u) colliding with carbon foils

NIM B Beam Interactions with Materials & Atoms

Nuclear Instruments and Methods in Physics Research B 256 (2007) 510–514 www.elsevier.com/locate/nimb

In-flight emission of projectile Auger electrons from highly energetic heavy ions (20 MeV/u < E < 100 MeV/u) colliding with carbon foils G. Lanzano`

a,*

, E. De Filippo a, S. Hagmann b, H. Rothard c, C. Volant

d

a

c

Istituto Naz. Fisica Nucleare and Dipartimento di Fisica, Via S. Sofia 64, I-95123 Catania, Italy b IKF, University of Frankfurt and GSI, Darmstadt, Germany CIRIL-Ganil (CEA/CNRS/ENSICAEN/Universite´ de Caen), BP 5133, F-14070 Caen Cedex 05, France d DAPNIA/SPhN, CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, France Available online 30 December 2006

Abstract Highly energetic projectiles (20 MeV/u < Ebeam < 100 MeV/u), which have been collisionally excited during penetration of thin solid foils, can deexcite by emission of Auger electrons. These in-flight emitted fast electrons are observed in the laboratory system with a velocity intermediate between vbeam (the ion beam velocity) and 2vbeam. Results obtained both at the Catania LNS superconducting cyclotron CS with 58Ni14+,19+ (23 and 45 MeV/u) and at Ganil with 78Kr32+,34+ (64 MeV/u) are presented. Absolute emission cross-sections and kinematic properties are discussed. Ó 2006 Elsevier B.V. All rights reserved. PACS: 34.50.Fa; 79.20.Rf; 25.70.z Keywords: Fast electrons; Absolute cross-section; High incident ion energy; In-flight Auger electron emission; KLL and LMM Auger transitions

1. Introduction Only few experiments have been dedicated to fast electron emission in collisions of swift highly charged ions with matter in the incident energy range between 20 MeV/u and 200 MeV/u [1–9]. The knowledge of e.g. absolute production cross-sections as a function of electron velocity and emission angle are important for testing atomic ionization and electron transport theories and in many applications of atomic and nuclear physics [10,11]. We refer the reader to [12] for a comprehensive overview on results obtained so far. Fast-electron velocity spectra exhibit three main distinct components [12]. Convoy electrons (CE) form a sharp cusp-like peak around 0° with a velocity close to the beam

*

Corresponding author. Tel.: +39 095 3785359; fax: +39 095 3785231. E-mail address: [email protected] (G. Lanzano`).

0168-583X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.12.099

velocity vbeam. Binary encounter electrons (BEE) are emitted in the forward direction with a velocity 2vbeam cos #lab. Finally, mostly weaker electron peaks from in-flight projectile Auger electron emission are in some cases observed at a velocity intermediate between vbeam and 2vbeam. In the following, we focus on this latter component of fast electron spectra at high incident energies. We pay particular attention to the most recent data obtained at Ganil with the Kr beams. 2. Experimental procedure Thin carbon targets have been bombarded by pulsed beams delivered both by Ganil 78Kr32+,34+ (64 MeV/u) and Catania CS 58Ni14+,19+ (23 MeV/u and 45 MeV/u). The burst-width of both beams was about Dtbeam  1 ns. To exploit the opportunity of large flight-paths (2–4 m) the big-volume scattering chambers Nautilus (Ganil) and

G. Lanzano` et al. / Nucl. Instr. and Meth. in Phys. Res. B 256 (2007) 510–514

3. Intermediate velocity Auger electrons and their kinematics Intermediate velocity electrons (IVE) with velocity between vbeam and 2vbeam fill the gap between the BEE and the CE peaks. In-flight emitted projectile Auger electrons can be observed as distinct peaks superimposed on a background of ionization electrons with a continuous velocity distribution related to electron transport in the solid [13,14,5]. Pioneering experiments on this subject at lower heavy ion incident energies are reported in [15–17]. Auger electron emission is the dominant decay channel allowing ions to deexcite especially for low atomic number ions. At least 2 electrons (and a vacancy) are involved. The energy of e.g. KLL Auger transitions (which yield the most energetic Auger electrons) can be calculated in a frozen core approximation as E0KLL ¼ E0K  E0L1  E0L2 :

ð1Þ

Here E0K and E0L1,2 are the ionization energies for a Kshell and an L-shell electron in the emitting excited ion, respectively, using Dirac–Fock approximation. They depend upon the atomic configuration at the moment of the Auger transition. Therefore, they can differ significantly from the values tabulated for neutral atoms. Other transitions, like LMM and MNN leading to emission of less energetic electrons are also possible. Of course, the emission cross-sections of in-flight Auger electrons depend strongly on the atomic configuration of the incident ion (i.e. the population of excited states). This last point is crucial, as can be seen in Fig. 1, where the fast electron timeof-flight spectra are shown for two 78Kr beams of the same incident energy, 64 MeV/u, but two different charge states, q = 32+ and q = 34+, respectively. Note that in the case of 78 Kr34+ (an ion with only two electrons) the KLL-Auger component of the spectrum has been completely suppressed, while the BE component is practically unchanged

400

350

63.7 MeV/u

78

64.1 MeV/u

78

250

Kr32+ + C (6.3 μg/cm2) Kr

34+

2

+ C (6.3 μg/cm )

Convoy

Θ=3.8o

300

Yield

Ciclope (LNS, Catania) were used. Fast plastic scintillators from the ARGOS multidetector were used as detectors at forward angles between 2° and 50°. Electron velocity spectra were obtained by measuring the electron time-of-flight tflight from the target to the detector with a relative resolution given by Dv/v  Dt/tflight. The time-of-flight tflight depends on both the electron energy and the distance between target and detector. Consequently, also the velocity resolution varies between, say, 2% and 5% for the results presented in this paper. For relative electron time-of-flight measurements the pulsed beam radiofrequency was used as a start and the fast photomultiplier output as a stop. The prompt target X-ray peak and the absolute calibration of the time-to-digital converter were used to obtain (off-line) the absolute electron time-of-flight. Electronic thresholds set a limit to the detection of low-energy electrons of typically vthr = 7– 8 cm/ns corresponding to energy of 20 keV. For more experimental details see [12] and references therein.

511

BE

200

150

100

Auger

50

0 400

425

450

475

500

525

550

575

600

Time-of-Flight (arb. units) Fig. 1. Time-of-flight spectra for fast electrons emitted in the laboratory system at 3.8°. The collision systems are: 78Kr32+ + C at 63.7 MeV/u (black-line histogram) and 78Kr34+ + C at 64.1 MeV/u (grey-line histogram). The carbon target thickness is 6.3 lg/cm2. The binary encounter (BE), KLL-Auger and convoy components of the spectra are indicated.

and the CE component is drastically reduced, with respect to the case of the 78Kr32+ (an ion with four electrons). The second important point is given by the kinematic transformation of electron-velocity and electron-yield from the projectile frame of reference to the laboratory frame. We suppose in the following that an electron is emitted isotropically in the rest frame of the projectile with velocity v0 and energy E0. Following forward (h0 6 90°) or backward (h0 P 90°) emission in the projectile rest frame, one obtains two kinematical solutions at the same angle hlab of the laboratory system, when in the emitter frame v0 < vbeam. The corresponding x and y velocity-components are given by [18] bxlab ¼

bbeam  bx0 1 þ bbeam bx0

bylab ¼

by0 : cbeam ð1 þ bbeam bx0 Þ

ð2Þ

In these equations the electron velocity, blab. , is in qexpressed ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  units of the velocity of light c and cbeam ¼ 1 1  b2beam . Two main consequences follow from these equations. First, electrons are observed in the laboratory system (see below) only in a restricted angular range from 0° up to a limiting angle hlim, depending mainly on vbeam and the electron velocity v0 in the emitter frame. For a given v0, electrons are emitted isotropically in the laboratory system if vbeam  0. They are then focused into a certain angular range, which decreases as vbeam increases. Second, at a fixed observation angle hlab Auger electrons can be expected at two different velocities in the laboratory frame corresponding to forward or backward electron emission in the projectile frame. This follows from the addition of the velocity vectors of ejected electron and projectile, respectively.

G. Lanzano` et al. / Nucl. Instr. and Meth. in Phys. Res. B 256 (2007) 510–514

The velocity (energy) difference of the corresponding two peaks is maximum at 0° and equals 0 at the limiting angle (v1 = v2 = vbeam). Finally, if r0 (supposed constant and independent from the emission angle in the projectile frame) and rlab are the cross-sections of the Auger electron emission process in the projectile frame and in the laboratory frame, respectively, at an angle hlab, we find [18] rlab r0 1 ¼ : 1=2 c2beam ðcos hlab  blab Þ þ sin2 hlab cbeam ð1  blab cos hlab Þ ð3Þ

The approximation vCM = vbeam has been made for the system (electron – residual ion). Following this equation, the behaviour of this ratio is expected to slightly and monotonously increase starting from 0°. At the highest, limiting angle hlim it diverges. 4. Results In order to obtain the angle-dependent Auger electron yield, we need to subtract the background, since the Auger peaks are superposed on the high-energy side of the convoy peak. The deduced area (i.e. the yield) is sensitive to the integration interval and to the method used to subtract the background. In the case of Kr at 64 MeV/u (Fig. 1) where a very thin target has been used, the subtraction of the background did not present particular difficulties. The KLL Auger peak is sitting on the high-energy tail of the convoy peak. The area has been obtained by fitting a Gaussian distribution to the Auger peak and a linear function to the background. For the Ni-case (see also [6,12]) the estimation of the background has been more difficult, especially for those cases where the Auger peak was small with respect to the CE peak. The use of more complicated fitprocedures was necessary in some cases (two exponential functions plus a Gaussian, for example). The absolute values of the Auger electron ejection cross-sections are reliable within 20%–30%. We also note that the detection threshold of the scintillators at about 20 keV does not allow to observe the low-energy Auger electron peak (the lowenergy second solution of Eq. (2), corresponding to backward emission in the frame of the projectile). 4.1. The

78

Kr32+ projectile at 63.7 MeV/u

Fig. 2 shows the KLL Auger electron velocity as a function of the observation angle. Three series of data are shown. The detectors were placed on the one hand in the horizontal plane passing through the target at both sides with respect to the beam direction and on the other hand in a plane perpendicular to it. The experimental data taken in different half-planes with respect to the beam axis are very consistent amongst themselves from 2° up to 20°.

20

63.7 MeV/u

78

32+

Kr

2

+ C (12 μg/cm )

18

KLL Auger velocity (cm/ns)

512

16

14

12

Vbeam 10

8

Detection threshold

6 0

5

10

15

20

25

30

ΘLab (deg.) Fig. 2. The most probable KLL-Auger electron velocity is reported as a function of the laboratory angle. The collision system is: 78Kr32+ + C at 63.7 MeV/u. The carbon target thickness is 12 lg/cm2. The beam velocity and the detection threshold (shadowed area) are indicated. The line is the result of a kinematical calculation adapted to the data from Eq. (2). Open symbols are relative to detectors in a horizontal plane passing through the target, full circles belong to detectors in a vertical plane passing through the target and 0°.

No Auger electron peak is observed beyond 30°. The best agreement between experimental points and the prediction of kinematics is obtained by putting E0 = 9 keV in Eq. (2). This value is indeed in good agreement with a predicted value (see Eq. (1) and [19]) of E0KLL  9 keV. At the present time, however, the origin of the discrepancy observed for the last two data points at 27° and 30°, respectively, is not yet explained. Fig. 3 shows the absolute KLL Auger electron ejection cross-section as a function of the laboratory angle. The cross-section is rather constant with an average value of 4.5 kb from 2° up to 20°. This corresponds to almost 10% of the BEE ejection cross-section in the same angular range. An increase of the cross-section is observed starting from 20°. The prediction of the kinematics under the assumption that KLL Auger electrons are emitted isotropically in the projectile rest-frame from Eq. (3), is also reported. The calculated values were arbitrarily normalized to the cross-section at the most forward angles. The predicted behaviour is that the cross-section slightly increases with the laboratory angle. It increases by only 10% from 2° to 15°, reaches 30% at 20°, 50% at 23° and finally becomes more and more diverging approaching hlim. In our experimental data there is, however, no hint for a diverging trend close to the limit angle, in contrast to the prediction of Eq. (3). Nevertheless, an appreciable deviation from a constant value is visible in the data starting from 20°. More precise data, with a better resolved angular distribution close to

G. Lanzano` et al. / Nucl. Instr. and Meth. in Phys. Res. B 256 (2007) 510–514 30

16 63.7 MeV/u

78

32+

Kr

a

2

+ C (12 μg/cm )

58

19+

Ni

+C

KLL LMM

8 20

Intermediate Velocity (cm/ns)

3

45 MeV/u

12

25

KLL Auger dσ/dΩ (10 b/sr)

513

15

10

5

4

0

0

5

10

15

20

25

30

35

40

45

40

45

16

b

58

22.7 MeV/u Ni

14+

+C

12

8 0

0

10

20

30

ΘLab (deg.) Fig. 3. The singly differential cross-section for the KLL-Auger electron velocity component as a function of the detection angle. The collision system is 78Kr32+ + C at 63.7 MeV/u (target thickness: 12 lg/cm2). The line is the result of a kinematical calculation from Eq. (3) normalized to the most forward angles data. Symbols as in Fig. 2.

the limiting angle are needed to test the hypothesis of isotropic emission of KLL Auger electron in the projectile reference frame. In this respect, it is interesting to note that recently nuclear physics experiments in the same range of incident ion energies have shown evidence that light charged particles are indeed not emitted isotropically from the highly excited projectile or projectile-like systems [20]. 4.2. The

58

Ni14+,19+ beams at 23 MeV/u and 45 MeV/u

Fig. 4(a) and (b) show the Auger electron velocity as a function of the detection angle for the 58Ni beam, respectively at 45 MeV/u (q = 19+) and 23 MeV/u (q = 14+). KLL Auger electrons have been observed in both cases [12,7,6]. The electron emission energy in the projectile frame is found to be E0KLL = 5.1 and 5.7 keV, respectively. Simple calculations (Eq. (1) and [19]) predict a value of ’6.1 keV in reasonable agreement with the observed values. The slight discrepancy is due to the more complex electronic configuration of the Ni ions compared to the Kr ions. Therefore, the electron binding energies before emission cannot be calculated with the same accuracy. The observed values are consistent qualitatively with the fact that electron binding energies are higher for a Ni ion with charge state of q = 14+ than for q = 19+. Kinematical calculations predict a broader angular range of emission for the slower Ni ion beam. This is indeed observed experimentally, though no Auger electrons are observed in the vicinity of the limiting angle in both cases. Probably, the corresponding electron velocity falls below the detection

4

0

0

5

10

15

20

25

30

35

ΘLab (deg.) Fig. 4. The most probable KLL-Auger electron velocity as a function of the laboratory angle (full points). The collision systems are: (a) 58 Ni19+ + C at 45 MeV/u and (b) 58Ni14+ + C at 22.7 MeV/u. The target thickness is 23 lg/cm2 and 21 lg/cm2, respectively in (a) and (b). Also shown is in (a), a data point corresponding to LMM-Auger electron ejection (solid square). The lines are the result of a kinematical calculation adapted to the data from Eq. (2) for both KLL and LMM Auger transitions.

threshold and/or the peak is too broad to be unambiguously identified (see for instance Fig. 5 of [6]). Some discrepancy from kinematical predictions is also observed in the angular range starting from 13°. In the explored angular range, KLL Auger production cross-section are almost constant at about 12 kb (30% of the BEE peak) and 1.5 kb (1% of the BEE peak) at 45 MeV/u and 23 MeV/u, respectively. Probably, the initial electronic configuration of the Ni ions with charge state q = 14+ favours LMM Auger emission with respect to KLL Auger transitions. LMM Auger electrons should be emitted with an energy of about 300 eV in the projectile frame. Therefore, it is unlikely that they could be observed in the laboratory system at 23 MeV/u because of the detection threshold. In contrast, at 45 MeV/u LMM Auger electrons could be observable in the laboratory system very close to the CE peak. However, in this case with a Ni ion charge of q = 19+ LMM transitions are not favoured by the initial electronic configuration of the ions. In fact, a LMM transition could occur only after a previous transfer of two electrons to the M shell. Furthermore, the observation of the angular distribution of LMM Auger electrons would be restricted to the most forward angles (see Fig. 4). Nevertheless, this transi-

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tion is observed at 2° as shown in Fig. 4 (see also the component IV2 in Fig. 2 of [12]) with an ejection production cross-section of about 3 kb (7% of the BE peak). 5. Conclusions Auger electrons from in-flight deexcitation of highly excited ions are observed in the interaction of highly energetic ions (20 MeV/u < E < 100 MeV/u) with thin carbon foils. They are emitted with a velocity intermediate between the beam velocity and two times the beam velocity, in a certain angular range in the laboratory system given by basic laws of kinematics. At a given laboratory angle, forward and backward emission in the projectile frame leads to emission of Auger electrons at two different velocities below and above the projectile velocity. Due to detection threshold effects, only the higher velocity component of the two peaks is observed in the present experiment. The velocity of this component decreases as a function of the laboratory angle, reaching almost the beam velocity close to the limiting angle. KLL Auger electron emission is influenced by the initial electronic configuration of the projectile. As expected, no KLL transitions have been observed for 78Kr34+ at 64 MeV/u. 58Ni14+,19+ (23 and 45 MeV/u) show evidence for important KLL Auger electron ejection with a crosssection of up to 30% of the BEE ejection cross-section. Since this BEE ejection cross-section is proportional to the target atomic number [13,9], the KLL production cross-section is comparable to and in some cases even more important than BEE ejection, depending on the collision system. In particular, 58Ni19+ has a favourable electronic configuration with initially two electrons in the K shell and seven electrons in the L shell and therefore is an important source of KLL Auger electrons (more than 30% of the BEE emission at the same angle). The KLL Auger crosssection is almost a factor of 2 larger than the BEE crosssection in a single interaction with a target electron. At the most forward angles, the emission of LMM Auger electron from the same ion is also observed. The KLL Auger electron production cross-section as a function of the laboratory angle is in general rather constant. A divergency close to the limit angle is predicted by kinematical calculations under the hypothesis that KLL Auger electrons are emitted isotropically in the projectile frame. This divergency is not observed experimentally for the collision system 78Kr32+ on C foil at 64 MeV/u. More refined experiments are required to clarify this point. Acknowledgements We would like to thank the CS and Ganil staff for providing Ni and Kr beams of good quality, N. Giudice, N.

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