(e,2e) and (e,3-1e) coincidence experiments for studying the PCI effect of low energy ionizing electrons in the Auger process of Ar

Journal of Electron Spectroscopy and Related Phenomena 185 (2012) 602–608

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(e,2e) and (e,3-1e) coincidence experiments for studying the PCI effect of low energy ionizing electrons in the Auger process of Ar B. Paripás ∗ , B. Palásthy Department of Physics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary

a r t i c l e

i n f o

Article history: Received 21 September 2012 Received in revised form 7 December 2012 Accepted 21 January 2013 Available online 28 January 2013 Keywords: Post-collision interaction Auger decay Coincidence spectroscopy

a b s t r a c t Our (e,3-1e) measurements for studying the post-collision interaction (PCI) after electron impact inner shell ionization of argon were continued and completed at different energy conditions. Emitted LMM Auger electrons are detected in coincidence with the ionizing scattered electrons and the energy of the slow PCI inducer ejected electron was calculated from energy conservation. Particularly the effect of the very low energy (i.e. 0–5 eV) ejected electrons (strongly asymmetric energy sharing) is studied at 500 and 460 eV primary electron energies. In the latter case, the background caused by outer-shell electrons was measured by itself and then removed from the coincident spectrum. Nevertheless, the evaluation of PCI distorted Auger lines is still considerably disturbed by the resonant Auger electrons from the high Rydberg states, their (e,2e) contribution was estimated in the paper. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The post-collision interaction (PCI) is considered as the Coulomb interaction between the electrons scattered or ejected due to innershell ionization and the Auger electrons ejected during the decay of the ionic state. This effect – which is manifested (among others) in the line-shape distortion (including the energy shift) of the Auger peaks – has been widely studied in the last decades. In non-coincident Auger measurements, however, the scattered and ejected (ionizing) electrons are not detected. Therefore in these experiments the PCI effect can only be partially studied since it heavily depends on the velocity vector of these electrons. We also made such investigations [1,2]. Coincidence techniques open new opportunities for detailed studies of PCI via better exploration of the collision kinematics. The first such results on electron impact Auger process were published in 1984 [3,4]. Afterwards there were several similar experiments [5,6,7], but in recent years the experiments were made mainly by photon impact [8,9,10]. The main reason for this is that the process is more complicated by electron impact than by photon impact. Partly, because at electron impact much more reaction channels are open, and partly, because there is one more electron in the final state. A few years ago in our laboratory we started the coincidence measurements and (e,2e) research. Although there are three electrons, (scattered, ejected (ionization) and Auger electron) in the

∗ Corresponding author. Tel.: +36 46 565156. E-mail address: fi[email protected] (B. Paripás). 0368-2048/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.elspec.2013.01.011

final state of a normal (diagram) Auger process, we can detect only two of them. In such case we can name our method (e,3-1e) technique. Fortunately, in most cases the kinetic energy of the third (i.e. not detected) electron can be calculated from energy conservation (since the recoil energy of the heavy target atom is negligible). The direction of the velocity of the undetected electron, however, remains unknown. For this reason it is suitable to make such experiments in which the PCI effect hardly depends on this direction. For example, the case of strongly asymmetric energy sharing, in which the excess energy is taken away almost exclusively by the scattered electron. So the energy of the other outgoing electron (the ejected electron) is necessarily close to zero (<4 eV in the cases considered here). This very slow ejected electron will remain in the vicinity of the newly formed ion even during its Auger decay, causing a significant PCI effect. (When the nominal energy of the ejected electron becomes zero the maximal PCI effect is expected.) Only the magnitude of the velocity of the slow ejected electron is of importance, the effect of other parameters on the PCI is negligible. In our laboratory we investigated the PCI effect by this technique in strongly asymmetric energy sharing on Argon at 500 eV primary energy and later at 350 eV, [11,12]. We found, that at around zero ejected electron energy – where a particularly strong PCI effect is expected – numerous disturbing peaks appeared in the high energy tail of the Auger spectrum. These satellite lines are partly resonant Auger lines (following e.g. the 2p1/2 → 3d and 2p1/2 → 4d inner-shell excitations), partly lines produced by outershell excited ionic states (mainly [3p2 ]nl). Without the elimination of these disturbing satellite lines the study of PCI is practically impossible. Further questions were also raised in these papers, which are mostly cleared up in the present paper.

B. Paripás, B. Palásthy / Journal of Electron Spectroscopy and Related Phenomena 185 (2012) 602–608

4p 3d 4d

4s L2 (2p1/2)

ionization a

b

b

b

c

4s

4p

603

c

d

d

3d 4d

L3 (2p3/2)

ionization

239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254

Electron energy [eV] Fig. 1. The positions of the applied transferred energy “windows” compared to the Ar ionization edges and the well-known inner-shell states: in the present measurements (a) at 500 eV, (b) at around 460 eV and in our previous measurements (c) at 350 eV, (d) at 500 eV primary energies.

2. The measuring method 2.1. Experimental setup Our experimental setup was described previously [13], so here we only give a brief description. The instrument consists of the two electrostatic spectrometers, both of the so-called “box” type distorted field cylindrical mirror analysers (CMA) [14]. The Auger electron energy spectrum was measured by a double pass cylindrical “box” type analyzer, while the scattered electrons having a given energy Esc were detected by the single pass spectrometer. The axis of the target gas beam was perpendicular to the common axis of the two spectrometers and also to the projectile electron beam. A relative energy resolution measured by the full-width-at-halfmaximum (FWHM) of the single and double pass spectrometers are 0.9% and 0.5%, respectively.

The positions of the applied transferred energy “windows” compared to the Ar ionization edges and the well-known inner-shell excited states are shown in Fig. 1. Considering the middle of each “window” (the nominal transferred energies), we put them really close (within 4 eV) to the ionization edges, in most cases below the ionization potential of the L2 sub-shell (250.8 eV). In these cases an “average” projectile electron cannot cause inner shell ionization in the L2 (or 2p−1 (2 P1/2 )) sub-shell, but inner-shell excitation is possible). The spread of the transferred energy (the width of the “window”) complicates the situation, and L2 ionization can happen after all if the L2 edge is in the “window”. (And even beyond it, because the realistic Gaussian energy distribution stretches out of the FWHM “window”.) For better understanding, consider the nominal energies for the studied Auger process in the (a) transferred energy “window” (Etr = 500 − 249.2 = 250.8; here and in the equations below the energy is given in eV):



2.2. The transferred energy “windows”



+ − e− 2p3/2 (248.6) + e− (2.2) p (500) + Ar → esc (249.2) + Ar ej



1



The energy transfer to the atom (Etr ) by the projectile electron equals to the difference of the primary and scattered electron energy:

 e.g. Ar++ 3p2

Etr = Ep − Esc

+ − − e− p (500) + Ar → eSC (249.2) + Ar [2p1/2 ] [250.8] + eej (0)

(1)

The value of the energy transfer determines the atomic processes which can be seen in the coincident spectrum. Inner-shell ionization is possible and the Auger peaks appear in the coincidence spectrum when the transferred energy (Etr ) equals or exceeds the corresponding ionization potentials (Eion ). The difference of these energies gives the kinetic energy of the ejected electron: Eej = Etr − Eion

(2)

The spread of this energy equals the spread of the transferred energy which is determined mainly by the energy resolution of the single spectrometer (since the energy spread of the electron beam is much smaller in our experiments): Etr (FWHM) ≈ Eej (FWHM) ≈ 0.009Esc

(3)

In strongly asymmetric energy sharing the two outgoing electrons (the scattered and the ejected ones) share the excess energy (Ep − Eion ) in a very asymmetric manner, i.e. the excess energy is taken away almost exclusively by the scattered electron (Eej ≈ 0; Esc ≈ Ep − Eion ). Therefore in our system the reduction of the energy spread of the detected electrons is possible by decreasing the transmission energy of the analyzers. The decrease of energy, however, decreases the probability of the Auger process and thus increases the measuring time.



D2



− (45.4) + eAu (203.2)

−  e.g. Ar++ 3p2 (1 D2 ) (45.4) + eAu (205.4)

(4a)

(4b)

During the measurements of the coincident Auger electron spectra we kept the coincidence condition of 249.2 eV, ensuring that nearly the total amount of the excess energy was taken away by the scattered projectile. Therefore the nominal energy of the ejected electron was close to zero (ejected from the L3 sub-shell) or exactly zero (ejected from the L2 sub-shell). Regarding the energy spread, too, the (−1.1 eV, +1.1 eV) interval (FWHM) would be possible in the latter case. Since negative kinetic energy is not possible, only half of the transferred energy “window” is used, namely the effective transmission of the coincident system for the L2 sub-shell compared to the L3 is 0.5 [11]. Decreasing the energy even further, the nominal energy of the electrons ejected from the L2 sub-shell becomes negative ((b) “windows”). In this case less then the half area of the Gaussian ejected energy “window” can be used by the ionizing electrons, so the effective transmission of the system for this sub-shell is less than 0.5 (Fig. 2). Fig. 1 also suggests that the accuracy of the transferred energy value (and its spread) is a key issue. Indeed, an error of some tenths of an eV is not allowable, because it can result a very different PCI effect and moreover it can result resonant Auger peaks in the

B. Paripás, B. Palásthy / Journal of Electron Spectroscopy and Related Phenomena 185 (2012) 602–608

Effective transmission

604

0

nominal ejectected energy

2.4. The shape of the Auger peaks

Etr

Eion

Energy

nominal transferred energy

Fig. 2. The transferred and the ejected (Eej = Etr − Eion ) energy Gaussian “windows” when the nominal energy of the ejected electrons is negative, but the ionization potential (Eion ) is still in the transferred energy “window”. The ejected electrons can only use the hatched part of the “window”.

coincident spectrum [15]. The transferred energy can be precisely measured, for example, by means of the 3s−1 outer-shell ionization in (e,2e) experiment [12]: + − − e− p + Ar → esc + Ar [3s] + eej

(5)

The energy of the Ar+ (3s−1 ) ionic state is 29.2 eV [16], so by knowing the kinetic energy of the ejected 3s electron (Eej ) the exact energy transfer to the atom (Etr ) can be calculated by Eq. (2). And by knowing the scattered projectile electron kinetic energy (Esc ) the exact primary energy (Ep ) can be calculated by Eq. (1). 2.3. The effect of the high-lying Rydberg states Fig. 1 does not show all the inner-shell excited states of Ar. Between the 4d state and the ionization edge there are a lot of (infinite number) unresolved excited states (Rydberg states). These states are formed mainly when the transferred energy “window” contains this energy interval. The oscillator strength density of these states goes smoothly into the continuum oscillator strength per unit energy interval [17]. It means also, that above the ionization potential the yield of the Auger spectra does not change suddenly, it can be seen well on the two dimensional photoelectron spectra [18]. The energy interval of high-lying Rydberg states is very small compared to the one of ionization, so their role in non-coincident Auger experiments is negligible. In our coincident experiments, however, this small interval can be increased and the role of high Rydberg states can become considerable. The decay of the [2p]nl Rydberg states is very similar to the decay of the [2p] ion states, because the effect of the distant Rydberg electrons is probably very small on the Auger process in the ion core. Due to their small shielding effect the energy of the outgoing Auger electron increases a bit. Their effect on the line shapes can be similar to the PCI effect of the low energy ionizing electrons. So the top of the Auger peaks are shifted by a few tenths of an eV towards the positive direction. It means, that above the ionization potential the shape of the Auger spectra does not change suddenly either it can also be seen well on the two dimensional photoelectron spectra [18]. The [2p]nl Rydberg states decay by Auger process into the resonant [3p2 ]nl final states. In this case the PCI effect is negligible because there is no low energy ejected electron. These final states, however, can be formed also when the transferred energy “window” is above the ionization potential. In such a case the low energy ionizing electron can be recaptured by the [3p2 ] double ion, which is the final state of the diagram Auger process [19]. This is the result of the energy exchange between the ionizing electrons and the Auger electrons, so it is a PCI effect. After all the [3p2 ]nl final states can be formed by PCI effect and without PCI effect as well.

In our previous experiments [1,2,11,12] we have successfully used the semiclassical eikonal approximation to describe PCI distorted, energy shifted, and asymmetric Auger-peak shapes. However at around the ionization threshold, when the energy of the ejected electron is very low, the conditions of the semiclassical approximation are not fulfilled. In these cases a more complete quantum mechanical description should be used for the description of the line shapes [20], but their application for the evaluation is quite difficult. Fortunately our experiences show us that the experimental spectra – even around the threshold – can be evaluated by the semiclassical line shapes [21]: y(E) = y0

k(, ε) , 1 + ε2

k(, ε) =

 exp(−2 arctan ε) sinh()

where ε =

(E − Enom ) , and 0.5L

(6) (7)

where y(E) is the electron intensity at energy E, y0 is a constant for a given kinematics, ε is the relative energy,  L and Enom are the natural line width and the nominal energy of the Auger electron. The k(, ε) function represents the PCI distortion of the Auger line, and the asymmetry parameter  is determined by the collision kinematics: =

1

vscA

−

1

vsc

+

1

vejA

−

1

vej

(8)

where vsc and vej are the velocities of the scattered projectile and the ejected electrons in the laboratory frame, while vscA and vejA are the corresponding velocities with respect to the Auger electron. We remark that over the validity conditions of the semiclassical theory, – in our case – the asymmetry parameter  is only a parameter for the fit, and it does not have the original meaning any more. The above equations are not valid, of course, also for the case when there is no ejected electron. Under the ionization threshold it is always true, but just above the threshold it is also possible if the electron is recaptured into a high-lying Rydberg state due to PCI effect. As we mentioned in the previous chapter, the decay of the [2p]nl high Rydberg states results resonant Auger peaks shifted by a few tenths of an eV towards the positive direction relative to the [2p] diagram Auger peaks. The series of the resonant Auger peaks can form a high energy “tail” on the diagram Auger lines, similarly to the “normal” PCI effect. It is impossible to separate this contribution from the “normal” PCI effect by the analysis of the peak shapes, so with the Eqs. (6)–(7) their common distortion effect can be approached. In this case the asymmetry parameter  has no kinematical meaning at all. In the computer fit of the Auger peaks and the quadratic background of the experimental spectra the PCI distorted line profiles were convoluted with a realistic spectrometer function. This slightly asymmetric function was derived from the measured energy distribution of the elastically scattered electrons at 500 eV primary energy. Its energy-dependent width was also treated as an adjustable fit parameter. At first, always the non-coincident spectrum was fitted at every scattered electron energy value. In the model spectrum the intensities and energies of the 10 diagram Auger lines were adjustable parameters, except for the triplets, where the intensity ratios and energy differences were fixed [22]. Both  and  L are common adjustable parameters for the diagram Auger lines. The very good statistics of the non-coincident spectra allowed the simultaneous fit of the typically 20 independent adjustable parameters and the results of the best fit were regarded as experimental values. In the coincident spectra, however, the statistics were not good enough, and the number of the adjustable parameters had to be minimized. Only the intensities and asymmetry parameters for the two sub-shells, the width of the

B. Paripás, B. Palásthy / Journal of Electron Spectroscopy and Related Phenomena 185 (2012) 602–608

3.2. Measurements in the (b) window (Ep ≈ 458 eV, Etr ≈ Eion (L3 ) = 248.6 eV)

10 2

L2-M

18 2

16

L3-M

2,3

1

S0

2,3

1

1

S0

D2

1

D2

3

P0,1,2

-2 3

9

3p ( P)4d

3

P0,1,2

6

Total yield [10 counts]

7

12

6

10

5

8

4

6

3

4

2

2

1

0

Coincidence yield [100 counts]

8

14

0 200

202

204

206

208

210

212

605

214

Electron energy [eV] Fig. 3. The total (non-coincident) electron energy spectrum (open square) and the one measured in coincidence with the 249.2 eV electrons (full circle) at 500 eV primary energy on Ar (the fitted model spectrum (thick solid line) and the spectrum components (thin solid lines) with its signs and the nominal energy values are also indicated).

spectrometer function and the background parameters were fitted, the other parameters were kept at the non-coincident values.

3. Results and discussion 3.1. Measurements in the (a) window (Ep = 500 eV, Etr = Eion (L2 ) = 250.8 eV) At 500 eV nominal projectile electron energy the L2,3 -M2,3 M2,3 Auger electron spectrum has been measured previously [11]. In that measurement, however, the inaccuracy of the transferred energy to the atom was quite big, it was estimated at 1 eV. Later [12] we introduced the energy calibration based on the Ar+ (3s−1 ) ionic state (described in Section 2.2) and decreased the error of the transferred energy to approx. 0.2 eV. Having this increased accuracy we returned to the primary energy, hoping for the retrospective corrections of previous energies. On the other hand our previous measurement at 350 eV primary energy was on the L2 ionization edge (Etr = Eion (L2 ) = 250.8 eV) and we wanted to return to this transferred energy, too. This new measurement fulfils both of our ambitions. In Fig. 3 the aggregated total (non-coincident) and coincident electron energy spectra are shown. The ratio of random coincidences was estimated by the correlation time spectrum and was kept below 35%. This contribution – proportionally to the primary counts – was removed from the experimental spectra. (See detailed description of the random coincidence removal at [13].) The spectrum contains a total number of counts of the order of 109 , and the measuring time was 20–25 days. The fitted model spectrum and the spectrum components are also shown in the figure. The numerical results of the best computer fit are given in Table 1 (Section 3.3). Here we remark that the background does not drop to zero at the high energy side of the coincident spectra (at 210–214 eV). This background, which is caused by the outer shell excited satellite states of Ar, is small here, but it becomes bigger at lower primary energy (see Section 3.2). This smooth background does not disturb the evaluation, especially when a small peak (or group of peaks) is put into the model spectrum at 212 eV. In [11] it was identified as the 3p−2 (3 P)4d group.

The resonant Auger lines were studied among others in a special experiment [23], where the energy of the scattered electrons fell also into the resonant Auger peaks energy region. At around 460 eV primary energy, besides the resonant Auger lines, the normal, but strongly PCI distorted Auger lines can also be seen. In this paper we study these spectra from the point of view of PCI. In Fig. 4 the total (non-coincident) and coincident Ar LMM Auger electron energy spectra are shown at two different primary energies around 458 eV. The coincident spectra were measured in coincidence with the 209.6 eV electrons. The satellite peaks, which appeared in the high energy tail of the Auger spectrum, catch our eye even at first glance. These lines are produced mainly by excited outer-shell ionic states. Without the elimination of these disturbing satellite lines we could not evaluate the spectrum. Fortunately, this contribution can be separately measured. Keeping the 209.6 eV coincidence condition, we decreased the primary energy to 442.4 eV, where inner-shell processes cannot be seen in the coincident spectrum (Etr = 232.8 eV  Eion ). This spectrum (with the non-coincident one) is shown in Fig. 5. We suppose that the coincident spectra of electrons from the outer-shells at 442.4 eV and at 458.3 (457.55) eV primary energies must be the same, except for an approximately 15–16 eV energy shift. Thus the 185–206 eV region of the coincident spectrum in Fig. 5, is the background of the coincident Auger spectra in Fig. 4, disregarding a factor, which is calculated from the ratio of the [3s] peak heights in Figs. 4 and 5. We note that the background below the 197.5 eV energy value is caused mainly by the electrons ejected during the creation of the Ar+ [3p2 ]4p excited ionic states and double ionic Ar++ [3p2 ] states. These latter electrons can interfere with the electrons coming from the two step Auger process. The possibility of this interference may influence the applied background subtraction. The “outher shell processes free” pure Auger spectra were obtained as the difference of the coincident spectra in Figs. 4 and 5 (disregarding a multiplication factor). These background free spectra are shown in Figs. 6 and 7. The fitted model spectrum and the spectrum components are also shown in the figures. In spite of the subtraction of the contribution of excited outershell ionic states, some small peaks are still seen at the high energy side of the spectrum and they do not correspond to diagram Auger lines. They can originate either from the error of the subtraction, or from resonant Auger decay. The decay from the 2p−1 (2 P1/2 )nl states to the 3p−2 (1 D)n’l final states (most probable state) [10,15]: 208.5 eV (2p−1 (2 P1/2 )3d → 3p−2 (1 D)4d), 210.7 eV (4p → 4p), 212.1 eV (4s → 4s). In case of 2p−1 (2 P3/2 )nl initial states these energies are about 2.1 eV smaller: 206.4 eV, 208.6 eV, and 210.0 eV. Some of these peaks were taken into account in the model spectrum to achieve a proper fit. 3.3. Conclusions and comparison to the previous results The evaluation of spectra has provided the numbers given in Table 1. For comparison the results of the previous measurements [11,12] are also given. Our old data match the new results well (it is shown also in Figs. 8 and 9) suggesting that the accuracy of the energy in [11] is much better (±0.2 eV) than it was previously estimated (±1 eV). The asymmetry parameter  values were obtained from the best fit. In accordance with our expectations the degree of asymmetry of the peaks in non-coincident spectra is much less then in the coincident spectra. It was visible even prior to the computer evaluation, since the coincident peaks have recognizable high energy tails and their maxima are shifted by some tenths of an eV

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B. Paripás, B. Palásthy / Journal of Electron Spectroscopy and Related Phenomena 185 (2012) 602–608

6 10

5

8

4

a.

3

6

Total yield [10 counts]

-1

3s

2

4 1 2

0 4

8 7

3

6

b.

5

2 -1

4

3s

Coincidence yield [100 counts]

6

1

3 2

0

1 200

202

204

206

208

210

212

214

216

218

220

222

Electron energy [eV] Fig. 4. The total (non-coincident) electron energy spectrum and the one measured in coincidence with the 209.6 eV electrons (a) at 458.3 eV and (b) at 457.55 eV primary energy on Ar (the data of the coincidence spectrum, marked by error bars, do not contain the random coincidences).

6

Total yield [10 counts]

6

-1

3s

8

background

5

7 4

6

3

5 4

2

3 1

2 1

0 186 188 190 192 194 196 198 200 202 204 206 208 210 212 214

Coincidence yield [100 counts]

9

Electron energy [eV] Fig. 5. The total (non-coincident) electron energy spectrum (thin line) and the one measured in coincidence with the 209.6 eV electrons (with error bars) at 442.4 eV primary energy for Ar, without random coincidences (the thick line is considered the background of the Auger spectrum).

12

6 2

11

L2-M 2

L3-M 10

2,3

2,3

1

S0

1

1

D2

3

1

S0

P0,1,2

D2

3

P0,1,2

5

7

6

Total yield [10 counts]

4

8

3

?

6 5 -1 2

4

2p ( P1/2)4p

-2 1

3p ( D)4p

2

3 1

2

Coincidence yield [100 counts]

9

1 0 200

0 202

204

206

208

210

212

214

216

218

220

Electron energy [eV] Fig. 6. The background free (see in the text) coincidence electron spectrum at 458.3 eV primary energy for Ar measured in coincidence with the 209.6 eV electrons (full circle). The fitted model spectrum (thick solid line), the spectrum components (thin solid lines) with its signs at the nominal energy values, and the total (non-coincident) energy spectrum (open square, dashed line) are also shown.

B. Paripás, B. Palásthy / Journal of Electron Spectroscopy and Related Phenomena 185 (2012) 602–608

607

Table 1 Experimentally determined and calculated parameter values of the non-coincident and coincident Auger spectra measured at different nominal energy conditions on Ar (See also the text). Primary en. (eV)/ transmitted en. (eV) (error ±0.2 eV)

Eej = Etr − Eion (L2 )/ Eej (L3 ) (eV) (±0.2 eV)

Asymm. of non-coinc peaks ()

Asymmetry of L2 peaks ()

Asymmetry of L3 peaks ()

Teff (L2 )/Teff (L3 )(calc.)

Teff (L2 )/Teff (L3 )(exp.)

500/251.5 (252) 500/249.5 (250) 500/250.8 350/250.8 458.3/248.7 457.55/247.95

0.7/2.8 −1.3/0.8 0/2.1 0/2.1 −2.1/0 −2.85/−0.75

−0.45(±0.03) −0.45(±0.03) −0.42(±0.03) −1.85(±0.1) −0.59(±0.05) −0.68(±0.05)

−4.0 (±0.4) −10.4 (±1.1) −4.6 (±0.4) −4.0 (±0.4) −12 (±3) −28 (±6)

−2.0 (±0.1) −3.9 (±0.1) −2.4 (±0.2) −3.0 (±0.2) −3.9 (±0.4) −5.7 (±0.5)

0.77 0.11 0.51 0.51 0.04 <0.01

0.96(±0.03) 0.61(±0.06) 0.86 (±0.06) 0.84 (±0.06) 0.45 (±0.06) 0.29 (±0.06)

10 2

L2-M 2,3 1S

9

2

L3-M

S0

D2

4.0

3

1

P0,1,2

D2

0

1

3

P0,1,2

3.5

Total yield [10 counts]

7

-1 2

3.0

-2 1

2p ( P1/2)4s

3p ( D)4s 2.5

6 -1 2

6

2p ( P1/2)4p

5 4

-1 2

-2 1

3p ( D)4p

2.0 1.5

-2 1

2p ( P1/2)3d

3p ( D)4d

3

1.0

2 0.5

Coincidence yield [100 counts]

8

1 2,3

1 0.0 0 200

202

204

206

208

210

212

214

216

218

220

Electron energy [eV] Fig. 7. The same as in Fig. 6, but measured at 457.55 eV primary energy.

in the positive direction. The asymmetry parameter of the noncoincident peaks depends on the primary energy. This had been studied previously in detail [1]. The coincidence condition cannot take effect on the non-coincident spectra, of course. This effect, however, is the most important factor on the coincidence spectra,

therefore their asymmetry parameters are determined mainly by the transmitted energy to the atom (thus by the ejected electron energy). This experimental relation, together with our calculations according to [11], is shown in Fig. 8. Our previous result [1] – that the absolute value of the average asymmetry parameter

1.0

Nominal ejected electron energy [eV] -3

-2

-1

0

1

2

0.9

3

0 0.8

-2 -4

-8 -10 -12 -14

Asymmetry parameter

-6

-16

Fig. 8. The experimental asymmetry parameter values (taken from the best fit of the measured coincidence spectra) as the function of nominal ejected electron energy. Fitted curve to the experimental points (thick solid line) and comparison to calculations according to [11] (thin solid line).

Teff(L2)/Teff(L3)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 247

248

249

250

251

252

253

Transmitted energy eV Fig. 9. The effective transmission ratio (experimental points: full squares with error bars) as the function of transmitted energy. Comparison to the calculations for diagram Auger transitions (thick solid line with open squares) with the possible shifts (thin solid lines) which can be caused by the error of transmitted energy (±0.2 eV). The difference of the measured and calculated ratios (open circles with error bars) is considered as the contribution of the resonant Auger decays.

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is necessarily higher than the experimental one – is confirmed again. The last two columns of Table 1 contain the ratios of effective transmissions of the system for the two sub-shells. In the course of calculation only the inner shell ionization (thus the diagram Auger transitions) is considered (Section 2.2). The experimental effective transmission ratio of the system for the given sub-shells is obtained from the comparison of the peak areas of the coincident and noncoincident Auger spectra. For example, if the ratio of the intensity sums of the 5–5 Auger lines originating from L2 , and L3 is 0.51 in the non-coincidence spectrum, and 0.43 in the coincidence spectrum, then the ratio is 0.84 (Ep = 350 eV, Etr = 250.8 eV). The ratios of these values for two sub-shells (Teff (L2 )/Teff (L3 )(exp.)) are also given in the table. The experimental ratios are far above the calculated ones, namely the Auger peak intensities are decreasing when approaching the ionization limit, but the decrease is less than expected. We experienced this in the previous measurements [11,12], too, but we did not know the reason. Now we believe that the resonant Auger decay of the inner shell excited high Rydberg states can cause this effect. Just below the ionization threshold these excitations (e.g. 2p → np, 2p → nd (n > 4), etc.) can occur with significant probability when the transferred energy “window” contains these high Rydberg states (see Section 2.3). The decay of these states produces Auger peaks with a bit greater energy than the corresponding diagram Auger lines. The series of these resonant Auger peaks forms a high energy “tail” for the diagram line, in the same way as the PCI effect. This spectrum contribution reduces the decrease of the Teff (L2 )/Teff (L3 )(exp.) ratio around and below the L2 ionization potential. The difference of the measured and calculated ratios can be caused by this contribution. The maximum of this contribution – as shown in Fig. 9 – is around 250 eV transferred energy, which is close to the possible positions of [2p1/2 ] Rydberg states. The energy, below which the [2p1/2 ] resonant Auger contribution exceeds the [2p1/2 ] diagram Auger contribution is just below the Eion (L2 ) energy, as it is expected. When the contribution of the resonant Auger peaks (originating from [2p1/2 ] excited Rydberg states) is big in the combined peak, its shape must be different from the shape of the PCI distorted diagram Auger line (described by Eqs. (6)–(7)). This is the real reason of our

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