Interatomic Auger decay in CO molecule

Journal of Electron Spectroscopy and Related Phenomena 161 (2007) 63–66

Interatomic Auger decay in CO molecule G.N. Ogurtsov a,∗ , V.M. Mikoushkin a , S.K. Semenov b , V.V. Kuznetsov b , N.A. Cherepkov b b

a A.F.Ioffe Physico-Technical Institute, 194021 St.-Petersburg, Russia State University of Aerospace Instrumentation, 190000 St.-Petersburg, Russia

Available online 21 February 2007

Abstract Energy spectra of electrons ejected in electron impact on CO molecules have been measured for the incident electron energy 1400 eV. The aim was to study the interatomic Auger transitions resulted from the filling in the O K-shell hole by a C K-shell electron. The corresponding peaks have been identified and their relative transition probabilities (partial widths) measured. Theoretical widths of these transitions calculated in the Hartree–Fock approximation are in good agreement with the experimental data. © 2007 Elsevier B.V. All rights reserved. Keywords: CO molecule; Auger spectroscopy; Hartree–Fock approximation

1. Introduction

2. Experimental technique

Interatomic coupling effects, in which correlation between electrons belonging to different atoms of a molecule is involved, have been a topic of vivid discussion during the past decade. These effects can manifest themselves both in photoemission and in Auger electron spectra. In the photoemission, they lead to enhancement of the photoelectron intensity when tuning the photon energy through the core-level absorption edges of a nearest-neighbor atom (multiatom resonant photoemission, MARPE [1–3]). In the Auger electron spectra, they result in appearance of new lines and in the line broadening (interatomic Auger effect, IAE [4–8], interatomic Coulomb decay, ICD [9–12]). Most of the activity was concentrated on studying properties of condensed matter systems, such as crystals, bilayers, dimers, and clusters. The final states of these systems are represented by doubly charged ions with two outer valence shell vacancies localized on two neighboring atoms. The present study of the interatomic Auger transitions in CO molecule is specific in that (i) KO –KC V transitions have been investigated (Intercore Auger effect), (ii) this effect has been investigated in free molecules, and (iii) a joint experimental and theoretical study has been performed.

The interatomic Auger effect has been studied by measuring the doubly differential cross-sections for electron ejection in fast electron collisions with CO molecules. The electron spectrometer [13] based on the cylindrical electrostatic mirror with the entrance angle θ = 54.5◦ and the energy resolution E/E = 0.5% has been used. Briefly, a beam from an electron gun entered a collision chamber with gas placed inside the cylindrical mirror. The energy analyzed electrons entered a detector consisted of a channeltron and a small conical deflector placed for discrimination against the spurious electrons. The latter reduced considerably unwanted background. The detector was working in the single particle counting mode. The usual statistics was of the order of 105 counts, so that the statistical uncertainty was less than 0.3%. The absolute values of the doubly differential cross-sections for electron ejection were determined by normalization of the measured relative values on the absolute doubly differential cross-sections measured earlier [13]. The peak at 250.4 eV corresponding to the transition 2σ → 5σ 2 (the line B3 in the assignments of Ref. [14]) was used as a reference line for the energy calibration of the spectrometer. 3. Theory

∗

Corresponding author. E-mail address: [email protected] (G.N. Ogurtsov).

0368-2048/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2007.02.020

In our theoretical consideration we implied that the two-step model is applicable to IAE according to which the Auger decay can be treated separately from the initial ionization [15,16].

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G.N. Ogurtsov et al. / Journal of Electron Spectroscopy and Related Phenomena 161 (2007) 63–66

Therefore, we consider only the second step in which a singly charged ion with the O K-shell hole decays producing a doubly charged ion. Wave functions of the initial and final molecular states are calculated in the Hartree-Fock (HF) approximation. In general, single particle HF wave functions ϕi (r) satisfy the following system of self-consistent equations (since we do not consider the spin effects, we omit for simplicity the spin variables in all equations) ⎡ ⎤ n 2  ⎣− ∇ − Z1 − Z2 + aij Jjj (r)⎦ ϕi (r) 2 r1 r2 j=1

n n   − bij Jij (r)ϕj (r) = εi ϕi (r) + εij ϕj (r). j=1

(1)

j=1

Here, Z1 and Z2 are the nuclear charges, r1 and r2 are the distances of electron to the nuclei, n is the number of occupied orbitals, i ≤ n, εi is the energy eigenvalues, and Jij (r) are the Coulomb integrals.  Jij (r)≡Jij (ϕi (r), ϕj (r)= ϕi (r )|r − r |−1 ϕj∗ (r ) dr . (2) The off-diagonal energy parameters εij are determined from the orthogonalization conditions  ϕi∗ (r)ϕj (r ) dr = δij . (3) The numerical values of the parameters aij , bij depend on the number of electrons in the shells and in the simplest case of a molecule with closed shells they are aij =2 , bij = 1. For the Auger electron wave function, ϕ␧lm , a similar equation is solved ⎡ ⎤ n 2  ∇ Z Z 1 2 ⎣− − + afj Jjj (r)⎦ ϕεlm (r) − 2 r1 r2 j=1

n 

−

bfj Jεlm,j (r)ϕj (r) = εf ϕεlm (r) +

j=1

n 

εf j ϕj (r),

(4)

j=1

where f > n, and the off-diagonal energy parameters εfj provide the orthogonalization of the ϕ␧lm to the bound state wave functions ϕi (r) of the doubly charged ion. The initial state wave function of the singly charged molecular ion is presented as a Slater determinant constructed from the solutions of Eq. (1). For the final state we solve at first the system of HF Eq. (1) for the doubly charged molecular ion, and after that calculate the Auger electron wave function in the field of the frozen core of the doubly charged ion according to Eq. (4). In this procedure, the single particle initial and final state wave functions are not orthogonal to each other therefore we must take into account the overlap integrals between all of them. We are doing it following the general ideas of Ref. [17]. The total Auger rate, integrated over all angles of the Auger electron emission is given by the equation  Γ = 2π |Al,m |2 . (5) l

The Auger amplitudes Al,m are expressed through the Coulomb integrals  (i) (i) l,m f∗ ∗ Vμ,ε,j,k = ϕμ (r) ϕεlm (r )|r − r |ϕj (r)ϕk (r ) dr dr , (6) and the overlap matrix,  (f) (i) S = (sjk ) = ϕj |ϕk ,

(7)

where the superscripts i and f denote the initial singly charged and the final doubly charged molecular ion states, respectively. The general equations for the Auger amplitudes Al,m were obtained in Ref. [17] using some additional assumptions. In particular, the assumption of the core–valence separability was used which means that the core electrons do not correlate with the other electrons. This assumption does not allow considering properly the interatomic Auger transitions because the core–valence correlations are here important. Therefore, we could not adopt this assumption in our treatment. As a result all formulae become more complicated, though the main features do not change. In particular, one can write Auger amplitudes for three different possible cases like in Ref. [17] as follows. Case a. Singlet final state, both electrons are removed from the same spatial orbital n as in the transition 2σ(2 ) → 3σ3σ(1 ), (+)

Al,m = Cn,n,j,k ,

(8)

where the notation is used

  (±)

n,n ,μ l,m Vμ,ε,j,k Qk,j,ν

Cn,n ,j,k =

μ =n

j,k(k =ν)



±

 n,n ,μ l,m Vμ,ε,j,k Qk,ν,j

.

(9)

j,k(k =j)

Index ν means the number of spatial orbital where the initial hole was produced. Case b. Singlet final state, electrons are removed from different spatial orbitals n and n as in the transition 1σ(2 ) → 2σ3σ(1 ),

1 (+) (+) Al,m = √ Cn,n ,j,k + Cn ,n,k,j . (10) 2 Case c. Triplet final state 1σ(2 ) → 2σ3σ(3 ),  3 (−) (−) Al,m = (C  − Cn ,n,k,j ). 2 n,n ,j,k

as

in

the

transition

(11)

Unlike Ref. [17], the additional summation on ␮ appeared here in the coefficients C. The coefficients Q in Eq. (9) have two additional indices compared to Ref. [17] and are calculated according to 



−1

,m −1 −1 2 j Qn,n j,k,μ = (S )j,n (S )k,n [det(S)] [(Sn ) j

]mμ .

(12)

Matrix Sn means the matrix S with elements both in the line n and column j being replaced by zero except for snj = 1. The Auger electron continuum wave functions are determined by the same procedure as described in Ref. [18] with 10 partial waves included.

G.N. Ogurtsov et al. / Journal of Electron Spectroscopy and Related Phenomena 161 (2007) 63–66

65

Table 1 Experimental and theoretical widths of the interatomic Auger transitions Transition

Energy (eV)

Partial width (a.u. experiment)

Partial width (a.u. theory)

1σ → 2σ3σ(1,3 ) 1σ → 2σ4σ(1,3 ) 2σ → 3σ3σ(1 )

182.7; 184.1 202.5; 203.5 195

0.38 × 10−4 0.22 × 10−4 2.2 × 10−4

0.31 × 10−4 0.18 × 10−4 2.23 × 10−4

when complementing our experimental data by available data on the total cross-sections for K-ionization, σ tot (K) [21], and on the total Auger widths, Γ tot (K) [22], for carbon and oxygen in CO. Then the partial widths Γ i can be determined from the relation σi Γi = (13) Γtot (K), σtot (K) Fig. 1. Energy spectra of electrons associated with interatomic Auger transitions in CO.

4. Results and discussion The experimental data on the doubly differential crosssections measured at the incident electron energy E0 = 1400 eV are shown in Fig. 1. As seen from the figure, three new features are found in the ejected electron energy range Ee = 180–210 eV. The double lines at 182.7–184.1 eV and 202.5–203.5 eV can be attributed to the intercore Auger transitions 1σ → 2σ3σ(1,3 ) and 1σ → 2σ4σ(1,3 ), while a broad line at 195 eV to the transition 2σ → 3σ3σ(1 ) (1σ = 1sO, 2σ = 1sC). Since the 3␴ orbital is mostly oxygenic [19], the transition 2σ → 3σ3σ can also be considered as an interatomic transition. The excitation function of the first double line matches very well the cross-section function for oxygen K-ionization of CO (Fig. 2) thus confirming the accepted identification. On the other hand, the threshold for excitation of the broad line at 195 eV lies at E0 < 300 eV [20], that corresponds to the KC ionization energy. It is of fundamental interest to estimate the partial widths of the observed interatomic Auger transitions. This can be done

where σ i is the cross-section for emission of the line “i” determined by integration of the line over ejected electron energy (the peak area) and angle. Assuming isotropic angular distribution of ejected Auger electrons one arrives at the values of partial widths for the transitions under consideration given in Table 1 together with the theoretical results. The data obtained can be compared with the values Γ tot (KO) = 4.94 × 10−3 and Γ tot (KC) = 2.23 × 10−3 [22] to estimate the relative contribution of the new lines to the total Auger process. 5. Conclusions The energy spectra of electrons associated with the interatomic Auger transitions resulted from the decay of the O K-shell in CO molecules have been measured. The lines attributed to the transitions 1σ → 2σ3σ, 1σ → 2σ4σ, and 2σ → 3σ3σ have been observed and identified. The partial widths of the above transitions have been determined, too. Theoretical calculations of these Auger widths have been performed in the Hartree–Fock approximation using the different self-consistent basis sets for the initial singly charged and the final doubly charged molecular ion states. There is a good agreement between the experimental and theoretical data for the Auger widths. The existence of these lines is a manifestation of correlation between the spatially well-separated O and C K-shell orbitals which frequently are considered as being noninteracting. It is evident that the width of these transitions must be a sharp function of the internuclear distance, therefore, studies of these transitions in different compounds containing CO or adsorbed CO molecules could give new information on interelectron correlations inside the molecule. Acknowledgement This work is supported by INTAS under grant No. 03 51 4706. References

→ 2σ3σ(1,3 )

Fig. 2. Excitation functions for interatomic transitions 1σ and K-ionization of O in CO molecule. Solid curve: K-ionization [21], full circles: interatomic transitions.

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