Zero-degree target electron spectroscopy: autoionizing resonances of helium excited by fast H +, He + and He 2+ impact

Transcription

1 INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS J. Phys. B: At. Mol. Opt. Phys. 35 (2) PII: S (2) Zero-degree target electron spectroscopy: autoionizing resonances of helium excited by fast H +, He + and He 2+ impact R Bruch 1,HWang 1, A L Godunov 2,PBIvanov 3, V A Schipakov 3 and H Merabet 1 1 Department of Physics, University of Nevada Reno, Reno, NV 89557, USA 2 Department of Physics, Tulane University, New Orleans, LA , USA 3 Troitsk Institute for Innovation and Fusion Research, Troitsk, 1492, Russia Received 9 August 1, in final form 15 February 2 Published 26 March 2 Online at stacks.iop.org/jphysb/35/1617 Abstract Two-electron excitation and decay of the autoionizing (2p 2 ) 1 D and (2s2p) 1 P states of helium in collisions with fast protons and helium ions have been studied using zero-degree target electron spectroscopy. The energy resolution of electron emission spectra is 8 mev. Experimental spectra were processed using a parametrization with allowance for the Coulomb interaction in the final state (CIFS) between the ejected electron, the scattered ion and the recoil helium ion. The Shore formula was applied as well. Calculations have been carried out with inclusion of CIFS in both direct and resonant ionization amplitudes and within an expansion of a two-electron excitation amplitude in powers of projectile target interaction up to the second order. Influence of the three-body Coulomb interaction and effects of the charge and mass of the projectiles are studied. 1. Introduction Autoionization resonances in electron emission spectra of helium excited by the fast charged particle impact have been actively studied experimentally and theoretically since the early 197s (see Stolterfoht 1987, 1991, Schulz 1995, Godunov et al 1997b and references therein). Since the first works (Rudd 1964, Boredenave-Montesquieu and Benoit-Catten 1971, Stolterfoht 1971, Schowengerdt and Rudd 1972), electron spectroscopy has been considered as the most powerful method for studying autoionizing resonances in cross sections of ionization. Electron spectroscopy of autoionizing resonances has the important virtue of high energy resolution and the availability of a number of parametrizations for different kinematic regions (Fano 1961, Shore 1967, Balashov et al 1973, Godunov et al ). Studying autoionization resonances in ionization cross sections integrates a number of traditional problems in atomic physics, namely, electron correlation, Fano interference between /2/ $3. 2 IOP Publishing Ltd Printed in the UK 1617

2 1618 R Bruch et al resonant (via autoionizing states) and direct ionization amplitudes, two-electron excitation, post-collision interaction (PCI) or the Coulomb interaction in the final state (CIFS) between the ejected electron, the scattered ion and the recoil ion. Beginning with the first Born calculations (Balashov et al 1973), the theory of autoionizing resonances in electron emission spectra excited by charged particle impact has become more and more elaborated. Thus, calculations for autoionizing resonances of helium excited by ion impact have been carried out with highly correlative wavefunctions (Bachau et al 1991, Moribayashi et al 1991), along with semiclassical coupled channel equations (Martin and Salin 1995, Morishita et al 1994) and the second Born approximation (Godunov et al 1991) for double electron excitation. The CIFS was included in both the resonant and direct ionization amplitudes (Godunov et al 1989). However, these calculations did not get overall satisfactory agreement with experimental data, particularly for the forward electron emission angles where CIFS is considerable. Considerable progress has been made in a joint experimental and theoretical study of excitation of lowlying autoionizing (2s 2 ) 1 S, (2p 2 ) 1 D and (2s2p) 1 P states of helium by kev proton impact (Moretto-Capelle et al 1997, Godunov et al 1997b, ). It was clearly demonstrated that an adequate solution must accurately account for all the important effects (electron correlation, Fano interference, CIFS, two-electron excitation). A new parametrization of resonance profiles has been theoretically suggested (Godunov and Schipakov 1993) that generalized the standard Shore formula to the case of significant CIFS influence. While providing a good fit to the experimental spectra (Moretto-Capelle et al 1996), this parametrization also allowed us to extract the cross sections of autoionizing state excitation, which was deemed impossible only a decade ago. Theoretically calculated parameters of resonances were in a reasonable agreement with those derived from experimental data, considering the complexity of the problem. Generally, the many-body problem is one of the most challenging problems in atomic physics (McGuire 1997). The CIFS is an example of the many-body problem in the continuum. In experimental studies of autoionizing resonances in electron emission spectra quasi-periodic changes of the shape of helium resonances for forward electron emission angles have been observed (Schowengerdt and Rudd 1972, Stolterfoht et al 1972, Bordenave-Montesquieu et al 1975). Moreover, when the relative velocity between the scattered ion and the ejected electron is small, the resonance profiles may be very different from the Fano shape (Arcuni and Schneider 1987, Moretto-Capelle et al 1996). It has been suggested that this behaviour might be determined by the Coulomb interaction between the ejected electron and the scattered proton. Subsequent theoretical studies supported this conjecture (Godunov et al 1989). In this work we exploit the zero-degree target electron spectroscopy method for studying autoionizing resonances of helium excited by ion impact. This method has an important advantage of high energy resolution (Bruch et al 1987, Wang et al 1993). Besides, the CIFS is stronger for small emission angles. Using different projectiles may provide additional information about collision mechanisms 4 (Toburen et al 1981, Itoh et al 1985, Wang et al 1993, Wang 1993). Experimental studies of autoionizing resonances of helium excited by fast electrons, protons, He +,He 2+,Li q+ (q = 1 3), C q+ (q = 4 6) and Fe q+ (q = 7 9) ions (Prost 1978, Arcuni 1986, Arcuni and Schneider 1987, Pedersen and Hvelplund 1989, Giese et al 199) revealed a well observed effect of the projectile charge on the resonance shape in a broad region of collision energies ( kev amu MeV amu 1 ) and electron emission angles ( 16 ). However, these studies had low energy resolution, which, together with the absence of an appropriate 4 It is worth noting that studying autoionizing resonances in ionization cross section as a function of the projectile scattering angle (Htwe et al 1994, Schulz et al 1995) can provide information on mechanisms of double electron excitation which cannot be determined in electron spectroscopy experiments. However, currently the resolution in such experiments is about one order lower than in electron spectroscopy.

3 Zero-degree target electron spectroscopy 1619 parametrization for the regions of strong CIFS, did not allow us to properly approach the problem. Insufficient resolution masks important details, like CIFS distortion, overlapping resonances etc. Much of the theoretical research on the projectile charge effects in excitation of autoionizing resonances (Fritch and Lin 199, McGuire and Straton 1991, Moribayashi et al 1991, Martin and Salin 1994) was centred around studying mechanisms of two-electron excitation. But for a reasonable comparison of theoretical results with experimental data a theoretical model should include interference of direct ionization with resonance transitions distorted by CIFS. In this work, we present a high-resolution study of autoionizing resonances of helium in electron spectra emitted in the forward direction after excitation by proton, He + and He 2+ ion impact. The collision velocities involved imply strong CIFS influence on resonance profiles. The new parametrization (Godunov and Schipakov 1993, Godunov et al 1997b) is employed for processing the measured spectra. Using the equivelocity projectiles may shed light on the dependence of resonance phenomena on the charge and mass of the projectile. 2. Basic formulae Our approach is based on a theory of atomic ionization by charged particles that has been described elsewhere (Godunov et al 1989, ). Here, we only present the key formulae used for data analysis and discussions in the other sections. The doubly differential cross section (DDCS) of ionization as a function of electron emission energy E e and emission angle θ e in the vicinity of autoionizing resonances can be written as (Godunov et al ) d 2 σ = F(E e,e i,ϑ e ) + ρ µ (ε µ ) de e d e µ εµ 2 +1{Ac int,µ (E i,ϑ e ) [ε µ cos ϕ µ (ε µ ) + sin ϕ µ (ε µ )] + Bint,µ c (E i,ϑ e ) [cos ϕ µ (ε µ ) ε µ sin ϕ µ (ε µ )]+Bexc,µ c (E i,ϑ e )ρ µ (ε µ )}, (1) where A c int,µ (E i,ϑ e ), Bint,µ c (E i,ϑ e ) and Bexc,µ c (E i,ϑ e ) are the resonant parameters, ρ µ (ε µ ) and ϕ µ (ε µ ) are the kinematic factors, ε µ = 2(E e E µ )/ Ɣ µ is the relative energy deviation from the resonance position E µ, E e is the ejected electron energy and Ɣ µ is the resonance width. The exact definitions for the resonance parameters, as well as the kinematic factors, can be found in Godunov et al (1997b, ). For an alternative representation, one can introduce a phase parameter δ µ (E i,θ e ) between the amplitudes of direct and resonant ionization as (Godunov et al ) δ µ (E i,θ e ) = arctan Bc int,µ (E i,θ e ) A c int,µ (E + πn (n =, 1,...). (2) i,θ e ) In the triply differential cross section the phase parameter δ µ (E i,θ e,θ f ) has a clear meaning of relative phase between the direct and resonant ionization amplitudes. On the other hand the phase parameter δ µ (E i,θ e ), which can be defined from the DDCS, is not the straightforward relative phase since the interference terms in A int (E i,θ e ) and B int (E i,θ e ) result from an integration over the scattering angle. Using the definition (2) one can rewrite equation (1) as d 2 σ = F(E e,e i,ϑ e ) + ρµ 2 (ε µ)b exc,µ (E i,ϑ e ) de e d e µ εµ 2 +1 {1+R µ (E i,ϑ e )[ε µ cos ω µ (E i,ϑ e ) + sin ω µ (E i,ϑ e )]}, (3) with ω µ = δ µ + ϕ µ. Parametrization (1), or (3), accounts for distortion of resonance profiles by CIFS.

4 16 R Bruch et al For fast ion atom collisions, the above kinematic factors can be calculated in the eikonal approximation (Godunov et al 1997b, ): ρ µ (ε µ ) = exp( ξ arctan ε µ ), ϕ µ (ε µ ) = ξln(εµ 2 +1)/2, (4) with ξ = Z ( ) p v f Z i, (5) v f v f v e where Z p and Z i are the charge of the projectile and the recoil ion respectively, v f is the velocity of the scattered particle and v e is the velocity of the ejected electron. It is worth noting that the kinematic factor ξ reflects the strength of CIFS influence on resonance profiles (Godunov et al 1992). The parameter Bexc,µ c (E i,ϑ e ) can be explicitly related to the components of the autoionizing state excitation cross section (Godunov et al ) πɣ µ 2 Bc exc,µ (E i,ϑ e ) sinh(πξ) = πξ L M= L σ LM exc,µ (E i)p 2 LM (cos ϑ e), (6) with P LM (cos ϑ e ) being the associated Legendre function and σ LM exc (E i) standing for the cross section of excitation to the magnetic sublevel M of the autoionizing state with total angular orbital momentum L. For forward emission ϑ e =, and P LM (1) = δ M,, so that equation (6) can be simplified: σ L exc,µ (E i) = πɣ µ 2 sinh(πξ) Bexc,µ πξ (E i), (7) where Bexc,µ (E i) Bexc,µ c (E i, ). That is, electron spectra for forward emission can only carry information on excitation of the states with M =. In our theory, we only consider collision kinematics with the scattered projectile faster than the ejected electron, i.e. v f >v e. With increasing collision velocity, the magnitude of the kinematic parameter ξ would decrease, and the influence of CIFS would become smaller. For fast enough collisions, one obtains ρ µ (ε µ ) 1, ϕ µ (ε µ ), so that equation (1) would reduce to the well known Shore parametrization (Shore 1967) d 2 σ = F(E e,e i,ϑ e ) + A µ (E i,ϑ e )ε µ + B µ (E i,ϑ e ) de e d e µ εµ 2 +1 (8) with the parameters A µ (E i,ϑ e ) = A c int,µ (E i,ϑ e ) (9) B µ (E i,ϑ e ) = Bint,µ c (E i,ϑ e ) + Bexc,µ c (E i,ϑ e ). () This allows us to consider equation (1) as a generalization of the Shore parametrization to the case of strong PCI (see Godunov et al () for more discussion). In this work, the computational model is the same as in Godunov et al (). 3. Experimental procedure Experimental study of autoionization resonances in helium excited by charged particle impact and distorted by CIFS requires a high energy resolution. Besides, an adequate parametrization must be used to process the experimentally obtained spectra.

5 Zero-degree target electron spectroscopy 1621 Figure 1. Detailed sketch of the spectrometer and the target chamber. Chamber I contains the gas target and projectile beam collimation and focusing system, while chamber II contains the electron spectrometers and Faraday cups Experimental apparatus A schematic diagram of the experimental apparatus for zero-degree electron spectroscopy is presented in figure 1. As can be seen, the set-up basically consists of two vacuum chambers (I and II), where chamber I houses the gas target and projectile beam collimation and focusing system, while in the second chamber (II) the tandem-electron spectrometer and Faraday cups are installed. As figure 1 shows, the incident ion beam traverses the gas target cell and enters chamber II along with the forward emitted electrons from the target cell. To analyse the emitted target electrons, two parallel-plate electron energy analysers are used in a tandem configuration. The ion beam current, which is used for charge normalization, is measured by a Faraday cup. Typical base pressures in the experimental chambers are of the order of 7 Torr. With gas pressures of 5 5 mtorr in the target cell, a background pressure of about 6 Torr is maintained. The beams of H +,He + and He 2+ ions used in these experiments were obtained from a 2 MeV Van de Graaff accelerator. After acceleration the ion beam was focused and mass and charge analysed, before entering the target chamber, which contained a differentially pumped gas cell. An additional gas stripper was used for production of doubly ionized He 2+ projectiles. For absolute zero-degree doubly differential electron emission cross section measurements, a special differentially pumped gas cell has been designed, with a well fixed reaction length of 8 mm and stable target gas pressure p. The stable target gas pressure is maintained by a Granville-Phillips 238 variable leak valve, where the target pressure is monitored by a Datametrics-57A absolute pressure manometer. The inner cylinder of the gas cell is insulated from the ground potential. This design allows us to accelerate the produced secondary electrons in the target cell for low-electron-

6 1622 R Bruch et al energy measurements, or to decelerate the emitted electrons (electron energy retardation) in order to improve the energy resolution (Ridder 1973). The gas target assembly comprises a cylindrical Einzel lens, located between the first collimator and the gas cell (see figure 1). The main purpose of this lens is to prevent low-energy electrons from reaching the gas target. In this work, target autoionization electrons emitted at zero observation angle were energy analysed in a high-resolution electron spectrometer system consisting of two parallel-plate electrostatic energy analysers configured in tandem (see figure 1). The first low-resolution analyser is used to separate the emitted electrons from the projectile beam for the electron impact measurements, while the second analyser is designed for high-resolution target electron measurements. The theoretical energy resolution is approximately 5% for the primary spectrometer and.2% or better for the high-resolution instrument. In high-resolution electron spectrometry, especially for low-energy electron measurements, shielding of magnetic fields is crucial. Using a combination of a double-layer structure of µ-metal and additional Helmholtz coils, the residual magnetic field has been reduced to less than 1 mg in both chambers. A complex data acquisition and control system has been used to operate the two electron spectrometers, namely to accumulate electrons to get spectra and normalize the data on-line to the incident particle flux (Wang 1993). All the measured cross sections were absolutely calibrated in our experiment for electron impact using DDCS for ionization of He by 1 kev electron impact recommended by Kim (1983) and Rudd (1991). The detailed procedure is described by Wang (1993). A maximum error of 16% is expected for the major part of obtained direct ionization DDCS. The uncertainties are mainly due to counting statistics and instrumental fluctuations. For resonance measurements, statistical uncertainties are greater than in background measurements and may be as high as 4% in some cases. The angular resolution of the analyser is about ± Typical results and line identification Typical high-resolution electron energy spectra of He produced in 366 kev H + +Heand 1 MeV He 2+ + He collisions are shown in figure 2. The most pronounced autoionization structures are labelled. The two strongest lines in the spectrum originate from the (2p 2 ) 1 D and (2s2p) 1 P resonances. The lowest-energy resonance structure measured in this spectrum comes from the (2s 2 ) 1 S state. In addition, some higher-lying (2lnl ) states have been observed. Since the intensity of the (2s 2 ) 1 S resonance as well as (2lnl ) resonances with n 3 is small in the experimental spectra, we limit further consideration to the dominant lines (2s2p) 1 P (1sεp) 1 P and (2p 2 ) 1 D (1sεd) 1 D Fitting procedure In the region of small emission angles, ionization of atoms by ion impact is known to be strongly influenced by CIFS affecting both direct ionization cross sections and the shape of the resonances (Schowengerdt and Rudd 1972, Moretto-Capelle et al 1996). The closer the velocity of the emitted electron to the velocity of the scattered ion the stronger the effect of CIFS. For low-lying autoionization resonances of helium, with 33 4 ev electrons emitted at zero angle, CIFS influence reaches its maximum approximately at 7 kev for H + impact, and 28 kev for He + and He 2+ impact. In the present work, the energies of the projectile ions covered a part of the strong CIFS region. To estimate the significance of CIFS, experimental spectra were processed with both parametric formulae, equations (1) and (8). Reliability of the new parametrization (1) in processing electron spectra distorted by CIFS has been recently

7 Zero-degree target electron spectroscopy (2s2p) 1 P a) 5 (2p 2 ) 1 D d 2 σ/de e dω e ( - cm 2 /ev/sr) (2s 2 ) 1 S (2p 2 ) 1 D (2s 2 ) 1 S (2p4p) 1 D (2p3p) 1 D (2p 2 ) 1 S (2s4p) 1 P b) (2s2p) 1 P (2p3p) 1 D (2p 2 ) 1 S (2p4p) 1 D (2s4p) 1 P electron energy (ev) Figure 2. Experimental high-resolution electron spectra of helium produced by (a) 366 kev proton impact and (b) 1 MeV He 2+ ion impact, at the electron emission angle of. proved by Moretto-Capelle et al (1996). Using both CIFS and Shore parametrizations allows us to determine the limits of applicability of the standard parametrization (8). Application of the CIFS parametrization (1) requires that the statistical errors are less than the differences in the kinematic factors multiplying the resonance parameters A c int,µ (E i,ϑ e ), Bint,µ c (E i,ϑ e ) and Bexc,µ c (E i,ϑ e ) in equation (1). Otherwise one may obtain spurious parameter values, leading to nonphysical values for the excitation cross section derived from equations (1) and (6), while providing a good fit for the original spectra. Moreover, the statistical error should be smaller than the least of the kinematic parameters ξ. In an earlier work (Moretto-Capelle et al 1997), the problem of statistical noise was solved using simultaneously fitted spectra for several emission angles, using the fact that excitation cross sections are not angle dependent. Since the present results were obtained for a single emission angle, and statistical noise was rather high, we could reliably determine only the sum Bint,µ c + Bc exc,µ, which was robust enough and did not change much with varying statistical noise and energy resolution. The same approach was earlier adopted in analysing electron resonance profiles in kev p + He collisions, for emission angles of 16 (Godunov et al 1997b). However, it is worth noting that the dimensionless phase parameter δ µ (E i,θ e ) defined by equation (4) is surprisingly quite stable even in the region of moderate CIFS influence. In the fitting procedure, we used a first-order polynomial fit for the direct ionization continuum. The spectrometer function was modelled with a Gauss curve with.8 ev dispersion. Resonance positions were varied together with the profile parameters, while fixed resonance widths were used: Ɣ D =.7 ev for the (2p 2 ) 1 D state, and Ɣ P =.37 ev for the (2s2p) 1 P state.

8 1624 R Bruch et al 95 9 a) kev d) 275 kev d 2 σ/de e dω e ( - cm 2 /ev/sr) b) 15 kev c) kev e) 5 kev f) 15 kev electron energy (ev) Figure 3. Experimental electron spectra in the vicinity of the (2p 2 ) 1 D and (2s2p) 1 P resonances of helium excited by 15 kev proton impact, at zero electron emission angle. Energy resolution 8 mev. Experiment: full circles. Fitting results: solid curve, spectra fitted with the CIFS formula (1); broken curve, spectra fitted with the Shore formula (8). 4. Results and discussion High-resolution spectra and DDCSs for ionization of He target atoms were measured at zero observation angle. For the projectiles, we used 15 kev protons and 4 16 kev He n+ ions. Zero-angle observations provide a unique opportunity to maximize interaction between the ejected electron, the ionized target atom and the charged projectile. Using an instrumental energy resolution not poorer than.2% allows a detailed inspection of autoionization line profiles for the (2l2l ) states of He. Two parametrization formulae, one including CIFS, and the standard Shore parametrization, were applied to fit the measured spectra in the vicinity of (2p 2 ) 1 D and (2s2p) 1 P resonances Resonance profiles The profiles of the (2p 2 ) 1 D and (2s2p) 1 P resonances of helium excited by 15 kev proton impact, at zero electron emission angle are presented in figure 3. For projectile energies of

9 Zero-degree target electron spectroscopy 1625 a) 4 kev d) 4 kev d 2 σ/de e dω e ( - cm 2 /ev/sr) b) 8 kev c) 1 kev e) 8 kev f) 5 kev electron energy (ev) Figure 4. Experimental electron spectra in the vicinity of the (2p 2 ) 1 D and (2s2p) 1 P resonances of helium excited by He + (a) (c) and He 2+ (d) (f ) impact, at zero electron emission angle. Energy resolution 8 mev. Experiment: full circles. Fitting results: solid curve, spectra fitted with the CIFS formula (1). and 15 kev we observe a characteristic distortion of the resonance profiles due to CIFS, including shift and asymmetric broadening of the resonances, as well as fast variations of the resonance shape with the projectile energy. As collision energy increases, the resonance shapes become more symmetrical. The CIFS parametrization adequately reproduces experimental spectra for all collision energies. In contrast, the Shore formulae can safely be applied for projectile energies above 275 kev. Moreover, up to 5 kev, the fit quality is much better for CIFS formulae than the Shore parametrization. At high collision energies both parametrizations give identical fits for the resonance profiles. Similar CIFS effects have recently been observed for small emission angles in helium ionization by proton impact (Moretto-Capelle et al 1996, Godunov et al 1997a, ). Experimental electron spectra for helium atoms excited by He + and He 2+ ion impact are presented in figure 4. Since both projectiles have the same collision velocity, the only difference is in the projectile charge. The comparison of the two parallel sets of diagrams indicates that increasing projectile charge from Z p = 1 to 2 results in a considerable increase of CIFS influence on the resonance profiles (compare figures 4(a) and (d)). Despite statistical noise

10 1626 R Bruch et al one can clearly observe typical deviation of the resonance profiles from the Fano resonance shape for 4 kev He 2+ ion impact, namely, resonance-like structure on the right wings around 36.3 ev. We wish to point out that there are no other resonances in this electron energy region than (2p 2 ) 1 D and (2s2p) 1 P with the following energies and widths: E D = ev, Ɣ D =.7 ev and E P = ev, Ɣ P =.37 ev (see figure 2 with resonance line identification). Besides, it was this broad structure on the right wings that was predicted theoretically (Godunov et al 1989) when the influence of CIFS is significant. The resonance shape in figure 4(d) is very similar to the resonance shape observed at an emission angle of 4 for excitation of helium by 85 kev proton impact (Moretto-Capelle et al 1996). This effect may be explained by the fact that the values of kinematic parameter ξ characteristic for the CIFS from equation (5) are very close for the two collision conditions. The CIFS parametrization well reproduces the observed profile oscillation. Evidently the Shore parametrization cannot be applied in this kinematic region. At high collision velocities, when the CIFS is small, the resonance profiles have the common Fano shape. The strong dependence of the magnitude of CIFS on projectile charge is quite expectable, since the strength of interaction between the scattered projectile and ejected electron is proportional to projectile charge, and Z p = 2 means PCI twice as strong as Z p = 1. Equations (4) and (5) show how the kinematic parameters connected to CIFS effects depend on the relative velocity v pe between the emitted electron and the scattered projectile, and the projectile Z p. Godunov et al (1992) demonstrated that the resonance profiles will be essentially different from the Fano shape, and a quasiperiodic behaviour is observed in both collision energy and emission angle dependence when ξ 1. Comparison of electron spectra for He + collisions (figures 4(a) (c)) with those for equivelocity proton impact ionization (figures 3(a), (c) and (d)) reveals a small but observable difference in the resonance profiles. This difference might be attributed to ether difference in the projectile masses or an effect of passive electrons in He + ions. However for v i = 3.3 au resonance shapes for 275 kev proton impact (figure 3(d)) practically match those observed in the 1.1 MeV He + impact spectrum, whereas there is still considerable difference in the resonance profiles with the He 2+ impact cross section (figure 4(f )). One might expect that the intensity of resonance profiles toward the direct ionization background should be stronger for He 2+ ion impact compared with H + and He + impact since we have double electron transition for excitation of autoionizing resonances and single electron transition for direct ionization. However, the CIFS affects strongly absolute value of direct ionization background for small emission angles. As the projectile charge increases, the CIFS influence increases as well. Figure 5 shows the contributions of individual resonances, i.e. (2p 2 ) 1 D and (2s2p) 1 P, in electron emission spectra. One can see that strong CIFS influence in 5 kev He 2+ impact ionization results in a strong overlap of two resonances due to the broadening of their right wings, which looks like resonance shift proportional to ξ Ɣ µ (Barrachina and Macek 1989) Resonance parameters In figure 6, we present the parameters A c int and Bc = B c int +Bc exc together with Shore parameters A µ and B µ for the (2p 2 ) 1 D and (2s2p) 1 P resonances of helium excited by proton impact. The parameters have been derived from experimental spectra using the fitting procedure described above. The results of our theoretical calculations both with and without CIFS are drawn in the same diagrams for comparison. As one can see Shore and CIFS parameters are very close for collision energies above 4 kev. This means that the resonances have a Fano profile for this collision region.

11 Zero-degree target electron spectroscopy 1627 d 2 σ/de e dω e ( - cm 2 /ev/sr) a) 5 kev electron energy (ev) b) 15 kev Figure 5. Experimental electron spectra in the vicinity of the (2p 2 ) 1 D and (2s2p) 1 P resonances of helium excited by (a) 5 kev He 2+ ion and (b) 1.5 MeV proton impact, at zero electron emission angle. Energy resolution 8 mev. Experiment: full circles. Fitting results: solid curve, total spectra fitted with the CIFS formula (1); broken curves, contribution of each resonance, namely dashed curve, (2p 2 ) 1 D resonance, and dash dot curve, contribution from (2s2p) 1 P resonances. ( - cm 2 /ev/sr) A c int B c ( - cm 2 /ev/sr) a) c) b) d) projectile energy (kev) Figure 6. Energy dependence of the resonance parameters A c int and B c = Bint c + Bc exc for the (2p 2 ) 1 D(a), (b) and (2s2p) 1 P(c), (d) resonances of helium excited by proton impact, for zero electron emission angle. Experiment: full circles, fitting with CIFS formula; open triangles, fitting with Shore formula. Theory: solid curve, calculation allowing for CIFS; broken curve, calculation in the second Born approximation. As collision energy decreases the difference between two sets of parameters increases. As we noted above, the Shore parametrization did not fit satisfactory experimental profiles for proton impact below 275 kev. Our theoretical calculations are in good agreement with experimental data for high collision energies. In the region of strong CIFS influence on resonance profiles the calculations show quasiperiodic behaviour for resonance parameters. Such behaviour

12 1628 R Bruch et al ( - cm 2 /ev/sr) A c int B c ( - cm 2 /ev/sr) a) c) b) d) relative velocity (a.u.) Figure 7. Fitted and calculated CIFS resonance parameters for the (2p 2 ) 1 D(a), (b) and (2s2p) 1 P (c), (d) states of helium excited by proton impact as a function of relative velocity. Experiment: full circles, present work; open squares, result of Bordenave-Montesquieu et al (Godunov et al 1997b). Theory: solid curve, calculation for the fixed electron angle of ; broken curve, calculation for the fixed proton energy of kev. reflects fast evolution of the resonance profiles with projectile energy. We need to have more experimental points in this region to demonstrate clearly such oscillatory behaviour for measured data. The oscillatory behaviour of the resonance parameters as a function of collision energy for zero emission angle (figure 6) resembles the variation of the same parameters as a function of emission angle, with fixed collision energy (Godunov et al 1997b, ). Such a similarity can be explained by the fact that the magnitude of the CIFS influence is determined by the kinematic parameter ξ (equation (5)), which depends on the relative velocity v pe between the emitted electron and the scattered particles. For ion impact, by neglecting the dependence of this velocity on the scattering angle, one can write vpe 2 = v2 f + v2 e 2v f v e cos(θ e ). Thus, we can compare, at least qualitatively, two sets of experimental data, namely, measurements for angular dependence of the resonance parameters at fixed collision velocity and experimental data for fixed emission angle. In figure 7, we present both theoretical and experimental data for resonance parameters as functions of relative velocity v pe for the (2p 2 ) 1 D and (2s2p) 1 P resonances of helium excited by proton impact. Results from two different sets of experiments are superimposed: zero-emission data from this work and Bordenave-Montesquieu et al data (Godunov et al 1997b) for a fixed collision energy of kev. Calculations in both cases were carried out in the same approximations. One can see a remarkable qualitative similarity between different sets of data, although some quantitative differences are also present. Resonance parameters for the (2p 2 ) 1 D and (2s2p) 1 P helium resonances scaled to Zp 2 are presented in figure 8 for He + and He 2+ ion impact. For collision energies above 1 MeV the resonance parameters reveal smooth behaviour, i.e. the resonance shape does not change considerable with collision energy. However, for the region of strong CIFS influence the

13 Zero-degree target electron spectroscopy 1629 ( - cm 2 /ev/sr) 2 a) c) ( - cm 2 /ev/sr) A c / Z int p - b) d) - - B c / Z p projectile energy (kev) Figure 8. Energy dependence of resonance parameters A c int and Bc = B c int + Bc exc for the (2p2 ) 1 D (a), (b) and (2s2p) 1 P(c), (d) resonances of helium excited by helium ions, for zero electron emission angle. He + ions, full squares and solid curves; He 2+ ions, open triangles and broken curves. experimental points are scattered around, especially for He 2+ impact. It is clear that we need to have more experimental points in this region to reveal a functional dependence of the parameters on collision energy. Keeping in mind the Zp 2 scaling, one can see considerable difference between He + and He 2+ data on absolute scale. Our calculations show quasiperiodic behaviour for the resonance parameters below 1 MeV with more oscillations for He 2+ impact. Better agreement between the calculations and the experiment can be seen for the He 2+ projectiles (open triangles and broken curve on figure 8). The He + projectiles were considered in our calculations as quasiparticles with the projectile charge Z p = 1. This could be a possible reason for poor agreement with the experimental data for He + ion impact. As we discussed above, the phase parameter δ µ defined by equation (2) was surprisingly stable at processing of the experimental data unlike A c int,µ (E i,ϑ e ), Bint,µ c (E i,ϑ e ) and Bexc,µ c (E i,ϑ e ) parameters. The other point in favour of this parameter is its dimensionless character, i.e. its value does not depend on normalization of experimental data. In this paper we did not extract excitation cross sections from resonance shapes. Therefore, to obtain δ µ we did not need to have resonance profiles for a few emission angles like Moretto-Capelle et al (1997). Theoretical and experimental collision velocity dependences of the phase parameter δ µ for the (2p 2 ) 1 D and (2s2p) 1 P resonances of helium excited by protons and helium ions are presented in figure 9. A good agreement between experimental and theoretical data can be observed. For collision velocities between 2 and 3 au the variations of the relative phase exceed 2π, which results in abrupt changes of the resonance shapes with collision velocity, and the oscillations of the resonance parameters (equation (1)). Projectile charge dependence is clearly observable in the relative phase, which varies in a twice as wide range for He 2+ impact as for ionization by singly charged He + ions or protons; in figure 9, we had to shift the He + curve up by 2π, to make it distinguishable from the proton curve.

14 163 R Bruch et al relative phase δ (π units) 4 3 (2p 2 ) 1 D He 2+ He + 4 He 2+ 3 (2s2p) 1 P He H + H + (a) (b) collision velocity (a.u.) Figure 9. Energy dependence of relative phase δ µ equation (4) for the (2p 2 ) 1 D(a) and (2s2p) 1 P (b) resonances of helium excited by protons and helium ions, for zero electron emission angle. Protons, full circles and solid curves; He + ions, open squares and dot dashed curves; He 2+ ions, full triangles and dashed curves. 5. Conclusions Analysis of autoionizing resonances of helium in electron emission spectra produced in collisions with fast ions made it possible to study the kinematic region where the CIFS is a dominant mechanism for the formation of the resonance profiles as well as effects of the projectile charge Z p and the projectile mass M p. We can summarize the results of our experimental and theoretical research. (1) There is very strong effect of the projectile charge Z p in formation of the autoionizing resonances (2p 2 ) 1 D and (2s2p) 1 P of helium excited by fast impact. (2) CIFS affects autoionizing resonances of helium in electron emission spectra at zero-degree observation angle in a very broad range of collision velocities, especially for He 2+ impact. (3) CIFS parametrization adequately fits resonance profiles distorted by CIFS not only for proton and ion impact but also for all kinematic regions considered in this work. (4) When ξ 1 (see equation (5)) the resonance profiles are essentially different from the Fano shape, and a quasiperiodic behaviour is observed in both collision energy and emission angle dependence in accordance with Godunov et al (1992). Acknowledgments This work was supported by the Nevada Business and Science Foundation and ACSPECT Corporation, Reno, NV.

15 Zero-degree target electron spectroscopy 1631 References Arcuni P W 1986 Phys. Rev. A Arcuni P W and Schneider D 1987 Phys. Rev. A Bachau H, Bhari M, Martin F and Salin A 1991 J. Phys. B: At. Mol. Opt. Phys Balashov V V, Lipovetskii S S and Senashenko V S 1973 Sov. Phys. JETP Barrachina R O and Macek J H 1989 J. Phys. B: At. Mol. Opt. Phys Bordenave-Montesquieu A and Benoit-Cattin P 1971 Phys. Lett. A Bordenave-Montesquieu A, Benoit-Cattin P, Rodière M, Gleizes A and Merchez H 1975 J. Phys. B: At. Mol. Phys Bruch R, Stolterfoht N, Datz S, Miller P D, Pepmiller P L, Yamazaki Y, Krause H F, Swenson J K, Chung KTand Davis B V 1987 Phys. Rev Fano U 1961 Phys. Rev Fritch W and Lin C D 199 Phys. Rev. A Giese J P, Schulz M, Swenson J K, Schöne H, Benhenni M, Varghese S L, Vane C R, Dittner P F, Shafroth SMand Datz S 199 Phys. Rev. A Godunov A L, Ivanov P B, Schipakov V A, Moretto-Capelle P, Bordenave-Montesquieu D and Bordenave- Montesquieu A J. Phys. B: At. Mol. Opt. Phys Godunov A L, Kunikeev Sh D, Novikov N V and Senashenko V S 1989 Sov. Phys. JETP Godunov A L, McGuire J H and Schipakov V A 1997a J. Phys. B: At. Mol. Opt. Phys Godunov A L, Novikov N V and Senashenko V S 1991 J. Phys. B: At. Mol. Opt. Phys. 24 L173 7 Godunov A L and Schipakov V A 1993 Proc. 18th Int. Conf. on Physics of Electronic and Atomic Collisions (Aarhus, 1993) ed T Andersen, B Fastrup, F Folkmann and H Knudsen p 524 Godunov A L, Schipakov V A, Moretto-Capelle P, Bordenave-Montesquieu D, Benhenni M and Bordenave- Montesquieu A 1997b J. Phys. B: At. Mol. Opt. Phys Godunov A L, Senashenko V S and Schipakov V A 1992 I V Kurchatov Institute of Atomic Energy (Moscow) Preprint IAE-5451/12, pp 1 55 Htwe W, Vajnai T, Barnhart M, Gauss A D and Schulz M 1994 Phys. Rev. Lett Itoh A, Zouros T J M, Schneider D, Stettner U, Zeitz W and Stolterfoht N 1985 J. Phys. B: At. Mol. Phys Kim Y-K 1983 Phys. Rev. A Martin F and Salin A 1994 J. Phys. B: At. Mol. Opt. Phys. 27 L Martin F and Salin A 1995 J. Phys. B: At. Mol. Opt. Phys McGuire J H 1997 Electron Correlation Dynamics in Atomic Collisions (Cambridge: Cambridge University Press) McGuire J H and Straton J C 1991 Phys. Rev. A Moretto-Capelle P, Benheni M, Bordenave-Montesquieu D and Bordenave-Montesquieu A 1996 J. Phys. B: At. Mol. Opt. Phys Moretto-Capelle P, Bordenave-Montesquieu D, Bordenave-Montesquieu A, Godunov A and Schipakov V 1997 Phys. Rev. Lett Moribayashi K, Hino K, Matsuzawa M and Kimura M 1991 Phys. Rev. A Morishita T, Hino K, Watanabe S and Matsuzawa M 1994 J. Phys. B: At. Mol. Opt. Phys. 27 L Pedersen JOPandHvelplund P 1989 Phys. Rev. Lett Prost M 1978 Master Thesis Freien University, Berlin Ridder D 1973 Master Thesis Freien University, Berlin (unpublished and private communication) Rudd M E 1964 Phys. Rev. Lett Rudd M E 1991 Phys. Rev. A Schulz M 1995 Int. J. Mod. Phys. B Schulz M, Htwe W T, Gauss A D, Peacher J L and Vajnai T 1995 Phys. Rev. A Shore B W 1967 J. Opt. Soc. Am Schowengerdt F D and Rudd M E 1972 Phys. Rev. Lett Stolterfoht N 1971 Phys. Lett. A Stolterfoht N 1987 Phys. Rep Stolterfoht N 1991 Nucl. Instrum. Methods B Stolterfoht N, Ridder D and Ziem P 1972 Phys. Lett. A Toburen L, Schneider D, Bruch R and Theodosiou C E 1981 Inner-Shell and X-Ray Physics of Atoms and Solids (New York: Plenum) pp 9 12 Wang H 1993 PhD Thesis University of Nevada Reno (unpublished and private communication) Wang H, Bruch R, Hao F, Fuelling S, Xu Z, Wang Z and Rauscher E 1993 Nucl. Instrum. Methods B