Photoabsorption cross section of C60 thin films from the visible to vacuum ultraviolet

CARBON

4 7 ( 2 0 0 9 ) 1 1 5 2 –1 1 5 7

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Photoabsorption cross section of C60 thin films from the visible to vacuum ultraviolet H. Yagia, K. Nakajimab, K.R. Koswattagec, K. Nakagawac, C. Huanga, Md.S.I. Prodhana, B.P. Kaflea, H. Katayanagia, K. Mitsukea,* a

The Institute for Molecular Science and Graduate University for Advanced Studies, Photomolecular Science, Myodaiji, Okazaki 444-8585, Japan b Science Research Center, Hosei University, Chiyoda-ku, Tokyo 102-8160, Japan c Graduate School of Human Development and Environment, Kobe University, Nada-ku, Kobe 657-8501, Japan

A R T I C L E I N F O

A B S T R A C T

Article history:

Absolute photoabsorption cross sections of C60 thin films are determined in the hm range

Received 8 June 2008

from 1.3 to 42 eV by using photon attenuation method. The spectrum shows a prominent

Accepted 27 December 2008

peak of 1180 Mb at 22.1 eV with several fine structures due to single-electron excitation

Available online 6 January 2009

similarly to the case of C60 in the gas phase. The complex refractive index and complex dielectric function are calculated up to 42 eV through the Kramers–Kronig analyses. From the present data of C60 thin films the cross section curve of a molecular C60 is calculated with an assumption that the polarization effect of surrounding C60 molecules can be expressed by the standard Clausius–Mossotti relation. The spectrum thus obtained shows an excellent agreement with that of C60 in the gas phase measured independently.  2009 Elsevier Ltd. All rights reserved.

1.

Introduction

Since the discovery of the method for synthesizing macroscopic amount of C60 [1], optical properties of solid C60, such as the photoabsorption cross section [2–5], refractive index [6,7], and normal reflectivity [8], have been studied by various techniques. Although strong electronic transitions are expected to lie between 15 and 21 eV by analogy to gaseous C60 [9–13], most of the above experimental works of solid C60 have been restricted to photon energies below 7 eV. Thus the complex dielectric function e(m) of solid C60 has been estimated only from the loss function of electron energy loss spectroscopy (EELS) through the Kramers–Kronig transformation [14]. A great care must, however, be taken before analyzing the EELS data to deal with the corrections for the effects of projectile electrons, i.e. quasielastic scattering, multiple scattering, and momentum transfer to the valence electrons of

solids. Obviously there is an increasing demand for a proper photoabsorption study of solid C60 which is essential to directly evaluate accurate absolute cross sections and to elucidate fundamental optical properties in the vacuum ultraviolet from revised complex dielectric functions. In this paper, we present the first determination of absolute photoabsorption cross sections of C60 thin films over a wide energy range from 1.3 to 42 eV. Below 7 eV many groups have studied photoabsorption of solid C60 with interest in its electronic structures, electron-vibration coupling, and interband transitions associated with r and p bands. In contrast, photoabsorption measurements above 7 eV are extremely scarce. Achiba et al. [4] have reported several fine structures on the relative photoabsorption spectrum of a C60 thin film from a steplike feature at hm = 7 eV to the absorption edge of an LiF substrate at 11 eV. The spectra were taken with a low photon flux less than 1010 photons s1, and a

* Corresponding author: Fax: +81 564 53 7327. E-mail address: [email protected] (K. Mitsuke). 0008-6223/$ - see front matter  2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.carbon.2008.12.053

low resolving power of 500, so that the reproducibility of their data needs to be further checked. Nevertheless all subsequent studies for photoabsorption of solid C60 were fulfilled below 7 eV. In the present work, the spectra over a much larger energy range permit a more detailed study of the higher electronically excited states and frequency-dependent polarizability of a single C60. Furthermore, we can achieve the e(m) curve directly from the absolute photoabsorption cross sections, examining the influence of the momentum transfer on the corresponding curve derived from the EELS study.

2.

photon flux and spectral resolution were 4 · 1011 photons s1 and 10 meV at hm = 9 eV, respectively. The sample was suspended on a rod of a linear-motion feedthrough inside the vacuum so the two regions of the collodion substrate were alternately put in the path of the photon beam. From 5 to 9.3 eV we inserted an LiF window in the upstream of the sample to eliminate the contamination of the second and higherorder lights. The photoabsorption cross section r of the C60 film was estimated by using the Lambert–Beer law r¼

Experimental

Samples of C60 films 11 to 55 nm in thickness were prepared by deposition of the C60 vapor on substrates in the vacuum. As the most appropriate substrate we have chosen a collodion thin film 10mm in diameter supported on a mesh of tungsten (80% transmission), because collodion shows good transparency in the whole energy range from 1.3 to 42 eV [15]. Commercial C60 powder (>99.98% purity, Material Technologies Research) loaded in a quartz vapor source was heated with a resistive heater, first kept around 150 C for 7 h to remove residual water and organic solvents, then heated up to 400 C to vaporize C60. The collodion substrate and a crystal-oscillator surface thickness monitor (Inficon, XTM/2) were mounted on a stainless steel block 90 mm above the vapor source so that their centers were equidistant from the vapor source. Thus the total amount of C60 on the substrate could be estimated from the deposition rate measured with the thickness monitor. The deposition rate was adjusted between ˚ /s. We exposed only the half of the substrate to 0.16 and 0.29 A the C60 vapor by using a semicircular Teflon mask to partition the substrate into two regions, i.e. the regions with and without C60. The thickness t of the C60 film on the substrate was calculated from t ¼ MTM =ATM q

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4 7 ( 20 0 9 ) 1 1 5 2–11 5 7

1 I0 ATM M I0 ln : ln ¼ I I tN MTM L

ð2Þ

Here, N is the number density of C60 in the sample, I is the light intensity measured downstream of the collodion substrate covered with a C60 film, I0 is the light intensity measured downstream of the collodion substrate without C60, L is the Avogadro constant, and M is the molar mass of C60. Though I and I0 could not be measured simultaneously, they were normalized by the ring current of the storage ring. The validity of this normalization is guaranteed because the radial distribution of the relative electron density in the UVSOR storage ring does not change throughout the user time.

3.

Results and discussion

3.1.

Photoabsorption cross section of the C60 film

Fig. 1 shows the absolute photoabsorption cross section curve rfilm of the C60 film constructed from the results of the sample with t = 28 nm. This curve is composed of three spectra measured using different gratings, i.e. G3 at 1.3 eV 6 h m 6 5 eV, G2 at 5 eV 6 hm 6 10 eV and G1 at 10 eV 6 h m 6 42 eV. To check the reproducibility of the data we fabricated two samples separately by the C60 vapor deposition and then took entire spectra

ð1Þ

where MTM is the total mass of C60 deposited on the thickness monitor, ATM is the effective area of the thickness monitor and q = 1.68 g cm3 is the mass density of solid C60 at 300 K [16]. The sample of the collodion substrate with C60 was removed from the vacuum chamber and taken to the UVSOR synchrotron radiation facility. Before going on to description of the next procedure we would like to mention the state and structure of the present C60 samples. Hebard et al. [3] have deposited C60 thin films in the vacuum and found that they are polycrystalline with a face-centered cubic (fcc) structure. The lattice parameter was estimated from neutron powder diffraction to be 1.416 nm at 290 K [16]. We have prepared C60 thin films in a similar way to these authors, so that our samples should also be polycrystalline with an fcc structure at room temperature. Optical absorption measurements were carried out by means of photon attenuation method at the bending magnet beamline BL7B of the UVSOR storage ring equipped with a 3 m normal incidence monochromator. This monochromator has three gratings (G1:1200 lines/mm, G2:600 lines/mm, G3:300 lines/mm) to provide radiation in the range of 1.2–42 eV [17]. A silicon photodiode (IRD Inc. AXUV-100) was employed for measuring the photon intensity. A typical

Cross section / Mb

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Colavita [19] σgas [13]

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Photon energy / eV Fig. 1 – Experimental and theoretical absolute photoabsorption cross sections of C60. The solid curve is obtained by photon attenuation measurements of the C60 film 28 nm in thickness (present study) and the dashed curve by ab initio calculations of a C60 molecule [19]. The dotted curve designates the cross sections of gaseous C60 [13]. This curve is the composite of the three cross section curves which were obtained by photoionization and photon attenuation measurements [11,12,18] and were reevaluated using the data of vapor pressure from [25] (see the text).

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twice for each sample. Essentially the same results have been obtained for the samples with t = 11 and 55 nm, with only an exception that the curve of the 55-nm sample deviates downwards in the range 12 eV 6 hm 6 27 eV from those of the other samples due to the saturation of the absorbance. The continuity between the spectra for the three gratings is found to be excellent. This suggests negligible contribution of the second and higher order lights from the gratings at least at hm = 5 and 10 eV. The rfilm curve of Fig. 1 exhibits a prominent broad peak, with a maximum value of 1180 Mb at 22.1 eV, being accompanied by several fine structures at 9.0, 10.5, 12.8, 17, 19, and 26 eV. The two shoulders at 9.0 and 10.2 eV were mentioned by Achiba et al. in their photoabsorption spectrum of a C60 thin film [4], but the other structures are demonstrated here for the first time because there has been no report on the absorption spectrum of solid C60 above 11 eV. As for gaseous C60 the absolute photoabsorption cross sections in the extreme UV region have been reported by only a few groups [10–13,18], owing to the difficulty in accurately estimating the sample density and effective path length in the interaction region. Among relevant papers Kafle et al. [13] have obtained a reliable absolute photoabsorption spectrum for the gas-phase C60 at hm = 3.5120 eV by piecing together the three cross section curves [11,12,18] after appropriate adjustments in the vapor pressures of C60. We shall come back to this point in more detail in Section 3.3; suffice it for the present to say that a divergence of rgas values among the papers published in the last decade is now being reconciled by the compilation described in [13]. In Fig. 1 we plot the cross section curve rgas of C60 in the gas phase proposed by Kafle et al. [13]. Evidently the spectral shape of the cross section of C60 is broader for condensed phase than for gas phase. Peaks or shoulders at 10.5, 12.8, 17, 19, and 26 eV in the present rfilm curve probably correspond to those at 10.5, 13.4, 17.8, 20 and 26 eV in the rgas curve. The origin of these fine structures have been investigated in the theoretical work by Colavita et al. [19]. They calculated the photoabsorption cross section of a solitary C60 molecule and interpreted such fine structures in terms of a manifold of shape resonances as single-electron excitation to vacant orbitals. Their calculation on a molecular C60 can be compared with the present curve of a C60 thin film because solid C60 is a molecular solid which is bonded by weakly interacting van der Waals force. The dashed curve in Fig. 1 illustrates the theoretical photoabsorption cross section curve of C60 by Colavita et al. A considerable difference is observed in the lineshape between the present rfilm and theoretical curves, but the peak positions of the two curves agree fairy well with each other. Fig. 2 shows an expansion of the present r film curve in Fig. 1, measured with G2 at 5 eV 6 hm 6 10 eV and with G3 at 1.5 eV 6 hm 6 5 eV. There are three peaks at 3.6, 4.6, and 5.6 eV and two shoulders at 2.8 eV and 6.4 eV, consistent with the information in the literature. These structures have been attributed to the p!p* transitions in many papers, but their assignments are still controversial [7,8,20–22] and we will not go into further details. Below the band gap of solid C60 (2 eV), our cross section curve does not fall to zero. Conceivably light scattering at grain boundaries causes the attenua-

σfilm (present)

Cross section / Mb

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Skumanich [2] 400

200

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8

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Photon energy / eV Fig. 2 – Expansion of the present photoabsorption cross sections of the C60 film 28 nm in thickness. The dotted curve represents the data of photothermal deflection spectroscopy [2] normalized to the solid curve at 3.6 eV.

tion of the light in the polycrystalline films of C60. Skumanich [2] has argued that photothermal deflection spectroscopy is helpful in determining accurate optical densities for the weak absorption of C60 thin films in the visible and near infrared regions, since this method is not affected by the light scattering at grain boundaries. The dotted curve in Fig. 2 denotes the optical density function reported by Skumanich after normalizing his data point of 3.6 eV to the present rfilm value.

3.2.

Complex dielectric constant

The photoabsorption cross section is related to the imaginary part of the complex refractive index nðmÞ as 4pmn00 ðmÞ cN nðmÞ ¼ n0 ðmÞ þ in00 ðmÞ:

rðmÞ ¼

ð3Þ ð4Þ

Here, c denotes the velocity of light in vacuum and m denotes the frequency of the electromagnetic field. The real part n0 ðmÞ can be obtained by the Kramers–Kronig transformation of n00 ðmÞ. We derived n0 ðmÞ and n00 ðmÞ from rfilm in Fig. 1 and plotted them in Fig. 3a and b, respectively, as a function of hm. At hm 6 3.6 eV we adopted the corrected curve based on Skumanich’s data [2] (the dotted curve of Fig. 2). At 42 eV < hm < 280 eV rfilm was assumed to be equal to 60 times the total photoabsorption cross section of a carbon atom, 60 · r(C), because the relation of rgas = 60 · r(C) has proved to be a good approximation for gaseous C60 in the above hm region [12,13]. We have neglected a small contribution of the photoabsorption of inner shell electrons to the calculation of n’’(m). Once the complex refractive index is given, one can calculate the complex dielectric function e(m) from the relation eðmÞ ¼ ½nðmÞ2 ¼ e1 ðmÞ þ ie2 ðmÞ:

ð5Þ

Fig. 4a and b show the hm dependences of real e1 ðmÞ and imaginary e2 ðmÞ parts, respectively, computed from those of n0 ðmÞ and n00 ðmÞ in Fig. 3. Sohmen et al. [14] have first determined the complex dielectric function of the C60 thin solid film by EELS just after the large-scale production of fullerenes by Kra¨tschmer et al.

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a

2.5

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a

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present Sohmen [14]

6 5 ε1 ( h ν )

n’(hν)

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Energy / eV

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present Sohmen [14]

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ε2 ( h ν )

n’’(hν)

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[1] in 1990. The dotted curves in Fig. 4a and b designate e1 ðmÞ and e2 ðmÞ obtained by applying the Kramers–Kronig transformation to the EELS loss function Imb1=ec at the energy loss of 0–40 eV. The e1 ðmÞ curve of the present photoabsorption study resembles very well that of EELS, with commonly observed peaks at 2.4, 3.3, 4.1, 5.3, 8.9, 11.5, 15.5, 18.2, 20.7, 26 and 30 eV. Similarly, both curves of e2 ðmÞ in Fig. 4b exhibit peaks at 2.7, 3.6, 4.6, 5.6, 8.9, 10.0, 12.2, 16.7, and 21.5 eV. On the whole, the complex dielectric function derived from the present results agrees strikingly well with that from EELS data. From the assignments by Sohmen et al. [14], we attribute the peaks below 7 eV in the e2 ðmÞ curve to the p!p* interband transitions, while those above 8 eV to r ! r * with some contribution from p!r* and r!p* transitions. A small but systematic deviation is seen in e2 ðmÞ of EELS at hm = 9–23 eV, which is ascribable to the effect of linear momentum transfer from the projectile electron to the electrons in the target C60 on the surface. In contrast to the thin films of C60 its single crystals have become the objects of the e(m) measurement solely in the hm region below 5 eV. Milani et al. [23] have determined e(m) at 1.5 eV < hm < 5 eV by ellipsometry of C60 single crystals. The

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Energy / eV

Photon energy / eV Fig. 3 – The hm dependences of complex refractive index nðmÞ ¼ n0 ðmÞ þ in00 ðmÞ of the C60 film 28 nm in thickness calculated by using the photoabsorption cross sections from the present measurements and those from photothermal deflection spectroscopy [2]. The data employed for calculations are the dotted curve in Fig. 2 below 3.6 eV, and the solid curve in Fig. 1 at 3.6–42 eV.

0

Fig. 4 – The solid curves show the hm dependences of the complex dielectric function eðmÞ ¼ e1 ðmÞ þ ie2 ðmÞ of the C60 film 28 nm in thickness calculated from the complex refractive index in Fig. 3. The dotted curves show e1 ðmÞ and e2 ðmÞ determined by the EELS studies [14].

peak positions on their spectra of e1(m) and e2(m) are in excellent agreement with those on the corresponding curves of Fig. 4.

3.3. phase

Summary of the previous studies on C60 in the gas

One of the principal goals of the present study is to compare the cross section curve of thin films with that of isolated molecules. Before attempting this comparison we will first discuss the recent advances in the photoabsorption studies of solitary C60 in the gas phase. Three groups have reported the absolute photoabsorption cross sections in relatively wide hv ranges: (a) from 3.5 to 11.4 eV by Yasumatsu et al. [18], (b) from 10 to 26 eV by Jaensch and Kamke [11], and (c) from 25 to 119 eV by Mitsuke et al. [12]. However, the cross section curve of one group deviated from that of another group in an overlapping hv region. Furthermore, none of the three curves were consistent with the absolute values of the cross sections that Berkowitz [24] obtained in 1999 through his elaborate analyses based on the Thomas–Kuhn–Reiche (TKR) sum rule associated with the optical oscillator strengths [13,24] Z 4me ce0 E2 rgas dE: ð6Þ f¼ 2 e h E1

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Here, me denotes the electron rest mass, e0 the vacuum permittivity, and e the electron charge. The integration is carried out in the hm range from E1 to E2. In 2008 Kafle et al. reinvestigated all the available data [13] and concluded that the above discrepancies are ascribable to the uncertainties of the vapor pressure of the C60 in the gas chambers used for photon attenuation measurements. From their investigations the most dependable equilibrium vapor pressures of C60 are considered to be those given by Piacente et al. [25]. Relying on their vapor pressure data, Kafle et al. made the following alterations in the photoabsorption cross sections of the three groups: the cross sections of (a) Yasumatsu et al. [18], (b) Jaensch and Kamke [11], and (c) Mitsuke et al. [12] were reevaluated by multiplying their original values by 0.25, 1.5 and 1.5, respectively. The rgas curve in Fig. 1 is the composite of these revised cross sections, the most reliable curve at present. Kafle et al. also computed the oscillator strengths from rgas and achieved 230.5 for the hm range from E1 = 3.5 eV to E2 = 119 eV. This value agrees well with the oscillator strength of 233.4 expected from the TKR sum rule.

3.4. Comparison between the cross section curve of thin films and that of solitary molecules With the optical quantities obtained in Section 3.2 we will make a comparison between the rfilm and rgas curves in Fig. 1. For this purpose we need correction for attenuation of the electromagnetic field acting upon a C60 molecule in the solid phase induced by the polarization of surrounding C60 molecules. Andersen and Bonderup [26] argued that the standard Clausius–Mossotti relation is applicable to C60 solid films to a good approximation. Assuming the associated Lorenz–Lorentz expression for the local electromagnetic field they achieved a relation between the photoabsorption cross section of a single molecule rm and that for a solid film, 2  1 eðmÞ þ 2 rfilm : ð7Þ rm ¼ 0  n ðmÞ 3  Applying this expression to the present rfilm curve in Fig. 1 allows us to calculate rm using n0 ðmÞ in Fig. 3a and eðmÞ in Fig. 4. Eq. (7) is applicable over the whole energy range in the present study, because the electronic transition is the main contributor of most of the photoabsorption intensities even at the lowest hm (=1.3 eV). Fig. 5 shows the spectrum of rm thus obtained, together with the reported cross section of gaseous C60 (the rgas curve in Fig. 1) [13]. The rm curve appears to change on a parallel with that for rgas. In particular their agreement below 25 eV is considerably good. The marked similarity between the two curves provides conclusive evidence that the rfilm curve in Fig. 1 on an absolute scale is accurate and reliable. Moreover, it is highly likely that the polarization of surrounding C60 molecules is responsible for a broader spectral shape for a thin film than for a solitary molecule. Closer inspection of the spectral shapes in Fig. 5 reveals that a sharp peak at 7.9 eV in the rgas curve completely disappears in the rm curve calculated from rfilm. Yasumatsu et al. [18] have assigned this peak to the member of the Rydberg series converging to the first excited state of C60+. The absence of this peak in the rfilm curve can be attributed to perturbation

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Photon energy / eV Fig. 5 – Absolute photoabsorption cross sections of a single C60 molecule. The solid curve is obtained by applying Eq. (7) to the present photoabsorption cross sections of the C60 film and those from photothermal deflection spectroscopy [2]. See the caption of Fig. 3 for the data actually employed. The dotted curve designates the cross sections of C60 in the gas phase [13]. This curve is the composite of the three cross section curves which were obtained by photoionization and photon attenuation measurements [11,12,18] and were reevaluated using the data of vapor pressure from [25] (see the text).

of the Rydberg orbital in solid C60. The radius of the Rydberg orbital at which the radial density is maximal can be approximated as (n*)2a0, where n* and a0 are the effective principal quantum number and the Bohr radius, respectively. Using the reported n* of 3.65 [18] the size of the Rydberg orbital at 7.9 eV is estimated to be 0.705 nm. For a solitary C60 the Rydberg orbital is large enough compared with the molecular radius 0.3557 nm [27] to have hydrogenic characteristics, but, for solid C60, it is not small enough to remain unperturbed from surrounding molecules because the nearest-neighbor distance in the fcc lattice of solid C60 is known to be 1.00 nm [28]. The effective number of excited electrons neff in the hm range from E1 to E2 can be represented by using the sum rule [14,29] Z Z 8pme e0 E2 4me ce0 E2 0 neff ¼ Ee2 ðEÞdE ¼ n ðEÞrfilm dE ð8Þ 2 2 2 e h Ne h E1 E1 for the C60 thin film. Using the e2 curve in Fig. 4b we calculated neff from Eq. (8) to be 205.5 when E1 = 3.5 eV and E2 = 40.8 eV. This value can be compared with the number of electrons involved in optical transitions of gaseous C60 estimated from the TKR sum rule. Using Eq. (6) Kafle et al. [13] have shown that the oscillator strength f accrues to 178.5 when E1 = 3.5 eV and E2 = 40.8 eV. The difference of 15% between neff for the solid film and f for the gas phase may arise mainly from the disagreement of the two curves in Fig. 5 at 25–35 eV.

4.

Conclusions

We have determined the absolute photoabsorption cross sections of C60 thin films in the photon energy range from 1.3 to 42 eV. The spectrum above 11 eV has been reported for the

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first time. The cross section data encompassing a wide energy range allow us to calculate the complex refractive index and complex dielectric function. The present e2 ðmÞ curve shows many features due to interband transitions and resembles the previous result from EELS experiments, though there is a noticeable difference at hm = 9–23 eV probably due to slight influence of momentum transfer on the latter curve. The validity of the present cross section curve of C60 thin films has been demonstrated from the following observation: (i) a good agreement of the complex dielectric function calculated from our data with that from the EELS loss function and (ii) a close similarity between the cross section curve of a molecular C60 calculated by Eq. (7) and that of C60 in the gas phase. In connection with the second point, the broader spectral shape of C60 obtained in the thin film has been interpreted in terms of the polarization of surrounding C60 molecules.

Acknowledgements We are grateful to the members of the UVSOR for their help during the course of the experiments. This work has been supported by the Joint Studies Program (2007–2008) of the Institute for Molecular Science, by national funds appropriated for special research projects of the Institute for Molecular Science, by Grants-in-Aid for Scientific Research (Grant Nos. 18350016 and 17750023) from the Ministry of Education, Culture, Sports, Science and Technology, Japan, and by a grant for scientific research from Research Foundation for Opto-Science and Technology.

R E F E R E N C E S

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