A systematic study of photoionization of free lanthanide atoms in the 4d giant resonance region

Journal of Electron Spectroscopy and Related Phenomena 169 (2009) 67–79

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A systematic study of photoionization of free lanthanide atoms in the 4d giant resonance region G. Kutluk a,∗,1 , H. Ishijima a,2 , M. Kanno a , T. Nagata a , A.T. Domondon b a b

Department of Physics, Meisei University, Hodokubo 2-1-1, Hino-shi, Tokyo 191-8506, Japan Division of Natural Sciences, International Christian University, Osawa, Mitaka-shi, Tokyo 181-8585, Japan

a r t i c l e

i n f o

Article history: Received 14 January 2008 Received in revised form 22 November 2008 Accepted 26 November 2008 Available online 3 December 2008 Keywords: Photoionization Giant resonance Lanthanide atom Cross-section Photoelectron Autoionization

a b s t r a c t Charge-separated photoion-yield spectroscopy using monochromatized synchrotron radiation was conducted on free Ce, Nd, Gd, Dy, and Er lanthanide atoms in the 4d giant resonance region to measure the relative partial cross-section curves (Mn+ ) for the formation of Mn+ (n = 1–4) ions. In addition, photoelectron spectroscopy was conducted on free Nd, Dy, and Er atoms to measure the cross-sections (nl) for photoionization of the nl (=4d, 5s, 5p and 4f) subshell electron. Drawing upon the obtained spectra and the results of previous photoion-yield studies on Xe, Cs, Ba, Sm, Eu, and Yb atoms, we discuss the character of photoionization processes in the 4d region. The obtained charge-state distribution shows that as the atomic number Z increases, the 4d giant resonance changes gradually, rather than suddenly, from a shape resonance to an autoionization resonance. One possible explanation for this change is that it is due to the dependence of the potential for the excited 4f electron and the corresponding 4f radial wavefunction on terms in the 4d9 4fn+1 configuration. For (M+ ) and (4f), which exhibit an asymmetric Beutler–Fano autoionization profile, a curve fitting analysis was conducted to obtain the profile parameters Er ,  , and q. It was found that for the Gadolinium atom, which has a configuration [Xe]4f7 5d6s2 characterized by a half-filled 4f7 subshell plus a 5d electron, both the asymmetry parameter q and the charge-state distribution varied peculiarly with the atomic number Z. © 2009 Published by Elsevier B.V.

1. Introduction Giant resonance structures that appear in the 4d region of photoabsorption (or photoionization) spectra of atoms and ions ranging from I (Z = 53) to Tm (Z = 69) have been the subject of many experimental and theoretical studies [1–4]. The characteristic feature of these structures is their broad and asymmetric shape. A considerable number of theoretical studies on atoms such as Xe, Cs, Ba, and Eu have shown that experimental spectra can be reproduced if electron–electron correlation is taken into account. There are, however, no systematic experimental studies that track how the giant resonance spectra changes as Z increases. Lanthanide atoms were recognized as possessing a distinctive electronic structure early in the history of atomic physics [5,6]. Each electron in the 4f orbital of these atoms is subject to an effective double-well potential, which gives rise to the so-called orbital col-

∗ Corresponding author. Tel.: +81 82 424 6298/6293; fax: +81 82 424 6294. E-mail address: [email protected] (G. Kutluk). 1 Present address: Hiroshima Synchrotron Radiation Center, Hiroshima University, Japan. 2 Present address: National Institute of Information and Communications Technology, 4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan. 0368-2048/$ – see front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.elspec.2008.11.004

lapse in the Rydberg series near the ionization limit. This effective potential changes with the number of electrons in the f-orbital. Within the lanthanide series, the La atom has one f electron, the Eu atom, having a half-filled f-shell, has seven 4f electrons, and the Yb atom, having a fully filled f-shell, has fourteen 4f electrons. This means that the effect of the number of electrons in the f-shell upon the 4d giant resonance spectra can be studied systematically by measuring the spectra of lanthanide atoms from La to Yb. The purpose of this research was to obtain experimental data on how the 4d giant resonance profile changes across the lanthanide series and to gain some understanding of the physics involved in those changes. Drawing mainly upon results of photoion-yield studies, we study how the 4d giant resonance in lanthanide atoms changes as the number of electrons in the f-shell increases. Although some of the data have been published in the conference proceedings [7–9] or elsewhere [10], we present them here again to provide a full picture of how the giant resonance changes across the series. For this purpose, we present and analyze experimental results of photoelectron spectroscopy on Nd, Dy, and Er and photoion-yield spectroscopy on Ce, Nd, Gd, Dy and Er, five lanthanides for which such spectroscopic data are currently lacking. Aside from Richter et al. [20,21], Dzionk et al. [22], and some presentations of our work in preliminary form at conferences [7–9], to the best of our knowledge there are no other works reporting

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Table 1 Previous experimental photoabsorption (ab), photoelectron (e), photoion-yield (ion), and coincidence (co) studies on the 4d region of rare-earth atomsa . Author(s)

Type of study

Target atoms

Mansfield and Connerade [11] Wolff et al. [12] Radtke [13] Radtke [14] Connerade and Pantelouris [15] Prescher et al. [16] Becker et al. [17] Svensson et al. [18] Meyer et al. [19] Richter et al. [20] Richter et al. [21] Dzionk et al. [22] Nagata et al. [23] Baier et al. [24] Kukk et al. [25] Richter [26] Kochur et al. [27] Kucas and karazija [28] Luhman et al. [29] Gerth et al. [30] Heinasmaki et al. [31] Ya Amusia et al. [32] Tong et al. [33]

ab ab ab ab e e e e e e, abb e, abb ion ion ion e co co (theory) ion (theory) co co ion (theory) ab (theory) ab (theory)

Eu Ce La, Tm Pr, Nd, Ho, Er, Tb, Sm, Dy Gd Sm Eu Yb Ce La, Ce Sm, Eu, Gd La, Ce, Pr, Nd, Gd, Tb, Dy c Sm, Eu, Yb Ho, Er, Yb Sm, Eu Eu Eu Nd, Eu, Gd, Dy Sm, Eu Ce, Pr, Nd, Sm, Eu Eu Eu Eu

a Theoretical studies published before 1996 are not included due to space limitations. Refs. [1], [2], and [4] include references to these earlier works. b The absorption measurements of these atoms, as well as those on Pr, Nd, and Tb are available in Refs. [2], [20], and [21]. c Results for Ce, Pr, Gd, and Dy are not shown in this paper.

approximation with exchange (RPAE), and time dependent local density function approximation (TDLDA). Each of these methods begins with a Hartree–Fock expression or a one-electron local density function, but takes into account the electron–electron correlation effects induced by the photoabsorption transition. In particular, MBPT [37,38] treats the optical–dipole interaction and electron–electron interaction as perturbations, and obtains a solution using perturbation methods in which specific coupling terms are selected on the basis of physical considerations. In contrast, RPAE [32] and TDLDA [33,39–41] take the basic Schroedinger equation as representing an atomic system in the presence of an electromagnetic field and transform it into an integral equation over time including a Green’s function. RPAE uses Hartree–Fock orbitals, eigenvalues, and linearized potentials to calculate the matrix elements, but TDLDA uses one-electron local density functions determined by self-consistent effective potentials. Both RPAE and TDLDA take into account electron–electron correlation effects accompanying the dipole transition. This paper is organized into five sections. Following this introduction is a section in which we present the details on the experimental apparatus. In the third section, the results section, we present the spectra that were obtained from the experiment. In the fourth section we interpret and discuss the experimental spectra. In the fifth and final section we close with a summary of our main findings. 2. Experimental apparatus and procedure 2.1. Beamline and energy calibration

experimental photoelectron and photoion-yield data for the five atoms just mentioned. Since this paper has an experimental focus, we will not attempt to give a detailed assessment of the validity of various theoretical methods to reproduce 4d giant resonance spectra, but we expect that our data will be useful in undertaking such an assessment. A summary of some of the previous experimental studies on the lanthanide series is given in Table 1 [11–26,29,30]. Results from several recent and important theoretical studies [27,28,31–33] are also included in the table. Recent experimental studies on the 4d giant resonance have taken two approaches. One approach consists of photoelectron–photoion coincidence studies with energy-resolved photoelectrons [26,29,30]. This approach provides detailed information about the decay processes from a specific 4d photoexcited (or photoionized) state to a final ionic state. A second approach consists of photoabsorption (or photoionization) experiments on ionic species such as I− , I+ , I2+ , Xem+ (m = 1–7), Cs+ , Bam+ (m = 1 and 2) [[34–36], and references therein]. In contrast to these two recent approaches, most experimental studies performed up to 1994 consisted of measurements using photoabsorption, photoelectron, or photoion spectroscopy. The present paper takes this earlier approach, rather than the two more recent approaches noted above. This is because, as noted earlier, there were lanthanide atoms for which no photoelectron and/or photoion-yield spectroscopic studies have been reported [see footnote c of Table 1]. The lanthanide series includes atoms that have the ground state configuration of [Kr]4d10 5s2 5p6 4fn 5s2 (or 5d6s2 ). In this paper, the configurations of ground and resonantly excited states are represented simply as 4d10 4fn and 4d9 4fn+1 [or 4d9 (4, ␧)fn+1 ], respectively. A number of theoretical studies have been carried out to understand the 4d giant resonance spectra. One of the difficulties in studying these spectra theoretically is that though the 4d resonance itself can be estimated using Hartree–Fock methods, these methods fail to reproduce the broad resonance structure obtained from experiments. Some methods that are more successful in this respect are many-body perturbation theory (MBPT), random phase

The present experiment was conducted using the BL-3B beamline at the “Photon Factory (PF)”, a synchrotron radiation facility at the High Energy Accelerator Research Organization (KEK) in Tsukuba, Japan. This beamline is equipped with a 24-m spherical grating monochromator (24 m SGM) with exchangeable gratings of 200, 600 and 1800 lines/mm, and provides monochromatized radiation in the 20–300 eV range with resolutions up to 5000 [42]. The monochromatized radiation required in the present experiment was in the range of 80–220 eV, and was obtained using the 600 and 1800 lines/mm gratings. One serious problem often encountered in experiments using synchrotron radiation, especially those involving photoion spectroscopy, is higher order light. For the present experiment, the influence of the second-order and higher order light was reduced to a negligible level by selecting an appropriate grating. More specifically, a 600 lines/mm grating was used for the 75–140 eV region, and an 1800 lines/mm grating was used for the 120–220 eV region [43]. Though at 120 eV, for example, the second-order light was approximately 6% when a 600 lines/mm grating was used, second-order light was not a problem because the photoabsorption cross-section at 240 eV was very small. The photon energy was calibrated using the following resonance excitation peaks of rare gases: Xe (4d5/2,3/2 )−1 6p (65.09 and 67.03 eV), Xe (4p3/2 )−1 5d (141.8 eV), and Kr (3d5/2,3/2 )−1 5p (91.20 and 92.43 eV). The resolution E/E was estimated to be 2000 for the 600 lines/mm grating when the entrance and exit slits were set at 100 ␮m. The error in the photon energy was less than 0.15 eV. 2.2. Photoelectron spectrometer Fig. 1 shows the experimental setup for the photoelectron spectrometer. The spectrometer consists of an analyzer chamber, an evacuation system, and a control system [10,44]. The analyzer chamber was combined with a hemispherical electrostatic energy analyzer, a cold trap using liquid nitrogen, a gas injection system,

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2.3. Time-of-flight mass spectrometer

Fig. 1. Photoelectron spectrometer viewed along the photon beam axis.

and an electron bombardment oven. The oven will be described in Sections 2–4. The electron–energy analyzer is hemispherical with a mean radius of 10 cm and a lens system in front of the incident slit. The lens system consists of four electrodes and is operated in an acceleration–deceleration mode with the beam-focusing point kept at the incident slit of the analyzer. To avoid polarization effects, the axis of the lens system was set at the magic angle (54.7◦ ) with respect to the polarization direction (horizontal) of the synchrotron radiation. The analyzer was operated in a constant pass energy mode using a personal computer. To obtain reliable results, special attention was given to the electron transmittance of the lens-analyzer system, the photon intensity, and the background noise. The lens-analyzer system was checked to ensure that the transmittance of the system was independent of the electron energy EK or was known as a function of EK . This was done by measuring the intensity of Xe 4d photoelectrons relative to that of Auger electrons arising from the decay of the 4d−1 states. It was found that the transmittance was almost independent of EK in the region EK ≥ EP + 20 eV, where EP is the pass energy (typically 17 eV). Below this critical energy, the transmittance decreased rapidly with decreasing EK . To ensure that the photon intensity was monitored correctly, the photon flux was monitored upstream by means of the drain current from the post-focusing mirror. To ensure that the background noise was negligibly weak compared to the photoelectron signals from the target atoms under study, two possible sources of background noise effects were identified. These two sources were noise due to the photoionization of background gases and noise due to thermal electrons from the oven. The noise due to the background gases was reduced to a negligible level using an evacuation system equipped with turbo molecular pumps. The typical background pressure was approximately 5 × 10−6 Pa, whereas the target atom pressure in the interaction section was estimated to be on the order of 10−3 Pa. The noise due to thermal electrons from the oven did not require any special measures to be taken because the transmittance of the lens-analyzer system for these electrons was close to zero.

For the photoion-yield measurements, we used the same timeof-flight mass spectrometer as described in our earlier publications [10,45]. In that machine, photoions are produced in an interaction zone and pushed into a drift tube by periodic rectangular voltage pulses from a pulse generator. The pulses had a period of 20 or 40 ␮s, a width of 2–3 ␮s, and a height of 100 V. The photoions were detected in counting mode with a microchannel plate (MCP). A computer program was used to measure both mass spectra and photoion-yield spectra (or photoionization spectra). In measuring the latter spectra, the intensities of all four types of photoions An+ (n = 1–4) were recorded simultaneously with the changing photon energy. In the present study, the energy of the ions incident on the MCP (Hamamatsu F1094) was a multiple of 3.9 keV. In other words, the energy of the incident ions is 3.9 keV multiplied by n, where n is the ionic charge expressed in units of elementary charge. It was necessary to examine whether the detecting efficiencies for An+ (n = 1–4) ions was the same for ions with different charges. The term “detecting efficiency” refers to how efficiently the entire system, including the MCP and the electronic system, detected the species of interest. To determine this, we measured the relative detecting efficiencies for five atomic species including Ba and Yb using the MCP [46]. It was found that the detecting efficiencies of Ba3+ and Ba4+ ions are almost the same, but the detecting efficiencies for Ba+ and Ba2+ ions relative to that of Ba3+ (or Ba4+ ) ions were 0.84 ± 0.02 and 0.98 ± 0.01, respectively. The corresponding detecting efficiencies for Yb+ and Yb2+ ions were 0.81 ± 0.02 and 0.97 ± 0.02, respectively. The yield curves of all the ions were corrected by taking into account these differences in detecting efficiencies. 2.4. Oven of electron bombardment type A beam of metallic atoms was produced using a hightemperature electron bombardment oven [10]. The oven has a cylindrical reservoir (anode) of 18 mm in outer diameter and 80 mm in height in its center. The reservoir is bombarded by energetic electrons from three tungsten wires of 0.3 mm in diameter. Outside the wires, cylindrical radiation shields are placed doubly. On the top of the oven, a cap with a hole of 10 mm in diameter is placed. A water-cooled cylindrical cap surrounds the entire oven. The reservoir, the inner radiation shield, and the electrodes near the reservoir are made of tantalum, and the others are made of stainless steel. A crucible was used to put the sample in the cylindrical anode. The crucible itself was either carbon or ceramic, depending upon the sample [47]. The oven temperature when photoelectron spectroscopy was performed was about 1450 K for Nd, 1250 K for Dy, and about 1260 K for Er. The vapor pressure corresponding to these temperatures was on the order of 10−1 Pa. The heating of the oven was done gradually over 3–4 h. Once the oven temperature stabilized, a sample of about 10–15 g (about 2 cm2 ) in the crucible lasted 20–30 h. When the photoion spectroscopy was conducted, the oven temperature was kept at approximately 100 K lower than the temperature used for photoelectron spectroscopy. In this case, the sample in the crucible lasted about five days. The purity of all the metallic samples exceeded 99.95%. 3. Results 3.1. Notation and calibration of the cross-sections Before describing the results obtained, we explain some notational conventions that we employ to describe the various kinds of cross-sections measured in our study. Three different kinds of

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cross-sectional sums are defined: t Qphi =  t (6s) +  t (4f) +  t (5p) +  t (5s) +  t (4d)

(1)

Qphi = (6s) + (4f) + (5p) + (5s) + (4d) + (nln l ) = Qdir + (nln l )

(2)

Qion = (M+ ) + (M2+ ) + (M3+ ) + (M4+ )

(3) Mn+

The letter M denotes the atomic species of interest, and (n = 1, 2, 3, 4) denotes ion of the species M with a positive charge of n. The t is defined as the sum of theoretphotoionization cross-section Qphi ical partial cross-sections  t (nl) for the nl subshell photoionization. The photoionization cross-section Qphi is the sum of the two crosssections Qdir and (nln l ). The cross-section Qdir is the sum over the experimental partial cross-sections (nl) for the direct single photoionization of nl subshell electron including shake-up contributions. The cross-section (nln l ) is the total cross-section for direct multiple (mainly double) ionization of all the nl subshells of interest. The cross-section Qion is the sum of the partial crosssections (Mn+ ), where (Mn+ ) denotes the cross-sectional yield of Mn+ ions. The cross-sections (nl) and (Mn+ ) for Nd and Dy atoms were scaled tentatively to an absolute value by assuming that





t Qphi

dE =

Qdir dE

(4)

where the integration was over the giant resonance region. The t was obtained by summing over the TDLDA cross-sections value Qphi  t (nl) reported by Dzionk et al. [22], the only calculations available for Nd and Dy at the present time. From the photoelectron spectra displayed in Figs. 5–7, we can see the effects of the background continuum. The background is due to the double ionization processes that produce (nln l )−1 state, and to double Auger processes in the decay of intermediate inner-hole states. It follows then that Qion should not be equated to Qdir , but to Qphi [=Qdir + (nln l )]. It was very difficult to estimate the cross-section (nln l ) from the experimental data, but it was possible to estimate the cross-section using physical considerations. Physical considerations suggested that most of M+ (4f−1 or 6s−1 ) ions end up forming M+ ions (see Section 4.1). This fact enabled us to relate the relative cross-section (M+ ) to the absolute cross-section as follows:





(M+ )dE =

(4f + 6s)dE

(5)

where the integrals are over the giant resonance region. The absolute cross-section (Mn+ ), where n = 2, 3, or 4, is obtained by using the charge-state distribution at the photon energy of interest. 3.2. Photoion-yield spectroscopy 3.2.1. Partial photoion-yield cross-sections Fig. 2 shows the time-of-flight mass spectrum obtained for the Er atom. The singly, doubly, triply, and quadruply charged ions are indicated in the figure. Similar spectra were obtained for the other atomic species studied. Gating each of the Mn+ peaks and recording their intensities by scanning the photon energy, we obtained the charge-separated photoion-yield cross-section curves simultaneously. To obtain the relative photoion-yield cross-sections (Mn+ ) shown in Fig. 3, we subtracted the backgrounds from these raw yield curves, normalized the resulting curves with respect to the incoming photon flux, and corrected these curves using the difference in detecting efficiencies for Mn+ ions.

Fig. 2. An example of time-of-flight mass spectra taken for Er atom. The photon energy is 164.5 eV.

The (Mn+ ) curves shown in Fig. 3 have several notable characteristics. First, the charge-state distribution varies drastically with the atomic number Z. The dominant products for processes involving the Ce atom were triply charged ions, but for processes involving Dy and Er the dominant products were singly charged ions. Second, for the Ce and Nd atoms, the largest cross-sections in the (M3+ ) and (M4+ ) curves were located at energies higher than the corresponding points in the (M+ ) and (M2+ ) curves. In contrast, for the Dy and Er atoms, the cross-section curves for each ion had a similar shape. Third, the (M+ ) curves of Nd, Gd, Dy and Er atoms exhibit an asymmetric Beutler–Fano autoionization profile. The first and second characteristics will be discussed in detail in Section 4.1, and the third characteristic will be discussed in Section 4.2. We notice that the fractions of Mn+ ions obtained for Nd and Dy atoms by Dzionk et al. [22] are considerably different from those obtained in this study. For example, the fractions at maxima of the Dy+ , Dy2+ , and Dy3+ curves obtained in their study are 0.47, 0.31, and 0.22, respectively. The corresponding fractions in this study are 0.54, 0.29, and 0.15 (see Fig. 10). In addition, though Dzionk et al. did not measure the Dy4+ curve, we obtained a value of 0.02 as the Dy4+ fraction. A more prominent difference is seen in the Nd results: the fractions of Nd+ , Nd2+ , Nd3+ , and Nd4+ ions in their measurement are 0.16, 0.23, 0.48, and 0.13, respectively, and these are markedly different from the corresponding values of 0.33, 0.29, 0.31, and 0.07 obtained in the present experiment. One difference between our results and those due to Dzionk et al. is that the fractions of Mn+ ions they obtained were generally larger than ours, especially for cases where n = 3 for Nd3+ , Nd4+ , and Dy3+ . This may be due to the higher detection efficiencies for higher charges in their measurement. In addition, the (Dyn+ ) curves increase with photon energy in the lower energy side of the 4d resonance peak. This behavior is different from the behavior observed in the present study, and may be due to the differences in how photon intensities were measured. 3.2.2. Relative total photoion-yield cross-sections The relative total photoion-yield cross-section curves Qion for all atoms of interest including those for Xe, Cs, Ba, Sm, and Eu obtained in the previous study [23] are shown in Fig. 4. These curves can be compared with their corresponding photoabsorption curves. In fact, they show a close resemblance to the absorption curves reported by Radtke [14], Richter et al. [21], and Sonntag and Zimmermann [2]. We see that the profiles of the Qion curves become narrower with increasing Z, and that they gradually change from having a shape resonance character to an autoionizing resonance character. In each curve, we see several weak peaks on the lower energy

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Fig. 3. Photoion-yield spectra taken for Ce, Nd, Gd, Dy and Er atoms. Singly , doubly , triply and quadruply charged ion are denoted by, +, 2+, 3+, and 4+, respectively. The vertical bars mark the positions of the 4d ionization limits.

side of the giant resonance peak. The assignments of these weak peaks has been a subject of much discussion, but have generally been ascribed to the excitations of low-lying discrete states of the 4d9 4fn+1 configuration [48].

3.3. Photoelectron spectroscopy 3.3.1. Photoelectron spectra (1) Nd Fig. 5(A) displays the photoelectron spectra of atomic Nd taken for h = 110 − 157 eV, which is an energy range that includes the entire 4d giant resonance region. The lowest 5 L6 level of the excited state [Xe]4f3 5d6 s2 (5 LJ ) lies at 0.72 eV above the lowest 5 I4 level of the ground state [Xe]4f4 6 s2 (5 IJ ) [49]. Since at the operating temperature of the oven, 1450 K, the thermal population of atoms in the excited 4f3 5d6 s2 (5 LJ ) state is

estimated to be less than 1%, the main peaks seen in the photoelectron spectra are understood to be excitations from the ground state.

The main photoelectron lines in the Nd atom spectra are marked as 4f−1 , 5p−1 , 5s−1 , and 4d−1 . The structure due to 4d ionization is seen in the bottom spectrum of Fig. 5(A), but the multiplet components are not resolved clearly. Also, groups of Auger lines, N4,5 O2,3 N6,7 and N4,5 O2,3 O2,3 , due to the relaxation of the 4d−1 states can be seen in the middle and bottom spectra. Fig. 5(B) shows the detailed photoelectron spectrum of the outer shell region taken at h = 110.5 eV. The weak line at EB = 5.52 eV is due to the emission of a 6s electron. Several weak satellites lines, including the P5 and P6 lines, accompany the two strong 4f lines P1 and P2 on the higher binding energy side (EB = 10–20 eV). Although

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Fig. 4. The “4d photoabsorption spectra” obtained by summing the partial photoionyield spectra. The results on Xe, Cs, Ba, Sm, and Eu atoms obtaned by Nagata et al. [23] are also included. The vertical bars mark the positions of the 4d ionization limits.

the existence of P3 and P4 lines is not clear in Fig. 5(B), these appeared more distinctly in the spectra taken at other photon energies. The binding energies and tentative assignments of the photoelectron lines are summarized in Table 2. The tabulated optical data due to Martin et al. [49] includes a number of quartet and sextet odd-parity states of 4f3 5d2 , 4f3 5d6s, and 4f4 6p configurations. Around the P1 peak, there are a number of states with the 4f3 5d2 and 4f3 5d6s configurations. It should be noted that Martin’s Table does not list any states with the configuration 4f3 6s2 , which corresponds to the single 4f ionization with the filled 6s2 shell retained. This may

Table 2 Binding energies EB of various excited states of Nd+ . EB (eV)a

Nd+ configurationb

Core hole

126.8 123.1 45.5 43.3 32.0 29.5 P8 27.6 25.5 P7 16.7 P6 15.0 P5 c 12.3 P4 10.9 P3 9.2 P2 7.4 P1 d 5.6

[Kr]4d9 5s2 5p6 4f4 6s2 [Kr]4d9 5s2 5p6 4f4 6s2 [Kr]4d10 5s5p6 4f4 6s2 (4 I4 ) [Kr]4d10 5s5p6 4f4 6s2 (6 I4 )

4d−1 5s−1 5p−1

[Kr]4d10 5s2 5p5 (2 P1/2 )4f4 6s2 [Kr]4d10 5s2 5p5 (2 P3/2 )4f4 6s2

4f−1

[Kr]4d10 5s2 5p6 4f3 6s7s(6 L, 4 L)

[Kr]4d10 5s2 5p6 4f3 6s2 (6 M, 6 L) [Kr]4d10 5s2 5p6 4f4 6s

6s−1

The uncertainties in EB are ±0.3 eV. b The ground state of Nd atom is [Kr]4d10 5 s2 5p6 4f4 6 s2 (5 I4 ). c This peak cannot be assigned unambiguously. Another possible assignment is 5d7s(6 L, 4 L), 6s6d(6 L, 4 L), or 5d6d(6 M, 6 L) (see text). d This peak cannot be assigned unambiguously. Another possible assignment is 5d6s(6 L, 4 L) or 5d2 (6 M, 6 L) (see text). a

Fig. 5. (A) Photoelectron spectra of Nd atom taken below (110 eV), at (125 eV) and above (157 eV) the 4d–(4, ε)f giant resonance peak. The 5p photoelectron lines are denoted as 5p−1 , and so on. The two line-groups indicated by N23 O23 N67 and N23 O23 O23 are Auger electrons associated with the decay of resultant 4d-hole (4d−1 ) states. (B) The photoelectron spectrum expanded over the region of EB = 0∼55 eV. The photon energy is 110.5 eV.

be due to the fact that the 4f3 6s2 –4f4 6s transition is forbidden by dipole selection rules. We think, however, that the P1 peak may be due to some states having the 4f3 6s2 configuration, but they cannot be assigned unambiguously because there is strong mixing among the three outer-shell configurations: 6s2 , 6s5d, and 5d2 . The states with a 4f4 6p configuration near the P2 peak may be unimportant because they can be excited only through the conjugate shake-up process in the 6s ionization. There are no other states of any configuration in the same region as the P2 peak. The pair of peaks P5 and P6 had similar relative peak intensity and energy spacing to the P1 and P2 pair. This suggested that the P5 and P6 peaks are due to shake-up states corresponding to the peaks P1 and P2 , respectively, and that the outer-shell configuration of P5 is 6s7s, 6s6d (or 5d7s), or 5d6d. (2) Dy the photoelectron spectra taken for atomic Dy at three different photon energies is shown in Fig. 6(A). The details of the 4f spectrum are shown in Fig. 6(B). The lowest excited state [Xe]4f10 (5 I8 )5d6s(3 D) lies at 2.17 eV above the lowest 5 I8 level

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Table 3 Binding energies EB of various excited states of Dy+ . EB (eV)a 162.8 155.1 53.7 43.3 42.3 38.1 36.8 34.5 32.4 31.7 29.3 28.1 19.6 P9 18.5 P8 16.4 P7 15.5 P6 14.4 13.9 P5 11.7 P4 10.7 P3 8.6 P2 7.8 P1 6.1 a b

Dy+ configurationb 9

2

6

10

Core hole 2

[Kr]4d 5s 5p 4f 6s [Kr]4d9 5s2 5p6 4f10 6s2 [Kr]4d10 5s5p6 4f10 6s2 (4 I8 ) [Kr]4d105s5p64f106s2(6I8)

4d−1 5s−1 5p−1

[Kr]4d10 5s2 5p5 (2 P1/2 )4f10 6s2

[Kr]4d10 5s2 5p5 (2 P3/2 )4f10 6s2 4f−1 [Kr]4d10 5s2 5p6 4f9 5d6d(6 H) [Kr]4d10 5s2 5p6 4f9 5d7s(4,6 H, 4,6 I, 4,6 K) ————— 6d6s(4,6 H, 4,6 I, 4,6 K) [Kr]4d10 5s2 5p6 4f9 6s7s(6 H)

[Kr]4d10 5s2 5p6 4f9 5d2 (6 H, 6 I, 6 K) [Kr]4d10 5s2 5p6 4f9 5d6s(4,6 H, 4,6 I, 4,6 K) [Kr]4d10 5s2 5p6 4f9 6s2 (6 H) [Kr]4d10 5s2 5p6 4f10 6s

6s−1

The uncertainties in EB are ±0.3 eV. The ground state of Dy atom is [Kr]4d10 5s2 5p6 4f10 6s2 (5 I8 ).

Xe atom [50], Cs [16], and Sm [16], the branching ratio 5p3/2 /5p1/2 varied markedly against the photon energy in the giant resonance region. The 4d photoelectron lines are very weak, but they are easily identified in the spectrum taken at h = 205 eV [Fig. 6(A)].

Fig. 6. (A) Photoelectron spectra of Dy atom taken below (149 eV), at (159 eV) and above (205 eV) the 4d–4f giant resonance peak. (B) The photoelectron spectrum expanded over the region of EB = 2–22 eV. The photon energy is 148.5 eV.

of the ground state [Xe]4f10 6s2 (5 IJ ) [49], which means that the contribution from excited species is negligible. The tentative assignments of the Dy photoelectron lines are given in Table 3. The 4f, 5p, and 5s photoelectron lines are clearly observed in the spectrum taken at h = 149.0 eV, which is below the giant resonance. In Fig. 6(B), we see four strong and clearly separated 4f lines at EB = 7.8 (P1 ), 8.6 (P2 ), 10.7 (P3 ), and 11.7 eV (P4 ). Several satellites (P5 –P9 ) accompany these main 4f lines. The optical data table due to Martin et al. [49] lists a number of sextet and octet states in the region where the lower three 4f lines (P1 –P3 ) appear. These states include states with the following outer shell configurations: 4f9 6s2 (7.65–8.20 eV), 4f9 5d6s (7.80–9.50 eV), and 4f9 5d2 (9.40–10.7 eV). This table, however, does not list any states that correspond to the position of P4 . As in the case of Nd atom, the P6 –P9 peaks are probably a duplicate of the P1 –P4 peaks. It is likely that these peaks are due to shake-up processes where the excitation of a 4f electron is accompanied by excitation of a 6s electron. The relative intensity of the 5p3/2 and 5p1/2 lines in the spectrum at 159 eV is different from that at 149 eV. This suggests that, as in the cases of

(3) Er Fig. 7 shows an example of the photoelectron spectra obtained for the Er atom, which has the ground state configuration [Kr]4f12 6s2 (3 H6 ). The photon energy is 170 eV near the third peak in the total photoion-yield spectrum. Three strong 4f lines dominate the spectrum, but only the lowest 4f line at EB ≈ 8 eV can be assigned unambiguously as 4f11 6s2 (4 Io ) state from Martin’s data [49]. Although the 5p and 5s lines can be identified, they are very weak. It was not possible to obtain the 5p and 5s photoionization cross-sections with sufficient accuracy because of the low S/N ratios. Also, it was not possible to resolve the 4d lines and their associated Auger peaks. 3.3.2. Partial photoionization cross-sections For the Nd and Dy atoms, a series of photoelectron spectra were taken at different photon energies, and this enabled determination of the relative partial cross-sections for the photoionization of nl = 4d, 5p, 5s, (4f + 6s) subshell electrons as a function of photon energy. In the photoelectron spectra presented in Figs. 5 and 6, the continuum level is also apparent. When the partial photoionization

Fig. 7. Photoelectron spectrum for the Er atom taken at photon energy 170 eV.

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Fig. 8. The present partial nl photoionization cross-sections (open and closed circles) for Nd atom. For comparison, the partial photoion-yield cross-sections (dotted lines) and the TDLDA partial nl cross-sections (dashed lines) [22] are also shown.

cross-sections (nl) were calculated from the series of photoelectron spectra, the continuum level was subtracted from the observed spectrum as background. All (nl) cross-sections, except those of the partial 4f lines in 5(B) and 6(B), were calculated including their corresponding satellite lines. Because the target atom’s density was not known, initially the relative (nl) curves were determined. These curves were later scaled to an absolute cross-section curves using Eq. (4).

decay of the Nd+ (4d−1 ) ions (open circles). For comparison, the same curve was also determined directly from the 4d lines in the higher photon-energy region 157–180 eV (closed circles). The photoelectron data thus obtained were normalized to the Auger data. It should be noted that in the 5s cross-section presented here, no data points were taken from the 125–134 eV region because here the 5s photoelectron lines merge with the N4,5 O2,3 N6,7 Auger lines.

(1) Nd Fig. 8 shows (nl) for the Nd atom (open circles) together with the results of TDLDA calculation (dashed curves) due to Dzionk et al. [22]. The related photoion-yield cross-sections (Mn+ ) are also included to show the correspondence between (nl) and (Mn+ ). The partial cross-sections for the two main 4f lines (P1 and P2 ) are shown as well. The vertical bars at the top in each panel indicate the 4d ionization limits obtained from the present photoelectron spectra. A Beutler–Fano profile is seen not only in the (4f) and (Gd+ ) curves, but also in the P1 and P2 4f lines. The relative (4d) curve was determined indirectly from the N4,5 O2,3 N6,7 Auger electron lines emitted upon the

The results of TDLDA calculations show marked differences from experimental results, especially in cross-section magnitudes. The maximum value of the present (4d) curve is about 60% of that given by the TDLDA calculation. The maximum values of the present (4f) and (5p) curves, however, are larger than those of the TDLDA calculations. Because the present data are normalized to the TDLDA calculation using the two sum cross-sections, these disagreements imply that the TDLDA calculation overestimates considerably the 4d cross-section with respect to the others. These differences between experimental and theoretical results reflect the difficulty in taking the electron correlation into account. Moreover, from numerical

G. Kutluk et al. / Journal of Electron Spectroscopy and Related Phenomena 169 (2009) 67–79

75

Fig. 9. The present partial nl photoionization cross-sections (open circles) for Dy atom compared with the partial photoion-yield cross-sections (dotted lines) and the TDLDA partial nl cross-sections (dashed lines) [22].

calculations using the results shown in Fig. 8, we found that at energies on higher energy side of the resonance peak the sum crosssection Qdir is usually less than Qion . This difference is due to direct multiple (mainly double) ionization processes associated with the nl photoionization that are not included in any of (nl) partial crosssections, but lead to the formation of multiply charged ions. For example, the difference at 140 eV amounts to about 10% of Qion , which indicates that the overall contribution of double photoionization processes amounts to about 10% at 140 eV.

Dy is unexpectedly large. The theoretical value of (4f) is larger than the experiment by a factor of about 2 and the (4d) by a factor of about 5. In contrast, the theory considerably underestimates the (5p) and (5s) values. Moreover, as in the case of Nd atom, the comparison between the two sums Qdir and Qion shows that in the 160–200 eV region Qdir is approximately 10% smaller than Qion . This shortfall is ascribed again to the contribution of double ionization processes. 4. Discussion

(2) Dy the cross-section (nl) obtained for Dy is shown in Fig. 9. The partial cross-sections for the two main 4f lines are also included. It should be noted that the TDLDA cross-sections  t (4f) and  t (4d) in Fig. 9 are scaled down by factors of 2 and 8, respectively. The relative (4d) curve was determined indirectly from the N4,5 O2,3 N6,7 Auger lines. Although large uncertainties (±30%) in the absolute values are estimated for the experimental points of (4d) because of the weaker Auger electron signals, the error in the relative variation is estimated to be less than 5%. The discrepancy between the experiment and the calculation in

4.1. The variation along Z of the photoionization processes in the 4d region Putting the results obtained in the present experiment together with previous experimental and theoretical studies enabled us to obtain further details on the giant resonance phenomena in the 4d region. This subsection will first summarize the current understanding of the 4d giant resonance [1,2,4], then the results of the observed charge-state distribution will be used to discuss the vari-

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ation of the 4d photoionization processes with Z. In particular, we will discuss how the 4d giant resonance spectra gradually change from having a shape resonance character to an autoionizing resonance character as Z increases. An important factor governing the 4d photoabsorption process is the effective single-particle potential for an f electron excited from the 4d shell. In the Xe atom, the effective potential consists of two wells separated by a positive centrifugal barrier [51,52]. Below and slightly above the 4d ionization limits, the excited f wavefunction is repelled from the core due to this barrier and lies in the shallow outer well region. As a result, the overlap between the 4d and (4, ε)f wavefunctions is very small, and the oscillator strength of the 4d–(4, ε)f transition also remains very small. When the photon energy increases to levels of the barrier height, the overlap of the 4d and εf wavefunctions becomes appreciable due to the penetration of the εf wavefunctions into the inner-well region. The oscillator strength of the 4d absorption then becomes larger, which induces 4d → εf transitions well above the 4d limit, and yields a giant resonance spectrum with a shape resonance character. As the atomic number Z increases from Xe, the inner well deepens because of the increase in nuclear charge. Corresponding to this variation, the barrier sinks from above the 4d ionization limit to below it, and the 4f wavefunction moves from the outer well to the inner well. This is called the collapse of the 4f wavefunction. In the neutral lanthanide atom series without the 4d hole, the 4f orbital collapse occurs suddenly between Ba and La, forming the first rare-earth series of elements [52,53]. In the case of the 4d photoabsorption, the effective potential on a f electron is due to the 4d-excited configuration [48,52]. This means that the atom in which the f wavefunction collapses is expected to be an atom lighter than Ba. Sonntag and Zimmermann [2], on the basis of experimental and theoretical data available to them, suggested that 4f orbital collapses gradually, not suddenly. The partial photoionization and photoion-yield curves obtained in the present experiment provide further evidence of this gradual change. To demonstrate the gradual character change in the (Mn+ ) curves, the charge-state distribution was calculated at the cross-section maxima as a function of Z as shown in Fig. 10. In addition to the results of the present experiment, Fig. 10 also includes results of a previous study by Nagata et al. [23]. Although the shape of (Mn+ ) curves and the positions of their maxima for a given atom are different for each curve, the distribution in Fig. 10 can be understood to represent the charge-state distribution averaged over the 4d resonance region. Fig. 10 shows that the charge-state distribution varies markedly with Z, and that this variation is not sharp but gradual. The sum of the populations of triply charged and quadruply charged ions for Ba(Z = 56) amounts to 71%. The sum of the populations decreases to 39% for Nd(Z = 60) and to 17% for Dy(Z = 66). Instead, the popula-

tion of singly charged ions increases from 0.6% for Ba, 32% for Nd, and 54% for Dy. This variation in the photoion population is in good qualitative agreement with the branching ratios of the nl photoionization channels obtained from the present experiment, as well as those from previous [15–21] experiments. The branching ratio of (4d), the resultant 4d ionization (4d−1 ) states decaying mainly to triply charged and quadruply charged ions, was 81% for the La, 20% for the Nd and 6% for the Dy. In contrast, the branching ratio of (4f), the resultant 4f−1 states decaying mainly to singly charged ions, is zero for the La, 39% for Nd atom, and 71% for Dy. The branching ratio of (5s) + (5p), the resultant 5s−1 and 5p−1 states decaying mainly to doubly charged ions, remained at 20–25% throughout. The aforementioned gradual variation is also seen in the peak positions of the (Mn+ ) and (nl) curves. The peaks of the (M+ ) and (M2+ ) curves for Ce and Nd atoms, the lighter atoms in the lanthanide series, lie at photon energies 10–15 eV below those of the (M3+ ) and (M4+ ) curves (see Fig. 3). Differences in the peak positions become smaller for the Sm and Eu atoms [23] and almost disappear for the Gd, Dy and Er atoms. Similar characteristics are seen in the (nl) curves obtained in the present and previous photoelectron spectra [16–21]. Zangwill and Soven have explained the shift of peak positions for Ce in terms of a local field model using the time dependent local density approximation [40]. More specifically, they note that the difference in peak position is due to the differing responses of the 4d shell electron density and the outer (5s, 5p) shell electron density to the external field. We note that such a shift in peak position was observed by Becker et al. in the 4d, 5p, and 5s cross-sections in Xe [50], and was well reproduced by RPAE calculations by Kutzner et al. who took into account inter-channel coupling and relativistic effects [56]. As a natural consequence of the variation in the charge-state distribution mentioned above, the profile of Qion curves for intermediate to heavier lanthanide atoms is dominated by the profiles of the (M+ ) curves. The (Ce+ ) curve bears a profile similar to a shape resonance, but in this case it influences the profile of the Qion curve of Ce very little because it makes only a small contribution to Qion . In moving from Ce to heavier atoms, the (M+ ) curves begin to show an asymmetric Beutler–Fano profile of characteristic of autoionization, which is also reflected in the corresponding Qion curves. We also notice that the (M+ ) curves for the Gd atom show a higher degree of symmetry than the corresponding curves for neighboring atoms. This point will be examined further in Section 4.2 (see profile index q in Table 4). The variation in the charge-state distribution and those in the (Mn+ ) and (nl) curves mentioned above can be interpreted in terms of three processes. In the Ce atom, both processes, shape resonance and a Coster–Kronig type process, dominate over the 4d resonance. The shape resonance decays to the 4d ionization continuum in the following way: 4d10 4fn → 4d9 (4, ε)fn+1 → 4d9 4fn + εf

(6)

The Coster–Kronig type process ends in the ionization of the outer subshell: 4d10 4fn → 4d9 (4, ε)fn+1 → 4d10 4fn (5s, 5p, 6s, 5d)−1 + εl,

(7)

where n = 1 for Ce. These two processes give rise to different energy dependence [22,50]. In the Nd atom, the autoionization (a super Coster–Kronig type process), which can be expressed symbolically as 4d10 4fn → 4d9 4fn+1 → 4d10 4fn−1 + ε(d, g),

Fig. 10. Charge-state distribution as a function of Z determined at maxima of the photoion-yield cross-sections. Results obtained in a previous study by Nagata et al. [23] are also included.

(8)

takes part appreciably in addition to processes (6) and (7). The main part of the dipole-allowed terms of the resultant 4d10 4fn–1 configuration is below the Nd2+ threshold (16.3 eV. see Table 2), and so they end up forming Nd+ ions. The yield curve of Nd+ ions shows an asymmetric Beutler–Fano autoionization profile, and it is different

G. Kutluk et al. / Journal of Electron Spectroscopy and Related Phenomena 169 (2009) 67–79 Table 4 Fano parameters obtained by the fitting the experimental (4f) and (M+ ) curves to the Beutler–Fano profile [47]. √ Cross-section Curves Er (eV)a  (eV) q q  Ce

(Ce+) (4f)M

120.4 (1) 120.4

6.7 (1) 4.4

3.83 (15) 4.0

Nd

(Nd+ ) (4f)

120.7 (3) 121.6 (5)

7.5 (5) 10.0 (8)

1.02 (10) 1.23 (14)

2.8 3.9

Sm

(Sm+ ) (4f)R (4f)P

133.2 (2) 133.8 133.4

5.3 (3) 4.6 4.7

1.63 (16) 2.0, 3.9b 1.78

3.8 4.3, 8.4b 3.8

Eu

(Eu+ ) (4f)R

139.1 (1) 139.3

5.5 (2) 4.6

2.01 (8) 1.9–2.0

4.7 4.2

Gd

(Gd+ )

148.3 (1)

5.0 (1)

2.67 (9)

6.0

Dy

+

(Dy ) (4f)

153.8 (3) 154.4 (2)

7.3 (7) 7.6 (4)

1.04 (9) 1.22 (7)

2.8 3.4

Er

(Er+ )

169.0 (2)

5.1 (2)

1.77 (2)

4.0

Tm

 ab

173.15 (10)

2.8 (2)

3.6 (4)

6.0

Rad

77

interesting case to study. Since Eu has been treated using various methods, it is possible to compare them to each other and to experimental results. In fact, in 1991 Pan et al. [38] calculated partial photoionization cross-sections for 4d, 4f, 5s, 5p, and 6s electrons employing MBPT and compared the results to RPAE [57] and RTDLDA (relativistic TDLDA) [58] calculations as well as to experimental results [1,17,21]. Although their MBPT calculations showed reasonable agreement with other calculation methods and experimental data, small but significant discrepancies still remained among different calculations. In particular, their study showed that RTDLDA calculations overestimated the experimental 4d cross-section. In recent years there have been a number of theoretical attempts to address this problem. Two recent approaches that have led to improved agreement are the SPRPAE (a spin-polarized version of RPAE) approach by Ya Amusia et al. [32,59,60] and TDLSDA (time dependent local spin density approximation) approach by Tong et al. [33]. Both calculations demonstrate the importance of treating spin polarization effects properly.

a

The uncertainties in Er shown in the parentheses includes the standard deviation obtained from the curve fitting and the uncertainty in the energy calibration. b The two values are due to the excitation of [Xe]4f5 6s2 (6 H, 6 F) and [Xe]4f5 6s2 (6 P) states, respectively. R: experimental results obtained by Richter et al. [21]; P: experimental results obtained by Prescher et al. [16]; Rad: from absorption curve obtained by Radtke [14]; M: experimental results obtained by Meyer et al. [19].

from both that of the Nd2+ curve due to the process (7) and those of the Nd3+ and Nd4+ curves due to process (6). Eventually, the Nd atom gives rise to three different kinds of photoion-yield curves. In the heavier Gd, Dy and Er atoms, the shape resonance character in the M3+ and M4+ curves disappears almost completely because process (6) hardly occurs once the 4f wavefunction collapses. The coexistence of processes (6) and (8) in Nd can be ascribed to term-dependent effects in the 4d9 4fn+1 configuration. Termdependent calculations of the potential curve and the wavefunction corresponding to the 4f electron for the Ba 4d9 4f configuration [52] reveal that the 4f wavefunction in Ba 4d9 4f(1 P) term is pushed towards the outer well. This behavior is different from the other nine terms, which cause the 4f wavefunction to collapse in the inner well. For Ba, the 4d photoabsorption is dominated by a shape resonance because 1 P is the only dipole-allowed term. In the case of Nd atom whose ground state is 4d10 5f4 5 I4 , however, there are three dipole-allowed terms (5 H, 5 I, 5 K) for the excited 4d9 4f5 configuration. Although no calculations on these terms have been reported, it is likely that some of these terms have potential curves that push the 4f wavefunction towards the outer well while the other terms cause the wavefunction to collapse in the inner well. This means that some of the dipole-allowed terms of the 4d9 4f5 configuration lead to shape resonance and the remainder to an autoionizing resonance. For the Nd, Dy and Er atoms, the quadruply charged M4+ ions are produced from the 4d−1 4fn nl excited states lying below the 4d limits. It is unlikely that these excited states decay to M4+ ions by stepwise Auger processes because so few of the necessary intermediate states have energies that can be easily accessed by the excited states of interest. It is more likely that multielectron processes, such as Auger shake-off (mainly double Auger) processes, are responsible for the formation of the M4+ ions. In the above discussion, the experimental cross-sections (nl) for the Nd and Dy atoms have been compared with theoretical cross-sections obtained from the TDLDA calculations of Dzionk et al. [22] because their calculations on these atoms are the only ones available at the present time. In contrast to Nd and Dy, there have been a number of theoretical studies on Eu because its half-filled subshell (4f7 ) configuration makes it an especially

4.2. Beutler–Fano profiles in the (4f) and (M+ ) curves As we noted in Sections 3.2.1 and 3.3.2 of this paper, the (4f) and (M+ ) curves for the mid-weight to heavy-weight lanthanide atoms whose 4f subshell is partially filled clearly display the well-known asymmetric Beutler–Fano profile of autoionization (Figs. 3, 8, 9). The partial cross-sections for the separated 4f photoelectron lines Pi [see Figs. 5(B) and 6(B)] also display the Beutler–Fano profile, though the experimental uncertainties are larger. The interpretation of this profile is now well established [1,53–55,61,62]. It is a consequence of the strong interference between the direct 4f photoionization channel and the indirect photoionization channel. The indirect channel is expressed by process (8), in which the resonant 4d9 4fn+1 excitation is followed by a super-Coster–Kronig transition. The Beutler–Fano profile is expressed by (E) = a

(q + ε)2 + b 1 + ε2

(9)

with ε=

E − Er  /2

(10)

In the present case, (E) corresponds to (M+ ) or (4f). The quantity  is the width of the resonance state, q is the profile index,  a and  b are the resonant and non-resonant portions of the cross-section, and Er is the resonance energy [60,61]. The index q is expressed as



q=

2 < ϕ|T | 0 > · ,  < E |T | 0 >

 = 2| < E |H|ϕ > |2 ,

(11) (12)

where 0 is the ground state, ϕ is the discrete autoionizing state,

E is the continuum state, and T is the transition operator. Using Eq. (12) with the observed resonance width  enables us to determine the strength of the interaction between the ϕ and E states. It is relatively easy to deduce the resonance parameters  , q and Er , the Fano parameters, from each of the experimental crosssection curves using a fitting program. Since the energy resolution of the optical spectrometer (0.05–0.10 eV) is very small compared with the  values, the parameters were obtained using Eqs. (9) and (10), where the bandwidth of the spectrometer is neglected. Table 4 summarizes the Fano parameters that were computed for the five atomic species considered here. Table 4 also includes Fano parameters for the (4f) curves of Sm, Eu reported by Richter et al. [20,21] and by Nagata et al. [23], those of Sm by Prescher et al. [16], and those for the 4d absorption curve of Tm by Radtke [13]. In the

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curve fitting, we excluded the portion of the weaker discrete features appearing on the lower energy side of the giant peak. For the Nd and Sm atoms, we see a small hump on the higher energy side of the giant peak. Therefore, we fitted the points using a formula consisting of two Beutler–Fano profiles. One peculiar feature that should be noted is that the profile index q increases around Gd atom in addition to atoms near lighter and heavier ends of lanthanide series. An increase in q corresponds to a decrease in asymmetry of the autoionization profile, and it indicates a decrease in the interaction of the resonance state with the continuum. It follows then that atoms having larger values of q have a longer lifetime, that is, a smaller values of  . Although not always clear, such a tendency is seen in Table 4. From Eq. (10), we see that √ the quantity q  provides information about the relative intensity √ between the matrices <ϕ|T| 0 > and < E |T| 0 >. The values of q  are shown in √ the last column of Table 4. The general tendency is that the q  value becomes larger around Gd and Tm, the latter being the heaviest atom considered. This means that, the discrete/continuum excitation ratio in these atoms is larger than those of other atoms. The Eu and Gd atoms √ have half-filled 4f shell configuration, 4f7 . The increase in the q  values around Gd atom may be an effect arising from the half-filled shell, but the exact reason for why such an increase occurs in atoms with the 4f7 configuration remains a topic for further study.

5. Summary To provide additional experimental data and to obtain further quantitative information about the 4d giant resonances in the photoionization of the lanthanide atom series, the photoelectron and photoion-yield spectra have been measured for free Ce, Nd, Gd, Dy, and Er atoms. The present results are consistent with the current understanding of 4d giant resonance phenomena. Our study also indicated that the 4d giant resonance spectra changed gradually, rather than suddenly, from having a shape resonance character to an autoionizing resonance character. One exception, however, is atomic Nd, for which the shape resonance and autoionization characters coexist. One possible explanation for this coexistence is that it is due to term-dependent effects because the potential for the excited 4f electron and the 4f radial wavefunction corresponding to this potential depend on terms in the 4d−1 4fn+1 configuration. For all the aforementioned five atoms, whose partial cross-sections (4f) and (M+ ) revealed an asymmetric Beutler–Fano profile, the resonance parameters Er , q, and  were determined. These parameters were also determined for Eu and Sm using results from a previous photoion-yield study due to Nagata et al. (1990). Finally, it was found that Gadolinium, which has a configuration with halffilled 4f7 subshell plus a 5d electron, showed peculiarities in the variation of both its asymmetry parameter q and its charge-state distribution as plotted against Z.

Acknowledgments We wish to express our gratitude to Prof. Akira Yagishita at Photon Factory in the National Laboratory for High Energy Physics at Tsukuba for his continual guidance and encouragement throughout the course of this study. We are grateful to Dr. Eiji Shigemasa for his advice, especially regarding the use of the monochromator. We appreciate Prof. Tsutomu Watanabe and Prof. X.-M. Tong at Tsukuba University for discussion regarding theoretical aspects of this paper. We thank Prof. Mark Greenfield for his suggestions on improving the clarity of the paper. We acknowledge Mr. Tokutaro Takaku, Dr. Kazuaki Iemura, and Dr. Shuichi Yagi, for their assistance with the experiment and analyses of the results.

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