Resonant inner-shell photoelectron spectra of ground

J. Phys. B: At. Mol. Opt. Phys. 29 (1996) 4641–4658. Printed in the UK

Resonant inner-shell photoelectron spectra of ground-state and laser-excited Cr atoms Th Dohrmann†, A von dem Borne†, A Verweyen†, B Sonntag†, M Wedowski‡, K Godehusen‡, P Zimmermann‡ and V Dolmatov§ † II Institut für Experimentalphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany ‡ Institut für Strahlungs- und Kernphysik, TU-Berlin, Hardenbergstraße 36, 10623 Berlin, Germany § S V Starodubtsev Physical–Technical Institute, 700084 Tashkent, Uzbekistan

Received 13 June 1996

Abstract. Photoelectron spectra and partial cross sections of ground-state and laser-excited Cr atoms in the range of the 3p → nd, ns excitations are presented. The experimental spectra are compared with results obtained by calculations within the spin-polarized random-phase approximation with exchange (SP RPAE), in which the dynamic relaxation upon core hole creation is taken into account.

1. Introduction The half-filled outer 3d and 4s shells make Cr unique among the 3d transition metal series. The special character of the Cr electron configuration manifests itself in the inner-shell spectra. Among the 3d metal atoms only Cr displays a set of well developed 3p → nd (n > 4) Rydberg series (Bruhn et al 1982, Meyer et al 1986). This unique 3p spectrum has been a puzzle for many years, particularly since the spectrum of the isoelectronic partner of Cr, the Mn+ ion, did not show any corresponding features (Cooper et al 1989, Costello et al 1991, Sonntag and Zimmermann 1992). The half-filled shells, on the other hand, considerably simplify the theoretical approaches and allow for the application of advanced methods like the spin-polarized random-phase approximation with exchange (SP RPAE). Exploiting this, in recent calculations Dolmatov (1993a, b) succeeded in shedding some light on the singular features of the Cr 3p → nd, ns core resonances; (i) the width and shape of the 3p → 3d giant resonance and (ii) the existence of 3p → nd (n > 4) asymmetric lines. The ad hoc introduction of incomplete relaxation by a transition state proved to be the key to the understanding of the spectra. Based on these ideas new calculations of partial cross sections have been performed. In order to test the predictions of the calculations, the Cr photoelectron spectra have been reinvestigated with much improved energy resolution and statistics. Furthermore, by laser pumping Cr atoms have been prepared in the excited 3d5 4p 7 P4 state. This allowed the verification of the extreme sensitivity of the spectra to changes of the valence configurations predicted by the calculations. c 1996 IOP Publishing Ltd 0953-4075/96/204641+18$19.50

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2. Theoretical model Our theoretical model is based on the many-electron spin-polarized random-phase approximation with exchange (SP RPAE) (Amusia et al 1986, Amusia 1990, Amusia and Dolmatov 1993), which has been developed for the study of the many-body dynamics in atoms with one or more semifilled shells. SP RPAE makes use of the spin-polarized Hartree–Fock (SPHF) approximation (Slater 1968, Slater et al 1969) as the the zero-order basis. 2.1. SPHF The restricted Hartree–Fock (HF) self-consistent-field method constrains all single-electron spin orbitals of a subshell nl of an atom to being spherically symmetric and having the same radial function Pnl (r) independent of the spin orientation µ and the magnetic quantum number m. For closed-shell atoms this approach is appropriate, since in this case, the different spin orientations of the electrons in the occupied shells balance each other; in addition, the HF Coulomb and exchange potentials are spherically symmetric (Slater 1960). The Cr atom in the ground state, on the other hand, has half-filled 3d and 4s subshells, their electrons all having the same spin orientation according to Hund’s rule. We indicate the spin orientation as spin-up (↑) and spin-down (↓), respectively, and let the spin orientation of the electrons in the semi-filled shells be spin-up; e.g. the ground state of Cr acquires the representation Cr 3p3 ↑3p3 ↓3d5 ↑4s↑. In a case like this one might expect a pronounced effect due to the dependence of the exchange interaction of an electron on its spin orientation. This so-called spin-polarization effect is taken into account by the SPHF approximation. It relaxes the restriction on the orbitals concerning the spin orientation, thus providing different radial functions and energy eigenvalues for spin-up and spin-down electrons, but retains the assumption of spherical symmetry. The total wavefunctions of the atom in the ground state are represented by single Slater determinants constructed from the spin-dependent single-electron radial wavefunctions Pnlµ (r) of an electron in a subshell nlµ having an energy Enlµ , which in turn are obtained upon solving the SPHF radial equation (Slater et al 1969) # " eff Zˆ nlµ l(l + 1) 1 d2 + − (1) Pnlµ (r) = Enlµ Pnlµ (r) . − 2 dr 2 r 2r 2 eff , which can be regarded as the operator of an effective nuclear charge The operator Zˆ nlµ seen by an electron in the orbital nlµ, is defined by " eff Zˆ nlµ Z X 1 n0 l 0 µ0 (Nn0 l 0 µ0 − δnlµ,n0 l 0 µ0 ) Y0 n0 l 0 µ0 ; Pnlµ (r) = − + − r r r r n0 l 0 µ0 # 1 nlµ Nnlµ − 1 X k Pnlµ (r) c (l0; l0) Yk nlµ; − 2l r r k>0 X n0 l 0 µ0 Nn0 l 0 µ0 ck (l0; l 0 0) 1 Yk nlµ; Pn0 l 0 µ0 (r) . (2) −2δµµ0 [(4l + 2)(4l 0 + 2)]1/2 r r k,n0 l 0 6=nl

Here atomic units are used; Nnlµ is the number of electrons in the subshell nlµ, and the summations extend over all occupied states n0 l 0 µ0 in the atom. The coefficients ck represent

Resonant inner-shell PES of atomic Cr

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products of three spherical harmonics (tabulated by Slater (1960), appendix 20) and the functions Yk are defined as Z ∞ k 1 n0 l 0 µ r< Pnlµ (r 0 )Pn0 l 0 µ0 (r 0 ) dr 0 (3) Yk nlµ; = r r r>k+1 0 where r< and r> represent the smaller and the greater of r and r 0 , respectively. We now turn to the calculation of the spin orbitals of the excited atomic configurations created by transitions of an electron from a ground-state orbital to an initially empty orbital. In general, this can be done in two opposite limits, known as the ‘frozen-core’ and ‘relaxed-atom’ approaches, respectively. As will be shown in section 2.3, the frozencore approximation is not well suited for the description of the Cr 3p → nd inner-shell resonance excitations. Consequently, the SPHF calculations reported here were performed in a relaxed atom model, which takes into account the many-electron response of the whole atom to the creation of an electron–hole pair. In order to determine the relaxed spin orbitals of the excited configurations one can also use (1) if the appropriate values for the occupation numbers Nnlµ are chosen. Note that in our calculations, no J LS term dependence of the orbitals is taken into account. 2.2. SP RPAE In a case like Cr, where the half-filled subshells nl consist of a filled (nl↑) and an empty (nl↓) spin-polarized subshell, in fact all occupied spin-polarized subshells of the atom are closed, which makes it convenient to take the wavefunctions obtained within SPHF as the zero-order basis for RPAE, a many-body theory developed for atoms with all subshells nl closed (Amusia and Cherepkov 1975). This generalization leads to SP RPAE, which is well suited to study the many-electron dynamics of atoms with semifilled shells. The SP RPAE equations for the amplitudes of the photoexcitation processes differ from the corresponding RPAE equations, in that they explicitly exclude all RPAE correlation corrections caused by the exchange interaction between spin-up and spin-down orbitals; for a detailed discussion, consult the references given at the beginning of the section. Given the amplitude D for one channel of the photoexcitation process, the corresponding photoionization partial cross section σ is readily obtained from the relation 4π 2 αa02 ω|D(ω)|2 (4) σ (ω) = 3 ¯ ω is the photon where α = 1/137 is the fine-structure constant, a0 is the Bohr radius, h energy and D is to be taken in the length form. The corresponding expression for closedshell atoms (Amusia and Cherepkov 1975) differs from the given one only by an additional factor of 2, which arises from the independent summation over the two spin orientations in the final single-electron state. As mentioned in the previous section, the SPHF code does not take into account the multiplet splitting of different LS terms. To correct for that we use the same J -averaged SPHF wavefunctions for all the multiplet split components, but substitute the corresponding exp experimental energies h ¯ ωi (J ) for the different J components into the final equations. Since resonances with different J do not interfere, the cross section is given by X σJ (ω) σ (ω) = J

2J + 1 exp σ (ω, ωi (J )) (2L + 1)(2S + 1) where each component is multiplied by its statistical weight. σJ (ω) =

(5)

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2.3. Application to Cr In this section we report the application of the above approaches to the 3p inner-shell spectra of Cr atoms. Before entering upon a detailed discussion of the calculations we present the most important excitation and decay processes in the simplified energy level diagram of figure 1. The 3p5 3d5 4s2 7 P core resonances, the giant 3p5 3d6 4s 7 P resonance and the 3p5 3d5 4snd (n > 4) states of the Rydberg series converging towards the 3p5 3d5 4s 8 P ionization limits are excited out of the Cr ground state by vacuum ultraviolet (VUV) photons. All these resonances can autoionize into the 3p6 3d5 6 S5/2 εl and 3p6 3d4 4s 6 D εl continua. Interference between these indirect ionization channels and the direct 4s and 3d ionization gives rise to asymmetric Fano-type resonance profiles.

Figure 1. Simplified Cr energy level diagram. Laser pumping and VUV photon excitations are indicated by arrows. Interference between direct 4s or 3d ionization channels and indirect ionization channels via discrete excitation followed by autoionization is depicted for the 3p5 3d5 4s2 7 PJ resonances.

We now focus on the SPHF study of the excited nd↓ orbitals upon Cr 3p → nd transitions†. Systematic calculations (Dolmatov 1993a) of these excited orbitals in the 3d metals from Sc to Ni lead to the conclusion that orbital relaxation becomes extremely strong in Cr, making Cr singular amongst the iron-group atoms in this respect. Furthermore, the † The arrows indicating the spin orientation will be omitted if the notation is unambiguous.


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self-consistent potential of Cr seems to be so delicate that it depends critically on the state of the outermost orbital (Dolmatov 1995). For example, Cr+ ions and valence-excited Cr∗ atoms show considerably different orbital relaxation from that of ground-state Cr. This has been confirmed experimentally by the dramatic difference of the absorption spectra of free Cr+ ions and Cr atoms (Costello et al 1991). Valence-excited Cr∗ will be discussed in section 5. Frozen-core excited orbitals, therefore, are a poor approximation in a calculation of Cr 3p → nd cross sections. The use of completely relaxed orbitals, on the other hand, would assume that the time scale of relaxation is much shorter than the lifetime of the resonant states. However, the lifetime of the Cr 3p → 3d giant resonance is short and probably comparable to the time scale of relaxation. In the following we present a semiempirical approach (Dolmatov 1993b) to the Cr relaxation dynamics, taking care of the fact that the decay of the giant resonance takes place while relaxation is still in progress. The relaxation alters the effective core charge Zceff seen by the excited electron, which in turn influences the resonant state itself. Pursuing this idea, we performed a set of calculations eff in the SPHF equation (1) by inserting different of the resonant orbitals for different Znlµ values for the nuclear charge Z into (2). The orbitals obtained in this way we call ‘relaxed transition orbitals’. Figure 2 shows the relaxed excited 3d↓ orbitals for Cr 3p5 3d6 4s for different values of Z. As Z increases from Z = 24.000 (curve 1) up to Z = 24.045 (curve 2), the amplitude of the excited orbital is seen to increase significantly in the inner region of the atom without an essential change of the gross appearance of the orbital. Here Z equal to 24.000 simulates full relaxation. The small increase of Z from 24.045 (curve 2) to 24.050 (curve 3) dramatically alters the wavefunction causing the relaxed orbital to collapse. Note that we failed to calculate relaxed orbitals lying between the two critical curves denoted by 2 and 3. The calculations have either resulted in curves extremely close to one of these

1.2

radial wavefunctions [a.u.]

1 0.8 0.6 0.4 0.2 0

3

5

6

1

2 4

-0.2 -0.4 -0.6 0

2

4

6

8 10 12 radius [a.u.]

14

16

18

20

Figure 2. Orbitals calculated within SPHF. 1–3, Cr 3p5 3d6 4s relaxed 3d↓ orbitals with Z = 24.000, 24.045 and 24.050, respectively; 4, Cr 3p5 3d5 4s4d relaxed 4d↓ orbital; 5, 6, 3d↑ and 3p↓ ground-state orbitals. In order to facilitate comparison, the 3p↓ ground-state orbital (curve 6) was multiplied by (−1).

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3d partial cross section [Mb]

1 2

80

17 3

60

32 29 36 24 44

40

20

0 37

38

39

40

4s partial cross section [Mb]

2.5

41 42 43 44 photon energy [eV]

45

46

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17 32

2

1.5

24

1

29 36

2

1

3

44

0.5

0 37

38

39

40

41 42 43 44 photon energy [eV]

45

46

47

Figure 3. Cr ground-state 3d (upper part) and 4s (lower part) partial cross sections calculated within SP RPAE. The resonances are numbered and assigned as proposed by Bruhn et al (1982) for their high-resolution absorption spectrum.

critical curves, or the solution of the SPHF equation (1) for 24.045 < Z < 24.050 could not be found at all. Orbital relaxation in Cr essentially results in delocalization of its excited 3d↓ and higher nd↓ orbitals. The nuclear charge Z = 24.045 seems to be the critical value for which the potential seen by the 3d↓ excited electron changes abruptly. The amplitude of the 3d↓ wavefunction in the inner part of the atom is strongly reduced, and the orbital is pushed into the outer region of the atom. This effect is opposite to what is called ‘orbital collapse’ (see e.g. Connerade and Mansfield 1982), and therefore has been named ‘orbital anticollapse’ (Dolmatov 1993a). Note that, in contrast, the spin-up 3d↑ relaxed excited


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orbital (curve 5 in figure 2) is located in the inner part of the atom, not showing any dramatic change. In a set of trial SP RPAE calculations the cross sections of the 3p → 4s, nd (n > 3) resonances have been determined by using different Z-dependent relaxed excited orbitals, as well as the 3p↓ ground-state wavefunction shown as curve 6 in figure 2. The sums of both 3d and 4s partial cross sections obtained in this way were compared with the experimental absorption data of Meyer et al (1986) in order to determine the ‘best value’ of Z and the optimal relaxed transition orbital (Dolmatov 1993a). These calculations resulted in the relaxed orbital for Z = 24.045 being the best suited for the description of the Cr 3p → 3d resonance ionization. Calculations based on a fully relaxed 3d↓ orbital significantly underestimated the strength of the giant 3p → 3d resonance. No fitting was performed for the nd (n > 4) Rydberg series and the 4s resonances. These resonances were calculated using completely relaxed orbitals with Z = 24.000 (see curve 4 in figure 2 for the 4d↓ orbital, for example), as the line widths of these resonances are narrow, their lifetime being long enough to let the atom relax before the autoionizing decay. In figure 3 we present the SP RPAE results for the 3d and 4s photoionization partial cross sections, calculated with the corresponding relaxed transition orbitals. The spectra can be separated into three parts: the sharp and intense 3p → 4s resonances (lines 1– 3), the broad 3p → 3d giant resonance (line 17) and the region of Rydberg excitations between 44.5 and 46.5 eV. The multiplet splitting of the 3p → 4s, nd resonances has been taken into account by substituting the experimental values of Meyer et al (1986) into the SP RPAE equations according to (5). The experimentally unresolved multiplet splitting of the 3p → 3d giant resonance has been taken from a term-dependent Cowan code calculation (Martins and Zimmermann 1993). The calculated values are E(7 P4 ) − E(7 P3 ) = 0.168 eV and E(7 P3 ) − E(7 P2 ) = 0.136 eV. In addition to the resonance transitions discussed so far, the SP RPAE calculations also included the continuum transitions 3d → εf, εp and 4s → εp which considerably affect the shapes and intensities of the resonances. The calculated photoionization partial cross sections will be compared to the experimental data in section 4. The similarity of the relaxed 3d↓ and 4d↓ orbitals in the excited Cr 3p5 3d5 4snd states (curves 2 and 4 in figure 2) already indicates a strong mixing. This is borne out by the SP RPAE calculations which predict a significant transfer of oscillator strength from the 3p → 4d Rydberg transitions to the giant 3p → 3d resonance (Dolmatov 1993a). 3. Experiment The experiments were performed at the U1–TGM6 wiggler–undulator beamline at the electron storage ring BESSY using the experimental set-up sketched in figure 4. Cr atoms emanating from an oven described below were interacting with the counterpropagating linearly polarized laser and synchrotron radiation in the source volume of a 180◦ cylindrical mirror analyser (CMA), in which the kinetic energy of the photoelectrons emitted at angles close to the magic angle 2CMA = 54.7◦ relative to the polarization axis of the synchrotron radiation were analysed with an energy resolution of 0.8% of the pass energy. The improvement of the energy resolution and statistics of the Cr ground-state spectra compared with the results of Meyer et al (1986) is mainly due to the high-flux undulator station which provides a photon flux of the order of 1013 photons/s in the energy region around 40 eV with a monochromator bandpass of E/1E ≈ 1000 (Gaupp and Koch 1988). A new high-temperature metal beam source was built to produce a stable and collimated beam of Cr atoms. In order to achieve an atomic density of 1010 –1011 atoms/cm3 in the

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Figure 4. Schematic picture of the experimental set-up. The linearly polarized synchrotron and laser radiation propagate in opposite directions, intersecting the beam of Cr atoms in the source volume of a cylindrical mirror electron analyser (CMA). The entrance slit of the CMA accepts electrons emitted under an angle of 2CMA = 54.7◦ with respect to the direction of polarization of the synchrotron radiation. The angle between the directions of polarization of the two radiation fields is given by η.

interaction region, the furnace has to be heated to about 1500 K. Niobium was chosen for the crucible and nozzle material because it has a very low vapour pressure even at these temperatures and does not react with Cr below 1900 K (Atlas of Binary Alloys 1973). The crucible and nozzle were heated separately by resistive heating elements (Boralectric, Advanced Ceramics Inc.). These consist of graphite conducting patterns coated on a boron nitride (BN3 ) substrate and can be operated up to 2000 K. Photoelectron spectra were collected in two different modes: electron distribution curves (EDC) were taken by scanning the pass energy of the analyser while keeping the photon energy fixed; partial cross sections of selected photoemission lines were determined in the constant ionic state (CIS) mode, where the photon energy and the pass energy are scanned simultaneously. Each point of a CIS spectrum was taken by measuring an EDC over the photoemission line at the respective photon energy and summing up all counts of the EDC thus approximating an integration over the area of the line. The energy resolution of a CIS spectrum for a given photoemission line depends solely on the bandpass of the monochromator. The energy calibration of the monochromator was established by the Ne 2s2 2p4 3s3p, 2s2p6 3p and 2s2p6 4p resonance positions in the 2p partial cross section given by Codling et al (1967). From the linewidth of the Ne resonances, the monochromator bandpass could be determined to be approximately 40 meV at a photon energy of 45 eV corresponding to E/1E & 1000. All spectra have been corrected for a constant background originating from the channeltron and the high-temperature furnace, as well as for the analyser transmission which is known to be proportional to the pass energy. The background of thermal electrons could be reduced by applying a retarding voltage of −8 V at an aperture in front of the channeltron. The background count rate, being independent of the CMA pass energy, photon energy and photon flux, could be determined in an EDC at a photon energy corresponding to a binding energy much lower than that of the Cr 4s valence electron. Special attention had to be paid to the normalization of the CIS spectra with respect


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to the photon flux. The intensity of VUV radiation could vary by an order of magnitude during the acquisition of a CIS spectrum since it was not possible to change the undulator gap simultaneously with the photon energy. Therefore, the incoming photon flux was monitored by measuring the total photocurrent emitted by a copper mesh. A preset counter driven by this photocurrent determined the integration period for the CMA signal; the energy dependence of the Cu yield was corrected for. The excited atoms were prepared by optical pumping with linearly polarized laser radiation tuned to the Cr 3d5 4s 7 S3 –3d5 4p 7 P4 transition at 425.56 nm (see figure 1). Between 150 and 200 mW of laser radiation was provided by a UV-pumped (4 W, all Ar UV lines) single-mode CW ring dye laser operating with stilbene 3. The laser frequency was actively stabilized to the resonance frequency of Cr atoms by measuring the intensity of the resonance fluorescence emitted by a reference beam of Cr atoms. At the atomic densities used in this experiment an alignment of the Cr atoms in the laser-excited state is induced (Dohrmann et al 1996). The partial cross section of excited Cr can be determined from the CIS spectra taken at different angles η between the polarization vectors of the two radiation fields. The angle η can easily be changed by rotating the polarization vector of the laser radiation by means of a Fresnel rhomb (see figure 4). The VUV beamline provides a very high degree of linear polarization of the radiation in the first harmonic of the undulator. Pahler et al (1992) obtained a polarization of 98% at 60 eV. For the analysis of the data we assumed the VUV light (as well as the laser radiation) to be 100% linearly polarized. The errors introduced in this way are small compared to the statistical uncertainties of the data points. For these conditions it can be shown (Dohrmann 1995, Dohrmann et al 1996) that the partial cross section can be well approximated by the relation I (η = 0◦ , ω) + 2I (η = 90◦ , ω) ∝ σ (ω).

(6)

4. Excitation of ground-state Cr 4.1. EDC results An EDC typical for the photoemission out of the ground state of Cr atoms is shown in the upper part of figure 5. The spectrum recorded in the maximum of the giant resonance at a photon energy of hν = 43.68 eV demonstrates that the 3d5 4s 7 S → 3d4 (5 D)4s 6 D εl photoemission channel (line 2) dominates. In the centre part the same spectrum is shown on an enlarged scale in order to bring out the main 4s line (line 1) and the satellites (lines 3–12). Table 1 gives a listing of the observed features and assignments based on the optical data of Sugar and Corliss (1977). The spectra are in good agreement with those published earlier (Meyer et al 1986, Bruhn et al 1982). In contrast, the EDC depicted in the bottom part recorded at a photon energy of 42.30 eV, i.e. in the maximum of resonance 13 (see table 2 and figure 6), indicates a dramatic increase of satellites 3–7 and 9, some of which (lines 4, 6 and 7) have not been resolved previously. These lines correspond to final ionic states in which the angular momenta of the 3d and 4s electrons are coupled differently than in the ground state. According to the assignment of resonance 13 to the 3p5 3d6 4s 7 D excited state (Bruhn et al 1982), the excitation process is forbidden in LS coupling. The large relative intensities of satellites belonging to ionic states which cannot be reached in the LS approximation could be a consequence of the selective excitation which forces the recoupling of angular momenta. We will come back to this point in section 4.4.

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Figure 5. Photoelectron spectra recorded in the maximum of the giant resonance line 17 (upper and centre parts) and in the maximum of resonance line 13 (lower part).

4.2. 3d partial cross sections Since the 3d photoionization is by far the strongest ionization channel in the region of discrete 3p excitations, the 3d partial cross section could be measured with quite good statistics and can therefore serve as a key to the understanding of the photoionization dynamics of Cr atoms. The diamonds connected with the full curve in figure 6 display the experimentally determined 3d cross section. For comparison, the SP RPAE results (broken curve) discussed in section 2, as well as a Fano-type profile (chain curve) fitted to the giant resonance are included. A comparison between the energy positions of the intensity maxima seen in absorption and those measured in this work in the 3d and 4s partial cross sections is given in table 2. The slight asymmetric shape of the 3p5 3d5 4s2 7 P2,3,4 resonances (lines 1–3) and their intensity relative to the giant resonance are very well described by SP RPAE. An analysis shows that the spectral profiles can be represented by three Fano-type profiles with a quite large asymmetry parameter of q = +8.1(3) and a natural width of about 40(10) meV which


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Table 1. Assignments and binding energies of Cr II states as obtained by the fit of a Gaussian to the corresponding photoemission lines (figure 5). The absolute energy values have been determined by using the first ionization potential of 6.766 eV (line 1) as a reference. For comparison the binding energies tabulated by Sugar and Corliss (1977) and the experimental values determined in previous experiments are included. The assignment of line 13 is less certain because there is a significant difference between the experimental and tabulated binding energies. Binding energy (eV) Line 1 2 3 4 5

6 7 8

9 10 11

12 13 a b

Term

Tabulateda

3d5 6 S5/2 3d4 (5 D)4s 6 D1/2−9/2 3d5 4 G1/2−11/2 3d5 4 D1/2−7/2 3d4 (3 H)4s 4 H7/2−13/2 3d4 (3 P)4s 4 P1/2−5/2 3d4 (3 F)4s 4 F3/2−9/2 3d4 (3 G)4s 4 G5/2−11/2 3d4 (3 D)4s 4 D1/2−7/2 3d4 (5 D)4p 6 F1/2−11/2 3d4 (5 D)4p 6 P3/2−7/2 3d4 (5 D)4p 6 D1/2−9/2 3d4 (5 D)4p 4 P1/2−5/2 3d4 (5 D)4p 4 D1/2−7/2 3d3 4s2 4 F3/2−9/2 3d3 4s2 4 G7/2−9/2 3d4 (5 D)5s 6 D1/2−9/2 3d4 (5 D)4d 6 P3/2−7/2 3d4 (5 D)4d 6 G3/2−13/2 3d4 (5 D)4d 6 D1/2−9/2 3d4 (5 D)4d 6 F1/2−11/2 3d4 (5 D)4d 6 S5/2 3d4 (3 G)5s 4 G9/2,11/2

6.766 8.284 9.309 9.871 10.521 10.551 10.630 10.931 11.517 12.638 12.784 12.919 12.880 13.541 13.403 13.533 17.059 17.519 17.540 17.617 17.659 18.167 19.834

This work

Previous workb

6.77 8.29(2) 9.31(7) 9.88(7)

6.77 8.27(5) 9.23(5) —

10.57(5)

10.54(5)

10.92(5) 11.51(5)

—

12.74(3)

12.74(5)

13.48(7)

13.7(1)

17.05(4)

17.0(1)

17.59(5)

17.7(1)

18.17(9) 19.97(4)

18.3(1) 20.1(1)

Sugar and Corliss (1977). Meyer et al (1986).

was deduced from the measured half width of 60(5) meV by the deconvolution of the monochromator bandpass of 40 meV. The low-energy part of the giant resonance (line 17) is reproduced surprisingly well by a single Fano-type profile with an asymmetry parameter of q = +3.1 and a width of 0 = 0.75 eV which shows that the interference between the 3p → 3d autoionizing dipole resonance and the direct photoionization is dominating the spectrum. Even the small cross section in the energy region between the 3p → 4s and the 3p → 3d resonances can be explained by this interaction. The SP RPAE overestimates the cross section between 40 and 42 eV whereas it lies somewhat below the experimental values at the onset of the giant resonance. Resonances 12–15, tentatively ascribed by Bruhn et al (1982) to 3p5 3d6 4s 7 D, 5 P autoionizing states, are not included in the SP RPAE calculations, which in part may be responsible for the differences between the calculated and the experimental curve. There is nearly perfect agreement between the SP RPAE and the experimental curve between the maximum of the giant resonance and the first 3p → 4d resonance (line 24). The characteristic features of the 3d cross section in the region of the Rydberg excitations are the multiplet split 3p → 4d, 5d resonances 24, 29, 32, 36 and 44. As was shown by

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1 60

17

3d main line 2 0.04 eV

50

32 29

3 40

24

36 44

30 14/15

20

12/13

10 0 39

40

41

42 43 44 photon energy [eV]

45

46

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Figure 6. Experimental 3d5 4s 7 S → 3d4 4s 6 D εl partial cross section of atomic Cr in the ground state (——). For comparison the 3d cross section calculated within SP RPAE, convoluted with a Gaussian of 0.04 eV FWHM accounting for the monochromator bandpass and matched to the experimental spectrum in the maximum of the giant resonance (line 17), is shown (- - - -). A Fano-type profile with an asymmetry parameter of q = +3.1 and a width of 0 = 0.75 eV obtained from a fit to the giant resonance is included (— · —).

Bruhn et al (1982) in their absorption spectrum, there is a series of weak and extremely sharp resonances in that region, most of which could not be resolved in this experiment. The SP RPAE calculations reproduce very well the characteristic features of the prominent Rydberg series which are unique among the 3p excitation spectra of the 3d transition metal atoms. The minima between the first series members are less pronounced in the SP RPAE spectrum and towards higher energies, the Rydberg lines seem to be superimposed on an increasing background. Part of these differences may be due to the simplified model for the coupling of angular momenta used for the calculations. In this model, the 3p → 4d, 5d states have been described as 3p5 3d5 4snd 7 P2,3,4 levels, whereas Bruhn et al (1982) use the notation 3p5 3d5 4s(8 P5/2,7/2,9/2 )nd which stresses the splitting of the 3p5 3d5 4s 8 P ionic core states. The nd Rydberg electron, coupled to the core, leads to a very weak finestructure splitting which cannot be resolved. Consequently, every 3p → 4d, 5d state contains contributions of all allowed total angular momenta J = 2, 3, 4, whereas in the simplified model used for the calculations the resonances are ascribed to states with one well defined J value. 4.3. 4s partial cross section The partial cross section of the second main photoemission line, the 4s line corresponding to the 3d5 6 S5/2 ground state of the ion, is typically more than one order of magnitude weaker than the 3d photoemission line. In comparison to experiment, the SP RPAE underestimates the strength of the 4s ionization channel relative to the 3d emission by approximately a factor of two. In figure 7 we present a comparison between our experimental data (diamonds with error bars) and the SP RPAE data (full curve) normalized to the experimental curve in the


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Table 2. Assignment and excitation energies of the 3p → ns, nd resonances of atomic Cr. The uncertainties are approximately ±0.02 eV. The resonances are assigned as proposed by Bruhn et al (1982) for their high-resolution absorption spectrum. The energies of the absorption lines have been lowered by 0.02 eV due to improved reference data. Resonance maximum (eV) assignmenta

Resonance

Term

1 2 3 12 13 14 15 16 17 20 21 22 23 24 25–28 29 30, 31 32 33–35 36 37 44 54, 55 59–63

3p5 3d5 4s2 7 P4 3p5 3d5 4s2 7 P3 3p5 3d5 4s2 7 P2 3p5 3d6 4s 7 D2,3,4

a

3p5 3d6 (4 P)4s 3p5 3d6 4s 7 P2,3,4 3p5 3d5 4s(8 P7/2 )5s 3p5 3d5 4s(8 P5/2 )5s 3p5 3d5 4s(8 P9/2 )4d 3p5 3d5 4s(8 P9/2 )6s 3p5 3d5 4s(8 P7/2 )4d 3p5 3d5 4s(8 P7/2 )6s 3p5 3d5 4s(8 P5/2 )4d, (8 P9/2 )5d 3p5 3d5 4s(8 P5/2 )6s, (8 P9/2 )6d 3p5 3d5 4s(8 P7/2 )5d 3p5 3d5 4s(8 P9/2 )7d 3p5 3d5 4s(8 P5/2 )5d, (8 P7/2 )6d 3p5 3d5 4s(8 P7/2 )7d, 8d 3p5 3d5 4s(8 P7/2 )10d–13d

Absorptiona

3d-CIS

4s-CIS

39.187 39.538 39.889 42.209 42.302 42.784 43.022 43.185 43.78 44.419 44.554 44.771 44.829 44.876 45.023–45.079 45.197 45.381, 45.478 45.546 45.668–45.770 45.850 45.980 46.180 46.352, 46.437 46.544–46.627

39.18 39.56 39.88 42.18 42.28 42.76 42.98 — 43.70 44.40 44.54 44.76 44.84 44.88 — 45.20 — 45.56 — 45.88 46.00 46.20 46.40 46.58

39.16 39.56 39.86 42.18 42.28 42.80 42.98 — 43.50 — — — — 44.84 — 45.20 — 45.52 — 45.86 — 46.18 — —

Bruhn et al (1982).

maximum of the giant resonance, as well as a best fit of a Fano-type profile (broken curve) to the giant resonance. The error bars show the statistical errors which are significantly larger than for the 3d cross section due to the smaller cross section. The most striking difference between the 4s and 3d partial cross sections is the change of the asymmetry character of the resonances. The giant resonance (line 17) can be approximated by a Fano-type profile with a negative asymmetry parameter of q = −4.2(3) in the 4s cross section whereas q has a positive value of a similar magnitude (q = +3.1) in the 3d cross section. The difference in the coupling to the ionization continua also results in a shift of the maximum of the giant resonance in the 4s channel by about 0.2 eV towards lower excitation energy with respect to the maximum in the 3d channel (see table 2). The sign reversal of the asymmetry parameter between the 4s and 3d photoionization cross sections was also observed for Mn (Whitfield et al 1994). The SP RPAE calculation underestimates the cross section in the energy range between the 3p → 4s and the 3p → 3d resonances which in part may be due to the neglect of transitions 12–15 contributing in this energy range. In comparison to the 3d cross section, the 4s channel is less enhanced in the 3p → 4s resonances (lines 1–3) than in the giant resonance (line 17). The asymmetry parameter of q = −3.9(5), obtained from a fit of Fano-type profiles to the 3p → 4s resonances, is considerably lower than in the 3d cross section (q = +8.1). The SP RPAE calculations

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4s partial cross section [arb. units]

6 4s main line

17

5 0.04 eV

15

4 14 3

1

12/13

24 29

2

36 44

3

2

32

1 0 39

40

41


45

46

47

Figure 7. Experimental 3d5 4s 7 S → 3d5 6 S εl partial cross section of ground-state atomic Cr ( with error bars), compared to the SP RPAE data (- - - -) convoluted with a Gaussian of 0.04 eV accounting for the monochromator bandpass, and a best fit of a Fano-type profile (q = −4.2, 0 = 0.75 eV) to the giant resonance (— · —). The 4s partial cross section has been normalized to the 3d partial cross section.

describe the profile of the 4s cross section in the region of 3p → 4s excitations very well, but considerably underestimate their strength in relation to the giant resonance. In the region of the Rydberg excitations 3p → 4d, 5d both the experimental and the theoretical 4s cross sections oscillate very strongly. The experimental cross section becomes very close to zero in the minima between the resonances, which is not fully reproduced by the SP RPAE results. This may indicate a slight overestimation of the line width by theory. Apart from this finding, which is consistent with the results for the partial 3d cross section, agreement between experiment and theory is very good. 4.4. Satellites To complete the discussion of our results on the photoemission of ground-state Cr atoms, in figure 8 the 3d partial cross section is compared with the partial cross sections of two selected satellite lines: the ‘4p shake-up satellite’ (line 8) and satellite line 4. The partial cross section of the ‘4p satellite’ displays all the main 3p → 4s and 3p → 3d, 4d, 5d resonances seen in photoabsorption or in the 3d and 4s partial cross sections. The relative intensities of most of the different resonances are quite close to those observed in the partial 3d cross section. The cross section of the ‘4p satellite’ seems to be a scaled copy of the partial 3d cross section; therefore it can be interpreted as 3d photoemission accompanied by a conjugate shake-up of the 4s electron into the 4p state. The only obvious difference between these two cross sections is the appearance of the two additional strong features at the energies of the absorption lines 33–35 and 54/55 (Bruhn et al 1982) in the satellite cross section. The tentative assignment of these resonances to 3p → 6s, 6d, 7d or 8d excitations, given by Bruhn et al (1982) (see table 2), does not provide an obvious explanation for the enhancement of the ‘4p satellite’. Invoking 3p5 3d5 4p2 states


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Figure 8. Cr ground-state partial cross sections of the ‘4p shake-up satellite’ (centre part) and of satellite line 4 (bottom part) compared to the 3d main line partial cross section (upper part). The partial cross sections of the satellites have been normalized to the 3d partial cross section.

arising from configuration interaction with the strong 3p5 3d5 4snd resonances seems to offer a reasonable way to account not only for the strong coupling of the ‘4p satellite’ but also for the very weak coupling of the main lines to these features. It is worth noting that a similar behaviour of a ‘4p satellite’ was also observed in the photoemission of manganese atoms by Whitfield et al (1994) and their interpretation is rather similar. Quite different from the 3d or 4s cross sections is the partial cross section of line 4 depicted in the bottom part of figure 8. Neither the giant resonance and Rydberg excitations nor the 3p → 4s excitations can clearly be discriminated from the background, which was not subtracted from the raw data in this spectrum. On the other hand the LS-forbidden resonances 12/13 and 14/15 are very prominent in the partial cross section of line 4 ascribed to the 3d5 4 D final state of the ion. They have been assigned by Bruhn et al (1982) to transitions to 3p5 3d6 4s 7 D and 3p5 3d6 (4 P)4s final states, respectively, which cannot be reached in LS coupling by a dipole transition from the ground state 3p6 3d5 4s 7 S. Therefore the oscillator strength of these excitations is weak as can be seen from the absorption spectrum (Meyer et al 1986, Bruhn et al 1982). These resonances are supposed to have strong admixtures of configurations in which the 3d electrons are coupled differently and

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therefore can easily decay into the 3d5 4 D final state. The absence of the giant resonance (line 17), the Rydberg resonances 24, 29, 32, 36 and 44 as well as the 3p → 4s resonances 1– 3 in the spectrum of satellite 4 shows that the decay of these resonances to the 3d5 4 D state of the ion is forbidden corroborating the description of the main resonances in the LS coupling. It should be noted that the partial cross section of line 4 has some analogy to the cross sections of the Mn satellites 5 and 9 reported by Whitfield et al (1994), although the suppression of the giant resonance is not that impressive there. 5. 3d photoemission from laser-excited Cr atoms The experiments on laser-excited Cr atoms focus on the anticollapse of the 3d↓ wavefunction upon the creation of the 3p↓ hole and on its sensitivity to changes of the valence configuration. The 3d↓ wavefunction of valence-excited Cr 3d5 4p calculated by Dolmatov (1993b, 1995) does not show the orbital anticollapse responsible for the formation of the prominent Rydberg series in the 3p spectra of ground-state Cr. The aim of the experiment was to probe the suppression of the Rydberg series in the 3d partial cross section by laser excitation of Cr (Dohrmann et al 1995). For the experiments on laser-excited Cr the energy level scheme in figure 1 must be modified. The excitation with VUV radiation starts from the laser-excited state 3p6 3d5 4p 7 P4 and not from the ground state, thus different autoionizing states with the same parity as the Cr ground state are reached. Also the final ionic states will be different, because 3d ionization of the 3p6 3d5 4p 7 P4 state leaves the remaining ion in the Cr+ 3p6 3d4 4p 6 P, 6 D or 6 F states. Laser pumping the transition 3d5 4s 7 S3 → 3d5 4p 7 P4 at 425.56 nm, which gives the highest excitation efficiency of about 10–15%, the occurrence of a 3d photoemission line from laser-excited Cr could be demonstrated by Dohrmann et al (1995). The 3d partial cross section displayed in figure 9 has been obtained from two CIS spectra taken at η = 0◦ and η = 90◦ by using (6) (see section 3). The spectrum can be

3d partial cross section

laser excited Cr 3p->4s

3d main line

3p->3d

3p->nd

40

42

44


52

54

Figure 9. ——, experimental 3d partial cross section of laser-excited Cr 3p6 3d5 4p 7 P4 . - - - -, Fano-type profile (q = +2.65, 0 = 1.15 eV) fitted to the giant resonance.


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divided into three parts: the 3p → 4s resonances, the 3p → 3d giant resonance and the region of 3p → nd (n > 4) Rydberg excitations. In the region of the 3p → 4s excitations two prominent resonances at photon energies of 40.51 and 40.96 eV were observed, as well as two weak resonances at 41.13 and 41.30 eV. The two strong 3p → 4s resonances can be well approximated by superposition of two Fano-type profiles with asymmetry parameters of q = +6.5 ± 1, q > +10 and half widths of 0 = 0.066 ± 0.005 eV, 0 = 0.077 ± 0.005 eV, respectively. Within the LS-coupling model one expects six different 3p → 4s resonances, namely 3p5 3d5 4s4p 7 D3,4,5 , 7 P3,4 and 7 S3 for excitation out of the 3p6 3d5 4p 7 P4 laser-excited state, so probably some of the lines are composed of more than one transition. As indicated by the Fano-type profile fitted to the spectrum given in figure 9 the giant resonance in the 3d photoemission is considerably broader for laser-excited Cr than for ground-state Cr. The full half width of laser-excited Cr of 0 = 1.15 eV lies between that of ground-state Cr (0 = 0.75 eV) and those of Mn and Mn+ which are 0 = 1.50 eV for Mn (Whitfield et al 1994) and 0 = 1.52 eV for Mn+ (Cooper et al 1989). Also the strength of the 3p → nd Rydberg excitations is somewhere between the Cr ground state and the Mn+ case. Although the complex multiplet structure of the resonances accessible from the laser-excited state is not well understood, the photoionization of laser-excited Cr seems to be intermediate between ground-state Cr with a well developed Rydberg series and a relatively narrow giant resonance, and Mn+ with a broad giant resonance and weak Rydberg structures. This finding is in agreement with the predictions of the SP RPAE calculations. The key to understanding of the 3p absorption spectra is the anticollapse of the 3d↓ wavefunction upon the creation of a 3p↓ hole in the photoionization of groundstate Cr. The step from ground-state Cr to laser-excited Cr reduces the screening of the core and prevents the anticollapse of the 3d↓ wavefunction (Dolmatov 1993b, 1995). For Mn+ the 3d↓ wavefunction is fully localized in the core region giving rise to a stronger overlap between the 3p and 3d levels which manifests itself in the broad giant resonance. Acknowledgments The authors wish to thank S Grum-Grzhimailo, N Kabachnik and N Cherepkov for many stimulating discussions and the BESSY staff for continuous assistance. The financial support by the Bundesministerium für Bildung und Forschung and by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. The theoretical part of this study was made possible by the support granted to V Dolmatov by the Alexander von Humboldt Foundation, the International Science Foundation (grant no MZH000) and the State Committee for Science and Technology of Uzbekistan (grant no 10). References Amusia M Ya 1990 Atomic Photoeffect (New York: Plenum) section 3.13 Amusia M Ya and Cherepkov N A 1975 Case Stud. At. Mol. Phys. 5 47–179 Amusia M Ya and Dolmatov V K 1993 J. Phys. B: At. Mol. Opt. Phys. 26 1425–33 Amusia M Ya, Dolmatov V K and Ivanov V K 1986 Preprint no 1014 (Leningrad: A F Ioffe Physical–Technical Institute) pp 1–48 (in Russian) Bruhn R, Schmidt E, Schröder H and Sonntag B 1982 J. Phys. B: At. Mol. Phys. 15 2807–17 Codling K, Madden R P and Ederer D L 1967 Phys. Rev. 155 26–37 Connerade J P and Mansfield M W D 1982 Phys. Rev. Lett. 48 131–4 Cooper J W, Clark C W, Cromer C L, Lucatorto T B, Sonntag B F, Kennedy E T and Costello J T 1989 Phys. Rev. A 39 6074–7 Costello J T, Kennedy E T, Sonntag B F and Clark C W 1991 Phys. Rev. A 43 1441–50

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Dohrmann Th 1995 Thesis Universität Hamburg Dohrmann Th, Arp U, Sonntag B, Wedowski M, Weisbarth F and Zimmermann P 1995 AIP Conf. Proc. vol 329 (RIS-94) p 415 Dohrmann Th, von dem Borne A, Verweyen A, Sonntag B, Wedowski M, Godehusen K and Zimmermann P 1996 J. Phys. B: At. Mol. Opt. Phys. submitted Dolmatov V K 1993a J. Phys. B: At. Mol. Opt. Phys. 26 L393–8 ——1993b J. Phys. B: At. Mol. Opt. Phys. 26 L585–8 ——1995 11th Int. Conf. on VUV Radiation Physics (Tokyo) Program and Abstracts p W17 Gaupp A and Koch E E 1988 Phys. Z. 19 48 Martins M and Zimmermann P 1993 Private communication Meyer M, Prescher T, von Raven E, Richter M, Schmidt E, Sonntag B and Wetzel H E 1986 Z. Phys. D 2 347–62 Pahler M, Lorenz C, von Raven E, Rüder J, Sonntag B, Baier S, Müller B R, Schulze M, Staiger H and Zimmermann P 1992 Phys. Rev. Lett. 68 2285–8 Sonntag B and Zimmermann P 1992 Rep. Prog. Phys. 55 911–87 Slater J C 1960 Quantum Theory of Atomic Structure vol II (New York: McGraw-Hill) ——1968 Phys. Rev. 165 655–69 Slater J C, Mann J B, Wilson T M and Wood J H 1969 Phys. Rev. 184 672–94 Staudhammer K P and Murr L E (eds) 1973 Atlas of Binary Alloys. A Periodic Index (New York: Dekker) Sugar J and Corliss C 1977 J. Phys. Chem. Ref. Data 6 317 Whitfield S B, Krause M O, van der Meulen P and Caldwell C D 1994 Phys. Rev. A 50 1269–86