charged ions. Each Auger transition increases the charge o the ion by one, while radiative transition leaves the charge state unaltered. In the case o x-ray processes the vacancy moves to an outer shell under emission o characteristic x-rays, while or non-radiative transitions one electron rom an outer shell ills up the inner-shell vacancy and another electron is ejected into continuum. In addition to the vacancy illing processes, there is an electron shake o process due to the change o core potential o the atom, which causes ater inner-shell vacancy creation and through the illing processes.

2 Yehia A. Loty 0 The study o successive radiative (x-ray) and non-radiative (Auger and Coster- Kronig) transitions ollowing inner-shell ionization and the highly charged ions which is connected with the cascades, is o interest in dierent ields o research such as solid state physics, plasma physics and astrophysics. The investigation o vacancy cascades is important or studying the storage o thermal multi-charged ions [] and or the decomposition o large molecules ollowing electron pick-up []. The study o post-collision interactions and relaxation processes in inner-shell ionization is usually perormed by analysis o electrons or ions produced by successive radiative (x-ray) and non-radiative (Auger and Coster-Kronig) transitions. The structure and the dynamics (e.g. energies, transition probabilities, and electron correlation) o atoms and molecules are probed via Auger cascades production. The readjustment o neon atom ionized in the K shell by x-ray has been measured with a coincidence time-o-light mass spectrometer [3]. However, in the case o neon atoms (Nobel gas) the highly charged ions producing ater inner shell ionization are not destroyed and can be observed experimentally. The relative abundance have been measured or the ions that are ormed as the result o atomic adjustment to vacancies in the K and L shell o rare gases atoms [4-8]. The charge state distribution o ions result rom de-excitation decay o inner-shell vacancies was measured by sweeping the photo energy across the ionization threshold [9-] using synchrotron radiation and time-o light spectrometer. There are two major theoretical studies to calculate the highly charged ions ater inner-shell ionization in atoms. The irst one is based on straightorward construction o the vacancy cascades accompanied with trees o radiative and non-radiative transitions [3-6]. The second method is based on simulation o all possible radiative and non-radiative pathways, which ill the inner-shell vacancies in atoms [7-]. In the present work, the inal charge state distributions ollowing s and s photoionization and resonant excitation are calculated. The vacancy cascades are based on simulation o radiative, non-radiative transitions pathway to ill the inner-shell vacancies and electron shake o processes in neon atoms. The radiative and non-radiative transitions are calculated or single ionized neon. The radiative and non-radiative transitions or multi-ionized (several vacancies) are obtained using the scaling procedure that is dependent on the occupation number o electrons in atomic conigurations through the vacancy cascade propagation. The results o inal charge state are compared with theoretical and experimental values.

3 Egypt. J. Solids, Vol. (7), No. (), (004) 03. Method o calculation: A radiative (x-ray) and non-radiative (Auger and Coster-Kronig) states are created by inner-shell ionization in atoms. Inner- shell (core) electrons are meant all electrons except the outermost electrons. The production o innershell vacancy in the target atom A is perormed by photoionization A + hυ A + + e () p Here, the resonant intermediate state A + is reerred as the initial state o the decay process and e is the primary emitted electron. In the case o x-ray p processes the vacancy moves to an outer shell under emission o characteristic x-rays A + A + + hυ ' where h υ ' is the characteristic x-ray. I the inner-shell vacancy is illed via Auger process resulting in two vacancies () A + A + + e Auger (3) The calculation o inal charge state distributions and average number o ejected electrons ollowing de-excitation decay o inner-shell vacancies has been carried out by the Monte-Carlo algorithms. This method is based on the simulation o all possible radiative and non-radiative pathways to ill the innershell vacancies in atom. The detailed description o the Monte-Carlo method has been given by El-Shemi et al. [0] and Abdullah et al. []. The radiative, non-radiative transitions and electron shake o processes are the principle mechanisms o a cascade originating rom an inner- shell vacancy in atoms. The electron shake o process caused by the change o atomic potential is due to the creation o core hole and the decay through radiative and non-radiative transitions. The radiative branching ratios (luorescence yields) and non-radiative branching ratios (Auger yields) give valuable inormation on the de-excitation dynamic o an atom with an innershell vacancy, are calculated. The radiative branching ratios (luorescence yields) ω is deined as the probability that the vacancy in an initial state i is illed through radiative transitions under the emission o characteristic x-ray rom inal state, and is given by:

4 Yehia A. Loty 04 A( i ) ω = (4) A( i) + A( a) where A (i ) is the radiative transition rate rom initial state i to inal state, A (i) is the total radiative decay rate o state i, and A( a) = A( a ) is the i total Auger and Coster-Kronig decay rate o inal state. The non-radiative branching ratios (a) are deined as the probability that the vacancy in an initial state i is illed through radiative transitions under emission o electrons state, and is given by: A( a ) i a = (5) A( i) + A( a) The radiative transition rates A (i ) or singly ionized atoms are calculated using Multiconiguration Dirac Fock (MCDF) wave unctions rom Grant et al. []. The non-radiative transition rates A( a ) or single ionized i atoms are calculated using the Dirac Fock Slater wave unctions using a code written by Lorenz and Hertmann [3]. The electron shake o process due to sudden change o atomic potential during vacancy cascade development leads to the ejection o additional electrons through monopole processes, this process is calculated using a code developed by El-Shemi [4]. The electron shake o probabilities are calculated by overlapping integrals between the wave unctions o initial state ϕ and the inal state i ϕ o the transition process A o berg [5, 6]. So the probability o an electron transition rom the orbital nlj to the orbital n l j is given by p nlj n l j = ϕ ( A ) ϕ ( A) dτ (6) nlj 0 n l j where ϕ (A) and ϕ ( A0 ) are orbital wave unctions or the orbital nlj nlj n l j and or the orbital in the ion A 0. The probability that at least one o the n l j N electrons located in the sub shall nlj becomes ionized is given by

5 Egypt. J. Solids, Vol. (7), No. (), (004) 05 p = - ( ϕ ( A0 ) ϕ ( A) dτ ) nlj n l j N p (7) where the quantity P represents a correction actor or transitions to occupied shells (not allowed transitions) and has the orm p = n lj N N j + ϕ ( A dτ (8) n lj 0 ) ϕ nlj ( A) with n n and N is the number o the electrons in the orbital n lj. An analysis o each cascade begins with the considration o all possible electron transitions which may ill an initial vacancy. In the ollowing development o the cascade in each step, the computer program selects one o the possible processes according to their relative probabilities by the use o random numbers. Ater realization o the selected transition, a new coniguration o vacancies appears. For each vacancy, irst determine whether electron shake o will take place or not, using the total shake o probability or that shell. I an electron shake o take place, the atomic shell, rom which the shake o electron is ejected, is determined according to relative shake o probabilities and the number o vacancies is increased by one. In the next step, the program decides rom the luorescence yield whether the transition is radiative or non-radiative transition. When it is radiative, the new position o the vacancy is selected rom the partial radiative transition probabilities. In the case o Auger and Coster-Kronig transitions, two new vacancies are generated according to the relative transition probabilities o the energetically allowed Auger channels. The creation o multiple vacancies in atomic conigurations during vacancy population causes transition energy shits and may result in an energetic closing o channel or certain Coster-Kronig transitions. In the determination o the population o the multiple vacancy states, the vacancy cascade modeling takes into account the act that the change o radiative and non- radiative transition rates due to transition energy shits. The correction o the transition rates quantum mechanically requires more complex calculations. Thereore the transition rates were calculated according to the ollowing scheme. At irst quantum mechanically determined transition rates were calculated or single ionized atoms. The corrected transition rates or multiionized atoms have coniguration with more vacancies are calculated using the scaling procedure proposed by Larkins [7]. So, the corrected radiative and non-radiative transition rates during vacancy cascade development are obtained using the scaling procedure as ollowing:

6 Yehia A. Loty 06 For radiative ( N n ) Γ = n Γ (9) r N R where n and n are the vacancies in initial and inal states respectively. N is the occupation numbers or the inal state. For non-radiative N N Γ = Γ a (4l + )(4l + ) A or non-equivalent electrons (0) and Γ a N ( N ) = Γ (4l + )(4l + ) A or equivalent electrons () where N and are the orbital quantum numbers. N are the occupation numbers or the inal state and l and l multi-ionized atoms and Γ or single ionized atoms. A Γ are the non-radiative transition rates or a For each new vacancy the computer program goes back to the irst step described above. The appearance o new vacancy conigurations continues untill all these vacancies reach the outer shell. Then the number o vacancies are recorded. Ater inishing with one cascade, the same initial vacancy will again be created in the inner-shell and the cascade will be again simulated. The probabilities o charged ions state distributions p ( Z ) and the average charged ions Z are recorded ater 0 5 histories. Ater 0 5 histories a stable inal charge state distributions p( Z ) and the mean charged ions Z are produced. where n is the degree o ionization. Z = n n p ( Z ) ()

7 Egypt. J. Solids, Vol. (7), No. (), (004) Results and Discussions: The inal Charge state o ions ormed ater s photoionization in Ne atom are illustrated in Fig. (). The photoionization create s vacancy as one electron removes into continuum s C, in this case the electronic 4 coniguration o single ionized neon atoms is given as s + s p p 3. The charge state distributions produced by the vacancy cascades ollowing rom s vacancy, in this case the s core hole created by photoionization energy is above the ionization threshold o the K shell. In the s vacancy situation, the decay lead to probabilities o inal charge Ne + =%, N + =78%, N 3+ =% and Ne 4+ =0.09 respectively. The Ne s ionization mainly yields doubly charged ions via non-radiative K-L L, K-L L, K-L L 3, K-L L, K-L L 3 and K-L 3 L 3 Auger transitions. The low intensity o Ne + ions produced ollowing the decay o s through K α radiative (x-ray) transitions, which occur in 0.7% o the cases as given by luorescence yield. In this path, a p electron ills a s hole and a x-ray is emitted. According to the selection rules or dipole transitions the s p is the only allowed transition. The probability o illing s hole through Auger transitions is 99.3% according to non-radiative yield. The (s,s), (s,p) and (p,p) Auger transitions are possible or illing the K shell vacancy in neon. These transitions lead to double charged Ne + ions. The radiative and non-radiative transitions are not permitted in the p hole situation in Ne, so the Ne 3+, Ne 4+ ions produce rom Double Auger processes and electron shake o process. The number o ejected electrons Z > yields ater s photoionization is equal.3. < 0.8 Ne <z>=.3 Present work Calc. [3] Calc. [6] Exp. [3] Exp. [] s / C Branching ratio Z Fig. (): Final charge state distributions ollowing photoioniztions in neon atom. The average number o ejected electrons are given in the let corner.

8 Yehia A. Loty 08 Figure (). shows the charge state distributions ollowing resonant excitation s 3p in neon atom. The emission o one electron rom K-shell to bound state 3p as resonant excitation produced the ollowing electronic + 4 coniguration s s p p 3p. The inal charge state ater Ne s resonant 3 excitation (s 3p) gives rise to Ne +, Ne + and Ne 3+ with the probabilities in percent P(Ne + ) =56%, P(Ne + ) = 43% and P(Ne 3+ ) = %. The average number o ejected electrons < Z > ater s 3p resonant excitation is equal.97. The results o inal charge state distributions ater photoionization (s C ) are compared with theoretical and experimental values, but the results produced ater resonant excitation (s 3p) are compared with available theoretical values. 0.8 Ne <z>=.97 present work Calc. [3] s/ 3p Branching ratio Z Fig. (): The inal charge state distributions ater excited resonant s-3p in neon. The average number o ejected electrons are given in let corner. The highly charged ions ormed ater photoionization s and resonant excitation s 3p in neon atoms are illustrated in Fig. (3) and 4. The photoionization create s vacancy as one electron removes into continuum, while the resonant excitation produce s vacancy as one electron removes into empty bound excited state 3p. The electronic coniguration ater

9 Egypt. J. Solids, Vol. (7), No. (), (004) 09 Ne Present work Calc. [3] 0.8 <Z >=.04 s c Branching ratio Z ` Fig. (3): Final charge state distributions ater photoionization s in neon atoms. The average number o ejected electrons is given in the let corner. 0.8 Ne <Z >=.0 present work Calc. [3] Exp. [3] s 3p Branching ratio Z s 3p in neon atoms. The average number o ejected electrons is given in the let corner. Fig. (4): Final charge state distributions ater resonant excitation

10 Yehia A. Loty 0 photoionization s is written as s s p p (as one vacancy created in L ). The emission o one electron rom s into empty bound excited + 4 state 3p leads to the atomic coniguration s s p p 3p. The inal charge state ater Ne s photoionization (s C) gives rise to Ne +, Ne + with the probabilities in percent P(Ne + ) =96%, P(Ne + ) =4%. The radiative and non-radiative transitions are not permitted in the s hole situation in Ne. The Ne + ions yield rom electron shake o process. The singly charged ions Ne + are predominate ater s resonant excitation in Ne atoms. The electron shake o probabilities not appears in the s resonant excitation situation Conclusion: The inal charge state distributions ater s and s photoionization and s 3p and s 3p resonant excitation in Ne atoms are calculated. The calculation method based on the simulation o possible deexcitation pathways including radiative and non-radiative transitions to ill the vacancies produced in atomic shell conigurations and electron shake o processes, which is due to the change o atomic potential ater primary hole production. The radiative transition probabilities (x-ray transitions) are calculated or single ionized atom and multi-ionized atom using a Multiconiguration Dirac Fock (MCDF) wave unctions. The non-radiative transitions (Auger transitions) are calculated using Dirac Fock Slater (DFS) wave unctions. The charged ions at s hole state ater photoionization mainly turns into Ne + and Ne 3+ ions. The production o Ne + ions is dominant ater photoionization, while ater resonant excitation mainly turns into Ne +. At s hole state ater photoionization and resonant excitation, the charged Ne + is predominate in the distributions. The results o charge state distributions o ions ater core hole production agree well with the experimental values. Reerences:. D. A. Church, S. D. Kravis, I. A. Sellin, C. S. O. J. C. Levin, R. T. Short, M. Meron, B. M. Johnson, and K. W. Jones; Phys. Rev. A 36 (987) K. Ueda, E. Shigemasa, Y. Sato, A. Yagashita, T. Sasaki and T. Hayaishi; Rev. Sci. Instrum., 60 (989) M. O. Krause, M. V. Vestal, W. H. Johnson, T. A. Carlson; Phys. Rev., 33, (964), T.A. Carlson and M.O. Krause; Phys. Rev., A 37, (965), M. O. Krause and T. A Carlson; Phys. Rev., A 58, (967) 8

11 Egypt. J. Solids, Vol. (7), No. (), (004) 6. T.A. Carlson and M.O. Krause; Phys. Rev. Letters, 4,(965), T.A. Carlson, W. E. Hunt, and M.O. Krause; Phys. Rev., A 5, (966), T.A. Carlson and M.O. Krause; Phys. Rev., A 37, (965), T. Hayaishi, Y. Morioka, Y. Kageyama, M. Watanabe, I. H. Suzuki, A. Mikuni, G. Isoyama, S. Asaoka and M. Nakamura; J. Phys. B: At. Mol. Phys., 0, (987), L T. Mukoyama, T. Tonuma, A. Yagishita, H. Shibata, T. Matsuo, K. Shima and H.. Tawara; J. Phys. B: At. Mol. Phys.,0, (987), N. Saito and I. H. Suzuki; J. Phys. B: At. Mol. Opt. Phys., 5, (99), H. Tawara, T. Hayaishi, T. Koizumi, T. Matsuo, K. Shima,T.Tonuma and A. Yagishita; J. Phys. B 5, (99), G. Omar and Y. Hahn; Phys. Rev. A, 43, (99), G. Omar and Y. Hahn; Phys. Rev. A, 44, (99), A. G. Kochur, A. I. Dudenko, V. L. Sukhorukov and I. D. Petrov; J. Phys. B: At. Mol. Opt., 7, (994), G. Kochur, V. L. Sukhorukov, A. I. Dudenko and P.V.Demekhin, J. Phys. B 8, (995), T. Mukoyama; Bull. Inst. Chem. Res. Kyoto Univ., 63, (985), N. Mirakhmedov and E. S. Parilis; J. Phys. B: At. Mol. Opt. Phys.,,(988), M. G. Opendak; Astrophysics and Space Science 65 (990) 9. A. M. El-Shemi, A. A. Ghoneim and Y. A. Loty; Turk. J. Phys., 7, (003), 5.. H. Abdullah, A. M. El-Shemi and A. A. Ghoneim; Rad. Phys. and Chem., 68, (003), I. P. Grant, B. J. Mckenzie, P. Norrington, D. F. Mayers and N. C. Pyper; Comput. Phys. Commun., (980), M. Lorenz, E. Hartmann; Report ZFI-09, Leipzig (985) A. El- Shemi; Egypt. J. Phys. 7, No. -pp. (996) T. Aberg; Phys. Rev. 56 (967) T Aberg; Ann. Acad. Sci. Finn. Ser. AVI Phys. 308 (969) F. P. Larkins; J. Phys. B: At. Mol. Phys. 4 (97) L9

Charge state distributions after sub-shells ionization in Lead atom

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