- Email: [email protected]
A new apparatus for electron–ion multiple coincidence momentum imaging spectroscopy
ARTICLE IN PRESS
Radiation Physics and Chemistry 75 (2006) 1977–1980 www.elsevier.com/locate/radphyschem
A new apparatus for electron–ion multiple coincidence momentum imaging spectroscopy Y. Morishitaa,, M. Katoa, G. Pru¨mperb, X.-J. Liub, T. Lischkeb, K. Uedab, Y. Tamenoric, M. Ourad, H. Yamaokad, I.H. Suzukia, N. Saitoa a
National Institute of Advanced Industrial Science and Technology (AIST), NMIJ, Tsukuba, Ibaraki 305-8567, Japan b Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan c Japan Synchrotron Radiation Research Institute, Sayo, Hyogo 679-5198, Japan d RIKEN, Harima Institute, Sayo, Hyogo 679-5148, Japan Accepted 27 July 2005
Abstract We have developed a new experimental apparatus for the electron–ion multiple coincidence momentum imaging spectroscopy in order to obtain the angular distributions of vibration-resolved photoelectrons from molecules fixed in space. The apparatus consists of a four-stage molecular supersonic jet and a spectrometer analyzing three-dimensional momenta of fragment ions and electrons in coincidence. r 2006 Elsevier Ltd. All rights reserved. Keywords: Multiple coincidence; Momentum imaging; Photoelectron; Vibrational resolution
1. Introduction Photoelectron angular distributions in the molecular frame have been intensively measured for K-shell photoemission from the diatomic or triatomic molecules (Saito et al., 2003; Weber et al., 2001; Hosaka et al., 2004). The measurement determines three-dimensional (3D) momenta of both fragment ions and a photoelectron from a molecule. 3D-momenta of the fragment ions can reconstruct the molecular axis at the time of the photoabsorption because the dissociation time ðp1014 sÞ of the molecule with K-shell hole is shorter than its rotation time of 1012 s. Therefore, 3Dmomenta of the photoelectron measured in coincidence with the ions give the angular distribution in the Corresonding author.
E-mail address: [email protected] (Y. Morishita).
molecular frame. We used the time-of-flight (TOF) technique and the two-dimensional (2D) position sensitive detectors to determine the 3D-momenta of the photoelectron and the fragment ions. In order to improve the momentum resolution of the fragment ions and photoelectrons and to use cluster targets in the experiment, we have constructed a new apparatus. We describe details of the apparatus and results of performance tests in the present report.
2. Experimental set-up The experimental chamber is divided (almost vacuum isolated) into four stages, first, second, main and dump stages, which are shown in Fig. 1. In the first stage, a nozzle with an aperture of 30 mm diameter is installed. The position of the nozzle can be adjusted
0969-806X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2005.07.050
ARTICLE IN PRESS Y. Morishita et al. / Radiation Physics and Chemistry 75 (2006) 1977–1980
1978
Liq N2 70 K
Nozzle(φ=30 mm) 1st stage (2000 l/s TMP)
5-12 mm Skimmer(φ=0.5 mm) 35 mm
2nd stage (400 l/s TMP) Aperture(φ=1 mm) Main stage (900 l/s TMP)
250 mm Photon beam
Aperture(φ=12 mm) Dump stage (400 l/s TMP)
second stage flows into the dump stage, and the geometrically expected jet diameter at the intersection with the soft X-ray beam in the main stage is 223 mm. Fig. 3 shows a schematic of the spectrometer, which is installed in the main stage perpendicular to both the soft X-ray beam and the gas jet. The residual magnetism (such as geomagnetism) around the spectrometer is compensated using Helmholtz coils placed in the vertical and horizontal direction. An additional Helmholtz coil is used to apply a weak magnetic field parallel to the spectrometer axis. The applied magnetic field is set to be around 0.1–1 mT depending on the kinetic energy of the photoelectrons, and is chosen such that all the photoelectrons can reach the active area of a 2D-detector explained below. Fragment ions and photoelectrons produced by inner-shell excitation are accelerated in the opposite directions (ions to the left and electrons to the (x10-6 Pa) 12.0 Main
Fig. 1. A schematic of the supersonic molecular beam.
Pressure difference (P(x)-P(0))
Dump
8.0 6.0 P(0)=2x10-6 Pa
4.0 2.0 0.0 0
1
2 3 4 5 Stagnation pressure (atm)
6
Fig. 2. Pressure variations from the base pressure ð2 106 PaÞ at the main and dump stages as a function of the stagnation pressure in the nozzle.
-2 kV
32.5 mm
65 mm -50 V
-80 V
Drift tube
Thin electrodes
Wider electrode
X-ray beam
Fig. 3. A schematic of the spectrometer.
Dealy-line anode
97.5 mm
Dealy-line anode
three-dimensionally from outside of the chamber. The highest stagnation pressure in the nozzle is tested up to around 10 atm. The nozzle can be cooled down directly with liquid nitrogen, which is used for the production of cluster jets from rare gases. The molecular gas from the nozzle flows into the second stage through the skimmer with a hole diameter of 0:5 mm, and a part of the gas transmits into the main stage through an edged aperture of 1 mm diameter. In the main stage where the spectrometer is installed, the gas jet intersects with the soft X-ray beam perpendicularly. The gas jet, then, flows into the dump stage through the 12 mm aperture in Fig. 1. We install a turbo molecular pump (TMP) at each stage, and their pump speeds are 2000, 400, 900 and 400 l=s from the first stage to dump stage, respectively. A rotary pump ð80 m3 =hÞ is used to pump the first stage, and another one ð18 m3 =hÞ is used to pump the remaining stages. We first aligned the skimmer and aperture positions by lighting up the inside of the nozzle and observing the leaking light from the nozzle aperture at the dump stage. Then we evacuated all stages to a pressure lower than 5 106 Pa, and measured the pressure in each stage changing the stagnation pressure of nitrogen gas from 0 to 6 atm. The pressures in the first and second stages changed in proportion with the stagnation pressure, and they were around 102 and 104 Pa, respectively, for 6 atm stagnation pressure. Fig. 2 shows the pressure variation at the main and the dump stages. As is seen, the dump pressure becomes higher as the stagnation pressure increases, while the main pressure changes only slightly. This means that most of the gas jet from the
10.0
ARTICLE IN PRESS Y. Morishita et al. / Radiation Physics and Chemistry 75 (2006) 1977–1980
3. Results We have examined the spectrometer system on the c branch of the soft X-ray photochemistry beam line 27SU at SPring-8. We measured, at first, the angular distribution of 1s photoelectrons emitted from neon atoms whose ionization potential is 870:1 eV (Hitchcock and Brion, 1980). The soft X-ray beam used is 874:5 eV, and has a linear horizontal polarization of 100% (Tanaka and Kitamura, 1995). The dots in Fig. 4 show the polar plot of the measured angular distribution. The
measured data were fitted according to the formula, ds s b ¼ 1 þ ð1 þ 3P cos 2yÞ , dO 4p 4
(1)
where bð¼ 2Þ is the dipole asymmetry parameter and P the polarization degree of the soft X-ray beam. The result of the fitting is shown by the solid line in Fig. 4, which reproduces the measured data well. We obtained 95% as the degree of the horizontal polarization. Next, we measured an N1s photoelectron spectrum of NO at the soft X-ray energy of 413 eV. We recorded only 90 120
60
150
30
0
180
210
330
240
300 270
Fig. 4. Angular distribution of photoelectrons from neon atoms at the photon energy of 874:5 eV. The photon beam has a horizontal polarization. The solid curve shows the calculated distribution.
600 3 2 1 0 v
500 Counts (arb. units)
right side in the figure) by a weak electric field ð0:7 V=mmÞ which is applied by the voltage suppliers (80 and 50 V) connected to the wider electrodes. The thin electrodes and the wider electrodes are connected through resistors to generate a homogeneous electric field. The photoelectrons are accelerated toward the 2D-detector circulating around the applied magnetic field, and then transmitted into the drift tube through the stainless mesh. The mesh is shown as a dashed line in the figure, and used to shield the electric field. The drift tube is twice as long as the acceleration region to satisfy the space-focusing condition (Wiley and McLaren, 1955). After passing through the drift tube, the photoelectrons are further accelerated to 200 eV and then hit the microchannel plate (MCP) in the chevron configuration. We use an MCP with its active area of 120 mm diameter for electron detection. The MCP produces electron clouds that hit the 2D-position sensitive detector. We use a hexagonal type delay-line anode as the 2D-detector (HEX120). Each signal from the MCP and the delay lines is amplified and transferred to a time-to-digital converter (TDC, c027, Hoshin Electronics Co. Ltd.). The TDC has a timing resolution of about 120 ps, a multi-hit capability of six events and a time span of 40 ms (Morishita et al., 2005). The MCP signal is used to measure the TOF of the photoelectron and the delay-line signals are used to determine the hit position of the photoelectron. Using the TOF and the hit position, 3D-momenta of the photoelectron are calculated. The fragment ions, on the other hand, are further accelerated by the electric field of 22 V=mm after the weak acceleration around the photoexcitation region. Similar to the photoelectron, the fragment ions hit the MCP (active area of 80 mm) mounted in front of the delay-line anode (HEX80) and then 3D-momenta of each fragment ion are calculated. Because the photoelectron and the fragment ions are measured in coincidence, the 3D-momenta of the fragment ions determine the molecular axis at the moment of the photoexcitation, and those of the photoelectron determine the emission direction of the photoelectron from the same molecule.
1979
400 300 200 1Π
100
3Π
0 0.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 Photoelectron kinetic energy (eV)
4.0
Fig. 5. N1s photoelectron spectrum of NO at the photon energy of 413 eV. The bars show energies for different vibrational states.
ARTICLE IN PRESS 1980
Y. Morishita et al. / Radiation Physics and Chemistry 75 (2006) 1977–1980
events in which an electron and two fragment ions were detected in coincidence. The resulting photoelectron spectrum is shown in Fig. 5. As is seen in the spectrum, there are two broad peaks around 0.7 and 2:2 eV. These correspond to transitions to 1 P and 3 P states. Ionization thresholds for 3 P and 1 P are 410.3 and 411:8 eV, respectively (Davis and Shirley, 1972). As can be seen in the 3 P transition, the spectrum is composed mainly of two peaks. The bars in Fig. 5 show energy differences of 0:23 eV (Ma et al., 1991) for different vibrational states (n). The peak positions and the published energy interval agree with each other, implying that the vibrational states are separately observed.
4. Summary In summary, we have developed a new apparatus for electron–ion multiple coincidence momentum imaging spectroscopy. Through the test measurements of 1s angular distribution of Ne and N1s photoelectron spectrum of NO, we confirmed that the apparatus works as we expected.
Acknowledgments The experiments were performed at SPring-8 with the approval of the program review committee. The work was partially supported by Grants-in-Aid for Scientific Research (B) from Japan Society for Promotion of Science and by the Budget for Nuclear Research of Ministry of Education, Culture, Sports, Science and Technology, based on the screening and counseling by the Atomic Energy Commission.
References Davis, D.W., Shirley, D.A., 1972. Splitting in nitrogen and oxygen 1s photoelectron peaks in two paramagnetic molecules: spin density implications. J. Chem. Phys. 56, 669. Hitchcock, A.P., Brion, C.E., 1980. Neon K-shell excitation studied by electron energy-loss spectroscopy. J. Phys. B 13, 3269. Hosaka, K., Adachi, J., Takahashi, M., Yagishita, A., Lin, P., Lucchese, R.R., 2004. Multiplet-specific N 1s photoelectron angular distributions from the fixed-in-space NO molecules. J. Phys. B. 37, L49. Ma, Y., Chen, C.T., Meigs, G., Randall, K., Sette, F., 1991. High-resolution K-shell photoabsorption measurements of simple molecules. Phys. Rev. A 44, 1848. Morishita, Y., Tamenori, Y., Machida, M., Oura, M., Yamaoka, H., Ohashi, et al., 2005. Three-dimensional electron–ion coincidence momentum imaging spectroscopy using an ultra-fast multi-hit TDC system. J. Electron Spectrosc. Relat. Phenom. 144–147, 255. Saito, N., De Fanis, A., Kubozuka, K., Machida, M., Takahashi, M., Yoshida, et al., 2003. Carbon K-shell photoelectron angular distribution from fixed-in-space CO2 molecules. J. Phys. B. 36, L25. Tanaka, T., Kitamura, H., 1995. Figure-8 undulator as an insertion device with linear polarization and low on-axis power density. Nucl. Instrum. Methods A 364, 368. Weber, Th., Jagutzki, O., Hattass, M., Staudte, A., Nauert, A., Schimdt, et al., 2001. K-shell photoionization of CO and N2 : is there a link between the photoelectron angular distribution and the molecular decay dynamics? J. Phys. B. 34, 3669. Wiley, W.C., McLaren, I.H., 1955. Time-of-flight mass spectrometer with improved resolution. Rev. Sci. Instrum. 26, 1150.
Radiation Physics and Chemistry 75 (2006) 1977–1980 www.elsevier.com/locate/radphyschem
A new apparatus for electron–ion multiple coincidence momentum imaging spectroscopy Y. Morishitaa,, M. Katoa, G. Pru¨mperb, X.-J. Liub, T. Lischkeb, K. Uedab, Y. Tamenoric, M. Ourad, H. Yamaokad, I.H. Suzukia, N. Saitoa a
National Institute of Advanced Industrial Science and Technology (AIST), NMIJ, Tsukuba, Ibaraki 305-8567, Japan b Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan c Japan Synchrotron Radiation Research Institute, Sayo, Hyogo 679-5198, Japan d RIKEN, Harima Institute, Sayo, Hyogo 679-5148, Japan Accepted 27 July 2005
Abstract We have developed a new experimental apparatus for the electron–ion multiple coincidence momentum imaging spectroscopy in order to obtain the angular distributions of vibration-resolved photoelectrons from molecules fixed in space. The apparatus consists of a four-stage molecular supersonic jet and a spectrometer analyzing three-dimensional momenta of fragment ions and electrons in coincidence. r 2006 Elsevier Ltd. All rights reserved. Keywords: Multiple coincidence; Momentum imaging; Photoelectron; Vibrational resolution
1. Introduction Photoelectron angular distributions in the molecular frame have been intensively measured for K-shell photoemission from the diatomic or triatomic molecules (Saito et al., 2003; Weber et al., 2001; Hosaka et al., 2004). The measurement determines three-dimensional (3D) momenta of both fragment ions and a photoelectron from a molecule. 3D-momenta of the fragment ions can reconstruct the molecular axis at the time of the photoabsorption because the dissociation time ðp1014 sÞ of the molecule with K-shell hole is shorter than its rotation time of 1012 s. Therefore, 3Dmomenta of the photoelectron measured in coincidence with the ions give the angular distribution in the Corresonding author.
E-mail address: [email protected] (Y. Morishita).
molecular frame. We used the time-of-flight (TOF) technique and the two-dimensional (2D) position sensitive detectors to determine the 3D-momenta of the photoelectron and the fragment ions. In order to improve the momentum resolution of the fragment ions and photoelectrons and to use cluster targets in the experiment, we have constructed a new apparatus. We describe details of the apparatus and results of performance tests in the present report.
2. Experimental set-up The experimental chamber is divided (almost vacuum isolated) into four stages, first, second, main and dump stages, which are shown in Fig. 1. In the first stage, a nozzle with an aperture of 30 mm diameter is installed. The position of the nozzle can be adjusted
0969-806X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2005.07.050
ARTICLE IN PRESS Y. Morishita et al. / Radiation Physics and Chemistry 75 (2006) 1977–1980
1978
Liq N2 70 K
Nozzle(φ=30 mm) 1st stage (2000 l/s TMP)
5-12 mm Skimmer(φ=0.5 mm) 35 mm
2nd stage (400 l/s TMP) Aperture(φ=1 mm) Main stage (900 l/s TMP)
250 mm Photon beam
Aperture(φ=12 mm) Dump stage (400 l/s TMP)
second stage flows into the dump stage, and the geometrically expected jet diameter at the intersection with the soft X-ray beam in the main stage is 223 mm. Fig. 3 shows a schematic of the spectrometer, which is installed in the main stage perpendicular to both the soft X-ray beam and the gas jet. The residual magnetism (such as geomagnetism) around the spectrometer is compensated using Helmholtz coils placed in the vertical and horizontal direction. An additional Helmholtz coil is used to apply a weak magnetic field parallel to the spectrometer axis. The applied magnetic field is set to be around 0.1–1 mT depending on the kinetic energy of the photoelectrons, and is chosen such that all the photoelectrons can reach the active area of a 2D-detector explained below. Fragment ions and photoelectrons produced by inner-shell excitation are accelerated in the opposite directions (ions to the left and electrons to the (x10-6 Pa) 12.0 Main
Fig. 1. A schematic of the supersonic molecular beam.
Pressure difference (P(x)-P(0))
Dump
8.0 6.0 P(0)=2x10-6 Pa
4.0 2.0 0.0 0
1
2 3 4 5 Stagnation pressure (atm)
6
Fig. 2. Pressure variations from the base pressure ð2 106 PaÞ at the main and dump stages as a function of the stagnation pressure in the nozzle.
-2 kV
32.5 mm
65 mm -50 V
-80 V
Drift tube
Thin electrodes
Wider electrode
X-ray beam
Fig. 3. A schematic of the spectrometer.
Dealy-line anode
97.5 mm
Dealy-line anode
three-dimensionally from outside of the chamber. The highest stagnation pressure in the nozzle is tested up to around 10 atm. The nozzle can be cooled down directly with liquid nitrogen, which is used for the production of cluster jets from rare gases. The molecular gas from the nozzle flows into the second stage through the skimmer with a hole diameter of 0:5 mm, and a part of the gas transmits into the main stage through an edged aperture of 1 mm diameter. In the main stage where the spectrometer is installed, the gas jet intersects with the soft X-ray beam perpendicularly. The gas jet, then, flows into the dump stage through the 12 mm aperture in Fig. 1. We install a turbo molecular pump (TMP) at each stage, and their pump speeds are 2000, 400, 900 and 400 l=s from the first stage to dump stage, respectively. A rotary pump ð80 m3 =hÞ is used to pump the first stage, and another one ð18 m3 =hÞ is used to pump the remaining stages. We first aligned the skimmer and aperture positions by lighting up the inside of the nozzle and observing the leaking light from the nozzle aperture at the dump stage. Then we evacuated all stages to a pressure lower than 5 106 Pa, and measured the pressure in each stage changing the stagnation pressure of nitrogen gas from 0 to 6 atm. The pressures in the first and second stages changed in proportion with the stagnation pressure, and they were around 102 and 104 Pa, respectively, for 6 atm stagnation pressure. Fig. 2 shows the pressure variation at the main and the dump stages. As is seen, the dump pressure becomes higher as the stagnation pressure increases, while the main pressure changes only slightly. This means that most of the gas jet from the
10.0
ARTICLE IN PRESS Y. Morishita et al. / Radiation Physics and Chemistry 75 (2006) 1977–1980
3. Results We have examined the spectrometer system on the c branch of the soft X-ray photochemistry beam line 27SU at SPring-8. We measured, at first, the angular distribution of 1s photoelectrons emitted from neon atoms whose ionization potential is 870:1 eV (Hitchcock and Brion, 1980). The soft X-ray beam used is 874:5 eV, and has a linear horizontal polarization of 100% (Tanaka and Kitamura, 1995). The dots in Fig. 4 show the polar plot of the measured angular distribution. The
measured data were fitted according to the formula, ds s b ¼ 1 þ ð1 þ 3P cos 2yÞ , dO 4p 4
(1)
where bð¼ 2Þ is the dipole asymmetry parameter and P the polarization degree of the soft X-ray beam. The result of the fitting is shown by the solid line in Fig. 4, which reproduces the measured data well. We obtained 95% as the degree of the horizontal polarization. Next, we measured an N1s photoelectron spectrum of NO at the soft X-ray energy of 413 eV. We recorded only 90 120
60
150
30
0
180
210
330
240
300 270
Fig. 4. Angular distribution of photoelectrons from neon atoms at the photon energy of 874:5 eV. The photon beam has a horizontal polarization. The solid curve shows the calculated distribution.
600 3 2 1 0 v
500 Counts (arb. units)
right side in the figure) by a weak electric field ð0:7 V=mmÞ which is applied by the voltage suppliers (80 and 50 V) connected to the wider electrodes. The thin electrodes and the wider electrodes are connected through resistors to generate a homogeneous electric field. The photoelectrons are accelerated toward the 2D-detector circulating around the applied magnetic field, and then transmitted into the drift tube through the stainless mesh. The mesh is shown as a dashed line in the figure, and used to shield the electric field. The drift tube is twice as long as the acceleration region to satisfy the space-focusing condition (Wiley and McLaren, 1955). After passing through the drift tube, the photoelectrons are further accelerated to 200 eV and then hit the microchannel plate (MCP) in the chevron configuration. We use an MCP with its active area of 120 mm diameter for electron detection. The MCP produces electron clouds that hit the 2D-position sensitive detector. We use a hexagonal type delay-line anode as the 2D-detector (HEX120). Each signal from the MCP and the delay lines is amplified and transferred to a time-to-digital converter (TDC, c027, Hoshin Electronics Co. Ltd.). The TDC has a timing resolution of about 120 ps, a multi-hit capability of six events and a time span of 40 ms (Morishita et al., 2005). The MCP signal is used to measure the TOF of the photoelectron and the delay-line signals are used to determine the hit position of the photoelectron. Using the TOF and the hit position, 3D-momenta of the photoelectron are calculated. The fragment ions, on the other hand, are further accelerated by the electric field of 22 V=mm after the weak acceleration around the photoexcitation region. Similar to the photoelectron, the fragment ions hit the MCP (active area of 80 mm) mounted in front of the delay-line anode (HEX80) and then 3D-momenta of each fragment ion are calculated. Because the photoelectron and the fragment ions are measured in coincidence, the 3D-momenta of the fragment ions determine the molecular axis at the moment of the photoexcitation, and those of the photoelectron determine the emission direction of the photoelectron from the same molecule.
1979
400 300 200 1Π
100
3Π
0 0.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 Photoelectron kinetic energy (eV)
4.0
Fig. 5. N1s photoelectron spectrum of NO at the photon energy of 413 eV. The bars show energies for different vibrational states.
ARTICLE IN PRESS 1980
Y. Morishita et al. / Radiation Physics and Chemistry 75 (2006) 1977–1980
events in which an electron and two fragment ions were detected in coincidence. The resulting photoelectron spectrum is shown in Fig. 5. As is seen in the spectrum, there are two broad peaks around 0.7 and 2:2 eV. These correspond to transitions to 1 P and 3 P states. Ionization thresholds for 3 P and 1 P are 410.3 and 411:8 eV, respectively (Davis and Shirley, 1972). As can be seen in the 3 P transition, the spectrum is composed mainly of two peaks. The bars in Fig. 5 show energy differences of 0:23 eV (Ma et al., 1991) for different vibrational states (n). The peak positions and the published energy interval agree with each other, implying that the vibrational states are separately observed.
4. Summary In summary, we have developed a new apparatus for electron–ion multiple coincidence momentum imaging spectroscopy. Through the test measurements of 1s angular distribution of Ne and N1s photoelectron spectrum of NO, we confirmed that the apparatus works as we expected.
Acknowledgments The experiments were performed at SPring-8 with the approval of the program review committee. The work was partially supported by Grants-in-Aid for Scientific Research (B) from Japan Society for Promotion of Science and by the Budget for Nuclear Research of Ministry of Education, Culture, Sports, Science and Technology, based on the screening and counseling by the Atomic Energy Commission.
References Davis, D.W., Shirley, D.A., 1972. Splitting in nitrogen and oxygen 1s photoelectron peaks in two paramagnetic molecules: spin density implications. J. Chem. Phys. 56, 669. Hitchcock, A.P., Brion, C.E., 1980. Neon K-shell excitation studied by electron energy-loss spectroscopy. J. Phys. B 13, 3269. Hosaka, K., Adachi, J., Takahashi, M., Yagishita, A., Lin, P., Lucchese, R.R., 2004. Multiplet-specific N 1s photoelectron angular distributions from the fixed-in-space NO molecules. J. Phys. B. 37, L49. Ma, Y., Chen, C.T., Meigs, G., Randall, K., Sette, F., 1991. High-resolution K-shell photoabsorption measurements of simple molecules. Phys. Rev. A 44, 1848. Morishita, Y., Tamenori, Y., Machida, M., Oura, M., Yamaoka, H., Ohashi, et al., 2005. Three-dimensional electron–ion coincidence momentum imaging spectroscopy using an ultra-fast multi-hit TDC system. J. Electron Spectrosc. Relat. Phenom. 144–147, 255. Saito, N., De Fanis, A., Kubozuka, K., Machida, M., Takahashi, M., Yoshida, et al., 2003. Carbon K-shell photoelectron angular distribution from fixed-in-space CO2 molecules. J. Phys. B. 36, L25. Tanaka, T., Kitamura, H., 1995. Figure-8 undulator as an insertion device with linear polarization and low on-axis power density. Nucl. Instrum. Methods A 364, 368. Weber, Th., Jagutzki, O., Hattass, M., Staudte, A., Nauert, A., Schimdt, et al., 2001. K-shell photoionization of CO and N2 : is there a link between the photoelectron angular distribution and the molecular decay dynamics? J. Phys. B. 34, 3669. Wiley, W.C., McLaren, I.H., 1955. Time-of-flight mass spectrometer with improved resolution. Rev. Sci. Instrum. 26, 1150.