- Email: [email protected]
Angular distribution of photoelectrons from fixed-in-space molecules
s __
Nuclear Instruments and Methods in Physics Research B 99 (1995) 132-135
__
B
LiWMl B
Beam lnteractlons with Materials& Atoms
ELSEVIER
Angular distribution of photoelectrons
from fixed-in-space
E. Shigemasa
molecules
*
Photon Factory, National Laboratory for High Energy Physics, Oho l-l, Tsukuba-shi, Ibaraki-ken 305, Japan
Abstract Angular distributions of Isa photoelectrons from spatially fixed N, molecules have been measured around the u * shape resonance in the K-shell continuum. This has been realized with the use of a coincidence technique: by detecting the photoelectron in coincidence with the fragment ion having the information on the molecular orientation at a moment of photoabsorption. The angular distributions obtained by this technique are rich in structure, which are completely different from usual photoelectron angular distributions from randomly oriented molecules. The orbital angular momentum properties of the Isa photoelectrons at the u * shape resonance have been revealed.
1. Introduction Photoelectron spectroscopy is one of the powerful tools to investigate the details of photoionization processes [l]. Angular distribution measurements of photoelectrons can access dynamical information on the process. The differential cross section on the angle 0’ between the ejection direction of the photoelectrons and the polarization direction of the incident light is measured in the usual gas phase experiment. The corresponding differential cross section is expressed by the familiar form [2]
2 =C[l
+ PP,(cos
e’)],
where (T is the integrated cross section, p is the asymmetry parameter, and P,(cos 0’) is the Legendre polynomial of degree two. Eq. (1) was obtained on the basis that molecules have random orientation. If it is possible to fix molecules in space, then the angular distribution of photoelectrons ejected from the molecules becomes much more complicated. The resulting differential cross section was derived by Dill [3] as
where the angles {0, $} describe the ejection direction of the photoelectron relative to the molecule .z axis, I,,, is the maximum orbital angular momentum in the partial wave expansion of the photoelectron wave function, and YKM are the spherical harmonics. Comparing Eq. (2) to
* Tel.
+81
298 64 5594,
[email protected].
fax
+81
298 64 2801,
e-mail:
Eq. (11, it is evident that experiments with fixed-in-space molecules can provide opportunities to investigate the orbital angular momentum composition of the molecular photoelectrons. Molecular shape resonances are intriguing targets to be investigated in such experiments. According to the theoretical interpretation by Dehmer and Dill [4], the molecular shape resonances are accounted for by centrifugal barrier effects, resulting from the interaction between the photoelectron and the anisotropic molecular potential, in high-l components of the final state wavefunctions. It is expected that such orbital angular momentum composition of the escaping photoelectrons can be directly observed by the photoelectron angular distributions from fixed-in-space molecules. The photoionization processes of fixed-in-space molecules in a gas phase have been realized by detecting photoelectrons in coincidence with fragment ions. Since the dissociation of the molecular ions produced by a subsequent Auger decay of the K-shell vacancy occurs in a much shorter time range than the molecular rotation-period, the direction of the fragment-ion emission is accounted to be coincident with the molecular orientation at a moment of photoabsorption. In this paper, the experimental results on the angular distributions of lsu photoelectrons ejected from nitrogen molecules fixed spatially around the u * shape resonance are shown as a prototype.
2. Experimental The experimental methods have been described elsewhere [5]; therefore it will only be briefly mentioned here. The experiments have been carried out on beam line BL-2B at the Photon Factory. The radiation from an undulator [6] monochromatized with a 10-m grazing inci-
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(94)00558-3
E. Shigemasa/Nucl.
Parallel-plate
133
Instr. and Meth. in Phys. Res. B 99 (1995) 132-135
Analyzer
(a) k0
--3 EC
=l.O .F = 0.6 r; 20.6 .e E 0.4 u 5 0.2 0.0 8 1.0 .tl 5 0.8 @ SO.6
Fig. 1. Schematic drawing of the experimental apparatus.
.e c” 0.4 2 + 0.2 0.0
dence monochromator [7] was focused onto an effusive beam of the sample gas at the center of the ionization region of an experimental chamber. The present experimental setup is shown schematically in Fig. 1, which is composed of two identical ion detectors with retarding grids and a rotatable electron analyzer with a position sensitive detector [8]. The ion detectors were set at 0” and 90” relative to the electric vector of the incident radiation. To obtain coincidence signals between photoelectrons and fragment ions, event signals from the electron detector were used as start signals of two time-to-amplitude converters, and signals from each ion detector were used to stop them. The fragment-ion detection by each ion detector determines the molecular orientation; this selects Isa,:, + EU,,~ ,s channels from the alternative ionization or Isa,,, + e7rTT, channels. It has been demonstrated in our previous work that the measurements of the energetic fragment ions emitted parallel and perpendicular to the electric vector of the incident light can decompose the degenerate ionization channels [S-16]. The fragment-ion yield curves of N2
15
Photo&c%
45 75 ejection a,$?? 0 (deg.)
3
Fig. 3. Angular distributions of 1s~ photoelectrons from fixedin-space N, molecules at the (T * shape resonance, for (a) the parallel transitions and (b) perpendicular transitions. The filled circles with error bars represent experimental data points, and the solid curves show the theoretical ones fitted to the experimental data (see text).
molecules [8], measured at 0” and 90” relative to the electric vector, are shown in Fig. 2 as an example. The symmetry decomposition of the alternative ionization channels, lsu, u + EU, s and 1s~~ u -+ ET~,~, is clearly seen. Then, the angular dependence of the coincidence signals between the photoelectrons and ions gives the angular distributions of the photoelectrons produced from the Isus+ + EU”,~, or from the lsu,,, -+ E~F,,~ ionization processes.
3. Results
I
I
Double
excitations I
420
430
Photon Energy
440 (eV)
Fig. 2. Symmetry-resolved photoabsorption spectra above the K-shell threshold of N,. The dots and solid line indicate the lsu + la(B symmetry) and lsu + EP(~ symmetry) ionization channels, respectively.
The angular distribution patterns of the Isa photoelectrons for the parallel and perpendicular transitions at the IJ * shape resonance (at 419 eV) are shown in Figs. 3a and 3b, respectively [5]. The angular distribution of the photoelectrons from randomly oriented molecules at the u * shape resonance, which corresponds to the angular dependence of the non-coincident signal intensities of the photoelectrons in the present experiments, is also shown in Fig. 4 as a comparison. In each graph, the maximum value is normalized to unity. It should be noted that 0 in Figs. 3a and 3b is the photoelectron ejection angle measured from the molecular axis, while 8’ in Fig. 4 is the ejection angle measured from the polarization direction. Comparing Figs. 3a and 3b with Fig. 4, it is evidently seen that the fixed-molecule photoelectron angular distributions are rich
I. ATOMIC/MOLECULAR PHYSICS
134
E. Shigemasa /Nucl.
Ins&. and Meth. in Phys. Res. B 99 (1995) 132-135
cients A, of the Legendre polynomials written for the parallel transitions by A;,=nahv( A’;=mhv
IDS,12+ (
@,“I*+
of Eq. (3) may be
IDdlr?+
21D,,I’+~ID,,12+~ID,,12
- 2&D,*, Ddo cos A,, - 6GD,t
O.01"
ID,,12),
D,,
cos A,,),
90
Photoelectron ejection angle 0’ (deg.)
Fig. 4. Angular distributions of Isa photoelectrons from randomly oriented Nz molecules at the o* shape resonance. The filled circles with error bars represent experimental data points, and the solid curve shows a fitting result based on Eq. (1). The p parameter obtained is about 0.5.
and
and for the perpendicular A,: = 2mhv( t
- 6gD;,
c
“”
7
OK
=
A,P,(cos B),
K=O
where i = (0, O} is the photoelectron ejection direction measured in the molecule frame, and PK are the Legendre polynomials. According to the theoretical calculations by Dehmer and Dill [4], the angular momentum components up to I = 3, in the partial wave expansion of the final state wave functions, predominantly contribute to the ionization process around the u * shape resonance. Thus, four channels for the parallel transitions, i.e., lsug -+ CPU,, Efu, and lsu, + ESU,, eda,, and three channels for the perpendicular transitions, i.e., lsu, -+ EP’TF”,efn, and lsu, + Edna, are taken into account as dominant ionization channels. Under these conditions, the expansion coeffi-
Table 1 Expansion
Photon energy hv (eV) -_
Photoelectron kinetic energy E, (eV)
412 419 447
2 9 37
Parallel transitions
by
A,i=2mxhv
-IDpJ2+~lDdn12 D,,
!
+ 6fiD;,
ID,, 1’
cm A,,) >
-~l~,,,l~+~lD~~ D,,
2
cm A,,),
and
Here (Y is the fine structure constant, D,, represents the dipole matrix element for the transition into the Elm state, and A,,,, indicates the phase difference between EZ and ~1’ partial waves. Here, we have obtained the relative values for the expansion coefficients A, of the Legendre polynomials by the least-squares fitting of Eq. (3) to the data points. The expansion coefficients A,, at hv= 412, 419, and 447 eV, derived from the fitting procedure are listed in Table 1. For the parallel transitions, a prominent increase of A: relative to A’;, is noticed at 419 eV where the shape resonance takes place. Since the expansion coefficient of A’I, is proportional to I D,, I 2, i.e., the square of the dipole matrix element related to the f partial wave (see Eqs. (4)), the present results reveal directly that the shape resonance is caused in a single channel, i.e., the f component of the u continuum wave functions. This supports the explanation for the u * shape resonance provided by Dehmer and Dill [4], that is, the resonance enhancement is caused by an
A, of the Legendre polynomials after normalization with A’; and A t
coefficients
transitions
1Dpn 1’ + 1Dda 1’ + I D,, I’),
A;=~T&v
in structure, which are completely different from usual photoelectron angular distributions expressed by Eq. (1). Quantitative analyses of the results have been performed [s] along with the formulation for the fixed-molecule photoelectron angular distributions by Dill [3]. The general expression of Eq. (2) can be simplified under the present experimental conditions, i.e., ionization of cylindrically symmetric molecules, by the photons with the electric vector parallel or perpendicular to the molecule z axis. The resulting differential cross section is given by
(4)
A’;,=mhv(~~Dr,~‘),
giving the isotropic angular distributions
Perpendicular
lsu + E(T
A\
A’;
A”4
A’;,
1.0 1.0 1.0
0.82 0.25 1.86
1.15 - 0.22 0.37
0.25 1.01 0.49
transitions
Isa + EAT
A,:
A;
A4’
Ah’
1.0 1.0 1.0
-0.16 -0.12 -0.51
- 0.45 - 0.47 - 0.23
- 0.02 - 0.05 -0.15
E. Shigemasa / Nucl. Ins&. and Meth. in Phys. Rex B 99 (1995) 132-135
1 = 3 centrifugal barrier in the u, continuum of N,. The angular distribution shown in Fig. 3a exhibits two maxima and two minima between 0 = 0” and 90”. One may notice that this is very similar to an f-wave (I = 3) pattern [ 171. In case of the pure f-wave pattern, none of the photoelectrons are emitted at a right angle to the molecular axis. The intensity at 0 = 90” in Fig. 3a suggests the contribution of the other partial waves (I = 0, 1, 2). In contrast to the parallel transitions, no increase of A: is seen in Table 1 at 419 eV for the perpendicular transitions, as predicted theoretically by Dehmer and Dill [4]. The contribution of At is negligibly small at 419 eV, which is related to 1II,, 1’. Assuming ] D,, 1’ = 0, it is found that the angular distribution pattern shown in Fig. 3b is regarded as being characterized by / Dpli / * and ] Dd,, / ’ (see Eqs. (5)). The angular distribution shows one broad maximum around 0 = 45”, which is attributable to the contribution of a d (I = 2) partial wave. The considerable intensity at 0 = 90” in Fig. 3b indicates the large contribution of a p (I = 1) partial wave, since the pure p-wave pattern has a maximum at 8 = 90“ while the pure d-wave pattern has two nodes at 0 = 0” and 90”. It has been shown that the fixed-molecule photoelectron angular distributions provide a sensitive and direct probe of the molecular photoionization dynamics. The measurements of such angular distributions enable one to investigate the orbital angular momentum properties of the molecular photoelectrons directly. The present results on the angular distributions have clarified the nature of the molecular cr * shape resonance in the K-shell spectrum.
Acknowledgement I would like to express my appreciation to Prof. A. Yagishita for his valuable discussions regarding the preparation of this manuscript.
135
References [l] For example, J.L. Dehmer, A.C. Parr and S.H. Southworth, in: Handbook on Synchrotron Radiation, Vol. 2, ed. G.V. Marr (North-Holland, Amsterdam, 1987), p. 241, and references therein. [2] For example, D. Dill, in: Photoionization and Other Probes of Many-Electron Interactions, ed. F.J. Wuilleumier (Plenum, New York, 1976) p. 387. [3] D. Dill, J. Chem. Phys. 65 (1976) 1130. [4] J.L. Dehmer and D. Dill, Phys. Rev. Lett. 35 (1975) 213; J.L. Dehmer and D. Dill, J. Chem. Phys. 65 (197615327. [5] E. Shigemasa, J. Adachi, M. Oura and A. Yagishita, Phys. Rev. Lett., in press. [6] H. Maezawa, Y. Suzuki, H. Kitamura and T. Sasaki. Appl. Opt. 25 (1986) 3260. [7] A. Yagishita, S. Masui, A. Toyoshima, H. Maezawa and E. Shigemasa, Rev. Sci. Instr. 63 (1992) 1351. [8] E. Shigemasa, K. Ueda, Y. Sate, T. Sasaki and A. Yagishita, Phys. Rev. A 45 (1992) 2915. [9] A. Yagishita, H. Maezawa, M. Ukai and E. Shigemasa, Phys. Rev. Len. 62 (1989) 36. [lo] E. Shigemasa, K. Ueda, Y. Sato, T. Hayaishi, H. Maezawa, T. Sasaki and A. Yagishita, Phys. Scripta 41 (1990) 63. [ll] A. Yagishita and E. Shigemasa, Rev. Sci. Instr. 63 (1992) 1383. [12] N. Kosugi, E. Shigemasa and A. Yagishita. Chem. Phys. Len. 190 (1992) 481. 1131 N. Kosugi, J. Adachi, E. Shigemasa and A. Yagishita, J. Chem. Phys. 97 (1992) 8842. [14] E. Shigemasa, T. Hayaishi, T. Sasaki and A. Yagishita, Phys. Rev. A 47 (19931 1824. 1151 A. Yagishita, E. Shigemasa. J. Adachi and N. Kosugi, Proc. 10th Int. Conf. on Vacuum Ultraviolet Radiation Physics, eds. F.J. Wuilleumier, Y. Petroff and 1. Nenner (World Scientific, Singapore, 1993), p, 201. 1161 A. Yagishita, E. Shigemasa and N. Kosugi, Phys. Rev. Lett. 72 (1994) 3961. [17] D. Dill, J. Siegel and J.L. Dehmer, J. Chem. Phys. 65 (1976) 3158.
I. ATOMIC/MOLECULAR
PHYSICS
Nuclear Instruments and Methods in Physics Research B 99 (1995) 132-135
__
B
LiWMl B
Beam lnteractlons with Materials& Atoms
ELSEVIER
Angular distribution of photoelectrons
from fixed-in-space
E. Shigemasa
molecules
*
Photon Factory, National Laboratory for High Energy Physics, Oho l-l, Tsukuba-shi, Ibaraki-ken 305, Japan
Abstract Angular distributions of Isa photoelectrons from spatially fixed N, molecules have been measured around the u * shape resonance in the K-shell continuum. This has been realized with the use of a coincidence technique: by detecting the photoelectron in coincidence with the fragment ion having the information on the molecular orientation at a moment of photoabsorption. The angular distributions obtained by this technique are rich in structure, which are completely different from usual photoelectron angular distributions from randomly oriented molecules. The orbital angular momentum properties of the Isa photoelectrons at the u * shape resonance have been revealed.
1. Introduction Photoelectron spectroscopy is one of the powerful tools to investigate the details of photoionization processes [l]. Angular distribution measurements of photoelectrons can access dynamical information on the process. The differential cross section on the angle 0’ between the ejection direction of the photoelectrons and the polarization direction of the incident light is measured in the usual gas phase experiment. The corresponding differential cross section is expressed by the familiar form [2]
2 =C[l
+ PP,(cos
e’)],
where (T is the integrated cross section, p is the asymmetry parameter, and P,(cos 0’) is the Legendre polynomial of degree two. Eq. (1) was obtained on the basis that molecules have random orientation. If it is possible to fix molecules in space, then the angular distribution of photoelectrons ejected from the molecules becomes much more complicated. The resulting differential cross section was derived by Dill [3] as
where the angles {0, $} describe the ejection direction of the photoelectron relative to the molecule .z axis, I,,, is the maximum orbital angular momentum in the partial wave expansion of the photoelectron wave function, and YKM are the spherical harmonics. Comparing Eq. (2) to
* Tel.
+81
298 64 5594,
[email protected].
fax
+81
298 64 2801,
e-mail:
Eq. (11, it is evident that experiments with fixed-in-space molecules can provide opportunities to investigate the orbital angular momentum composition of the molecular photoelectrons. Molecular shape resonances are intriguing targets to be investigated in such experiments. According to the theoretical interpretation by Dehmer and Dill [4], the molecular shape resonances are accounted for by centrifugal barrier effects, resulting from the interaction between the photoelectron and the anisotropic molecular potential, in high-l components of the final state wavefunctions. It is expected that such orbital angular momentum composition of the escaping photoelectrons can be directly observed by the photoelectron angular distributions from fixed-in-space molecules. The photoionization processes of fixed-in-space molecules in a gas phase have been realized by detecting photoelectrons in coincidence with fragment ions. Since the dissociation of the molecular ions produced by a subsequent Auger decay of the K-shell vacancy occurs in a much shorter time range than the molecular rotation-period, the direction of the fragment-ion emission is accounted to be coincident with the molecular orientation at a moment of photoabsorption. In this paper, the experimental results on the angular distributions of lsu photoelectrons ejected from nitrogen molecules fixed spatially around the u * shape resonance are shown as a prototype.
2. Experimental The experimental methods have been described elsewhere [5]; therefore it will only be briefly mentioned here. The experiments have been carried out on beam line BL-2B at the Photon Factory. The radiation from an undulator [6] monochromatized with a 10-m grazing inci-
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(94)00558-3
E. Shigemasa/Nucl.
Parallel-plate
133
Instr. and Meth. in Phys. Res. B 99 (1995) 132-135
Analyzer
(a) k0
--3 EC
=l.O .F = 0.6 r; 20.6 .e E 0.4 u 5 0.2 0.0 8 1.0 .tl 5 0.8 @ SO.6
Fig. 1. Schematic drawing of the experimental apparatus.
.e c” 0.4 2 + 0.2 0.0
dence monochromator [7] was focused onto an effusive beam of the sample gas at the center of the ionization region of an experimental chamber. The present experimental setup is shown schematically in Fig. 1, which is composed of two identical ion detectors with retarding grids and a rotatable electron analyzer with a position sensitive detector [8]. The ion detectors were set at 0” and 90” relative to the electric vector of the incident radiation. To obtain coincidence signals between photoelectrons and fragment ions, event signals from the electron detector were used as start signals of two time-to-amplitude converters, and signals from each ion detector were used to stop them. The fragment-ion detection by each ion detector determines the molecular orientation; this selects Isa,:, + EU,,~ ,s channels from the alternative ionization or Isa,,, + e7rTT, channels. It has been demonstrated in our previous work that the measurements of the energetic fragment ions emitted parallel and perpendicular to the electric vector of the incident light can decompose the degenerate ionization channels [S-16]. The fragment-ion yield curves of N2
15
Photo&c%
45 75 ejection a,$?? 0 (deg.)
3
Fig. 3. Angular distributions of 1s~ photoelectrons from fixedin-space N, molecules at the (T * shape resonance, for (a) the parallel transitions and (b) perpendicular transitions. The filled circles with error bars represent experimental data points, and the solid curves show the theoretical ones fitted to the experimental data (see text).
molecules [8], measured at 0” and 90” relative to the electric vector, are shown in Fig. 2 as an example. The symmetry decomposition of the alternative ionization channels, lsu, u + EU, s and 1s~~ u -+ ET~,~, is clearly seen. Then, the angular dependence of the coincidence signals between the photoelectrons and ions gives the angular distributions of the photoelectrons produced from the Isus+ + EU”,~, or from the lsu,,, -+ E~F,,~ ionization processes.
3. Results
I
I
Double
excitations I
420
430
Photon Energy
440 (eV)
Fig. 2. Symmetry-resolved photoabsorption spectra above the K-shell threshold of N,. The dots and solid line indicate the lsu + la(B symmetry) and lsu + EP(~ symmetry) ionization channels, respectively.
The angular distribution patterns of the Isa photoelectrons for the parallel and perpendicular transitions at the IJ * shape resonance (at 419 eV) are shown in Figs. 3a and 3b, respectively [5]. The angular distribution of the photoelectrons from randomly oriented molecules at the u * shape resonance, which corresponds to the angular dependence of the non-coincident signal intensities of the photoelectrons in the present experiments, is also shown in Fig. 4 as a comparison. In each graph, the maximum value is normalized to unity. It should be noted that 0 in Figs. 3a and 3b is the photoelectron ejection angle measured from the molecular axis, while 8’ in Fig. 4 is the ejection angle measured from the polarization direction. Comparing Figs. 3a and 3b with Fig. 4, it is evidently seen that the fixed-molecule photoelectron angular distributions are rich
I. ATOMIC/MOLECULAR PHYSICS
134
E. Shigemasa /Nucl.
Ins&. and Meth. in Phys. Res. B 99 (1995) 132-135
cients A, of the Legendre polynomials written for the parallel transitions by A;,=nahv( A’;=mhv
IDS,12+ (
@,“I*+
of Eq. (3) may be
IDdlr?+
21D,,I’+~ID,,12+~ID,,12
- 2&D,*, Ddo cos A,, - 6GD,t
O.01"
ID,,12),
D,,
cos A,,),
90
Photoelectron ejection angle 0’ (deg.)
Fig. 4. Angular distributions of Isa photoelectrons from randomly oriented Nz molecules at the o* shape resonance. The filled circles with error bars represent experimental data points, and the solid curve shows a fitting result based on Eq. (1). The p parameter obtained is about 0.5.
and
and for the perpendicular A,: = 2mhv( t
- 6gD;,
c
“”
7
OK
=
A,P,(cos B),
K=O
where i = (0, O} is the photoelectron ejection direction measured in the molecule frame, and PK are the Legendre polynomials. According to the theoretical calculations by Dehmer and Dill [4], the angular momentum components up to I = 3, in the partial wave expansion of the final state wave functions, predominantly contribute to the ionization process around the u * shape resonance. Thus, four channels for the parallel transitions, i.e., lsug -+ CPU,, Efu, and lsu, + ESU,, eda,, and three channels for the perpendicular transitions, i.e., lsu, -+ EP’TF”,efn, and lsu, + Edna, are taken into account as dominant ionization channels. Under these conditions, the expansion coeffi-
Table 1 Expansion
Photon energy hv (eV) -_
Photoelectron kinetic energy E, (eV)
412 419 447
2 9 37
Parallel transitions
by
A,i=2mxhv
-IDpJ2+~lDdn12 D,,
!
+ 6fiD;,
ID,, 1’
cm A,,) >
-~l~,,,l~+~lD~~ D,,
2
cm A,,),
and
Here (Y is the fine structure constant, D,, represents the dipole matrix element for the transition into the Elm state, and A,,,, indicates the phase difference between EZ and ~1’ partial waves. Here, we have obtained the relative values for the expansion coefficients A, of the Legendre polynomials by the least-squares fitting of Eq. (3) to the data points. The expansion coefficients A,, at hv= 412, 419, and 447 eV, derived from the fitting procedure are listed in Table 1. For the parallel transitions, a prominent increase of A: relative to A’;, is noticed at 419 eV where the shape resonance takes place. Since the expansion coefficient of A’I, is proportional to I D,, I 2, i.e., the square of the dipole matrix element related to the f partial wave (see Eqs. (4)), the present results reveal directly that the shape resonance is caused in a single channel, i.e., the f component of the u continuum wave functions. This supports the explanation for the u * shape resonance provided by Dehmer and Dill [4], that is, the resonance enhancement is caused by an
A, of the Legendre polynomials after normalization with A’; and A t
coefficients
transitions
1Dpn 1’ + 1Dda 1’ + I D,, I’),
A;=~T&v
in structure, which are completely different from usual photoelectron angular distributions expressed by Eq. (1). Quantitative analyses of the results have been performed [s] along with the formulation for the fixed-molecule photoelectron angular distributions by Dill [3]. The general expression of Eq. (2) can be simplified under the present experimental conditions, i.e., ionization of cylindrically symmetric molecules, by the photons with the electric vector parallel or perpendicular to the molecule z axis. The resulting differential cross section is given by
(4)
A’;,=mhv(~~Dr,~‘),
giving the isotropic angular distributions
Perpendicular
lsu + E(T
A\
A’;
A”4
A’;,
1.0 1.0 1.0
0.82 0.25 1.86
1.15 - 0.22 0.37
0.25 1.01 0.49
transitions
Isa + EAT
A,:
A;
A4’
Ah’
1.0 1.0 1.0
-0.16 -0.12 -0.51
- 0.45 - 0.47 - 0.23
- 0.02 - 0.05 -0.15
E. Shigemasa / Nucl. Ins&. and Meth. in Phys. Rex B 99 (1995) 132-135
1 = 3 centrifugal barrier in the u, continuum of N,. The angular distribution shown in Fig. 3a exhibits two maxima and two minima between 0 = 0” and 90”. One may notice that this is very similar to an f-wave (I = 3) pattern [ 171. In case of the pure f-wave pattern, none of the photoelectrons are emitted at a right angle to the molecular axis. The intensity at 0 = 90” in Fig. 3a suggests the contribution of the other partial waves (I = 0, 1, 2). In contrast to the parallel transitions, no increase of A: is seen in Table 1 at 419 eV for the perpendicular transitions, as predicted theoretically by Dehmer and Dill [4]. The contribution of At is negligibly small at 419 eV, which is related to 1II,, 1’. Assuming ] D,, 1’ = 0, it is found that the angular distribution pattern shown in Fig. 3b is regarded as being characterized by / Dpli / * and ] Dd,, / ’ (see Eqs. (5)). The angular distribution shows one broad maximum around 0 = 45”, which is attributable to the contribution of a d (I = 2) partial wave. The considerable intensity at 0 = 90” in Fig. 3b indicates the large contribution of a p (I = 1) partial wave, since the pure p-wave pattern has a maximum at 8 = 90“ while the pure d-wave pattern has two nodes at 0 = 0” and 90”. It has been shown that the fixed-molecule photoelectron angular distributions provide a sensitive and direct probe of the molecular photoionization dynamics. The measurements of such angular distributions enable one to investigate the orbital angular momentum properties of the molecular photoelectrons directly. The present results on the angular distributions have clarified the nature of the molecular cr * shape resonance in the K-shell spectrum.
Acknowledgement I would like to express my appreciation to Prof. A. Yagishita for his valuable discussions regarding the preparation of this manuscript.
135
References [l] For example, J.L. Dehmer, A.C. Parr and S.H. Southworth, in: Handbook on Synchrotron Radiation, Vol. 2, ed. G.V. Marr (North-Holland, Amsterdam, 1987), p. 241, and references therein. [2] For example, D. Dill, in: Photoionization and Other Probes of Many-Electron Interactions, ed. F.J. Wuilleumier (Plenum, New York, 1976) p. 387. [3] D. Dill, J. Chem. Phys. 65 (1976) 1130. [4] J.L. Dehmer and D. Dill, Phys. Rev. Lett. 35 (1975) 213; J.L. Dehmer and D. Dill, J. Chem. Phys. 65 (197615327. [5] E. Shigemasa, J. Adachi, M. Oura and A. Yagishita, Phys. Rev. Lett., in press. [6] H. Maezawa, Y. Suzuki, H. Kitamura and T. Sasaki. Appl. Opt. 25 (1986) 3260. [7] A. Yagishita, S. Masui, A. Toyoshima, H. Maezawa and E. Shigemasa, Rev. Sci. Instr. 63 (1992) 1351. [8] E. Shigemasa, K. Ueda, Y. Sate, T. Sasaki and A. Yagishita, Phys. Rev. A 45 (1992) 2915. [9] A. Yagishita, H. Maezawa, M. Ukai and E. Shigemasa, Phys. Rev. Len. 62 (1989) 36. [lo] E. Shigemasa, K. Ueda, Y. Sato, T. Hayaishi, H. Maezawa, T. Sasaki and A. Yagishita, Phys. Scripta 41 (1990) 63. [ll] A. Yagishita and E. Shigemasa, Rev. Sci. Instr. 63 (1992) 1383. [12] N. Kosugi, E. Shigemasa and A. Yagishita. Chem. Phys. Len. 190 (1992) 481. 1131 N. Kosugi, J. Adachi, E. Shigemasa and A. Yagishita, J. Chem. Phys. 97 (1992) 8842. [14] E. Shigemasa, T. Hayaishi, T. Sasaki and A. Yagishita, Phys. Rev. A 47 (19931 1824. 1151 A. Yagishita, E. Shigemasa. J. Adachi and N. Kosugi, Proc. 10th Int. Conf. on Vacuum Ultraviolet Radiation Physics, eds. F.J. Wuilleumier, Y. Petroff and 1. Nenner (World Scientific, Singapore, 1993), p, 201. 1161 A. Yagishita, E. Shigemasa and N. Kosugi, Phys. Rev. Lett. 72 (1994) 3961. [17] D. Dill, J. Siegel and J.L. Dehmer, J. Chem. Phys. 65 (1976) 3158.
I. ATOMIC/MOLECULAR
PHYSICS