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Measurement of the energy dependences of the photoelectron angular distribution parameters for Ar 3p and Kr 4p electrons using an electron-electron coincidence experiment
Journal of Electron Spectroscopy and Related Phenomena, 3 (1974) 123-128 @ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
MEASUREMENT OF THE ENERGY DEPENDENCES ELECTRON ANGULAR DISTRIBUTION PARAMETERS Kr 4p ELECTRONS USING AN ELECTRON-ELECTRON EXPERIMENT
G. R. BRANTON
OF THE PHOTOFOR Ar 3p AND COINCIDENCE
* and C. E. BRION
Department of Chemisby,
University of British Columbia, Vancouver 8, B.C. (Canada)
(First received 21 September 1973; in final form 5 October 1973)
ABSTRACT
The energy dependence of the photoelectron angular distribution parameter (p) has been measured for Ar 3p and Kr 4p electrons in the energy ranges 4-54 eV and 4-40 eV above threshold respectively, using 3.5 keV electron impact with coincidence detection of the scattered and ejected electrons. This energy range is considerably greater than that covered in previous experiments. The data over the whole energy range are compared with the Hartree-Fock calculations of Kennedy and Manson and with those of Amusia et al., using the random phase approximation with exchange method. For Ar the calculations of Amusia et al., which take into account many-electron correlations, are shown to agree more closely with the present data. The data are also shown to be in very good agreement with earlier experimental data obtained over a more limited energy range using electron synchrotron radiation. INTRODUCTION
Experimental data on the energy dependence of the photoelectron angular distribution parameter, #?, in the energy range O-23 eV above threshold have been determined for both Arl and Kr’, using electron synchrotron radiation. In addition, there have been several determinations of isolated values of B for Ar and Kr using He T and Ne I resonance radiations 3 - 7 _ These data generally support the validity of both the length and velocity formulation Hartree-Fock calculations of Kennedy and Manson’ and the calculations of Amusia et a1.9 in which many-electron correlations are taken into account in the random phase approximation with exchange * Permanent Canada.
address:
Department
of Chemistry,
University
of Victoria,
Victoria,
B.C.,
124 (RPAE). The data of Codling et al.” ‘, using electron synchrotron radiation, cover only a limited range of energies (O-23 eV above threshold), and in this energy range differences between the calculations are not sufficiently large that it is experimentally possible to distinguish between them (taking into account the error limits of the experimental data). At higher energies both sets of calculations predict that the value of p should pass through a maximum and fall to a Cooper minimum, before rising again to a constant value at even higher energies. In the region of the Cooper minimum and where the value of p is decreasing, relatively large differences between the theoretical calculations do exist. The present study was undertaken to extend the experimenta1 data into this energy range, in order to make a comparison with the differing theoretical models. EXPERIMENTAL
The technique used in the present study involved fast (3.5 keV) electron impact with coincidence detection of the energy analysed scattered and ejected electrons in order to simulate the conditions of photoelectron spectroscopy (in this technique the electron energy loss is equivalent to the photon energy). The validity of this simulation technique has been demonstrated in earlier experiments by van der Wiel and Brionr ’9 1 ’ and the method has been used to determine /I for neon12. The experimental arrangement has been described in detail elsewhere” and was employed in the present study without major modification. The application of this technique to the determination of p has been examined previously119 r2. The parameter, /I, may be determined from the expression”’ I2
Nminc(E,E) B(E) =(v(E) N(O”, E)a9-l1 1
[
where E is the energy loss (“photon energy”), E (= E - IP) the energy of the ejected electron, iV (0”, E) the number of forward scattered electrons, Nc,i”JE,E) the number of true coincidences, C(E) a known” simple function of the energy loss and T(E) a transmission factor for the ejected electron energy analyser. T(E) was determined as previously l1 from expression (1) using He 1s ionisation for which /? = 2. The above expression strictly only applies for the energies between the first ionization potential (removal of an outer p electron) and the ionization energy of the outer s electron (with the exception of the energy range where autoionizing levels contribute12). However, in tests conducted at energies above the outer s electron ionisation potential it was found (as was the case for Ne12) that the number of electrons ejected from the s-orbitals were so few in number, relative to the number from the p-orbitals, that eqn. (1) may be applied at energies greater than the s electron ionisation potentials. (Because of the length of time involved these tests were not conducted at energy losses greater than 40 eV.) Theoretical calculationsg9 13, l4
125 indicate
that this assumption
is certainly
valid up to an ejected photoelectron
energy
of 30-35 eV for Ar and greater than 40 eV for Kr. At larger energies there may be a significant contribution from s ionisation, thereby making the values of p determined in the present study to low (since the value of N(O”, E) used in eqn. (1) will contain significant contributions from both s and p ionisation). Our method, as with the method using electron synchrotron radiation yields the relative shape of the energy variation of p and thus the data require normalisation. For both the Ar and Kr data the low energy points (4-7 eV) were used for normalisation to the Hartree-Fock calculations of Kennedy and Manson’. (This arbitrary choice facilitates comparison with the data of Codling et al.” ‘.) RESULTS
AND DISCUSSION
The data for the Ar 3p and Kr 4p subshells are shown in Figures 1 and 2 respectively. Also shown are the data points obtained from the electron synchrotron experiments l, 2 as well as a few isolated values obtained using resonance line radiation sources3-7. The lengths of the error bars shown for the present data reflect the statistical uncertainties in the determination of both Ncoinc(&a) and in T(e), but do not include any contribution from possible systematic errors. For both Ar and Kr the present data and the data obtained using electron synchrotron radiation agree to within the error bars of the work. The only points which do not agree within these error bars are the points obtained in the present study which lie in the region of autoionising states just below the threshold for s ionisation. As discussed previouslyll, the energy resolution (1.3 eV FWHM) employed in the present study was insufficient to avoid some contribution from these
-1.0
0
IO
El&n
EnZ&
50
%
(eV)
Figure 1. Argon 3p shell b values: present study (0) normalised to theory8 at 4 eV. Included are the measurements of Codling et a1.l (a) and the values of Carlson and Jonas’ (I); Vroom et a1.4 (0); Berkowitz et al.3 (0); Sampson5 (A): Niehaus et al.8 (X); the theoretical results of Kennedy and Mansons () and of Amusia et al.9 (- - -).
126
Figure 2. Krypton 4p shell j3 values: present study (0) normalised to theory* at 5 eV. Included are the measurements of Codling et a1.2 (e) and the values of Carlson and Jonas’ (I); and Niehaus et aL6 (x); the theoretical results of Kennedy and Mansons () and of Amusia et aLg (- - -1.
levels,
and
as in the case of neon1 2, this
leads to an anomalously
low value for B
at these energies. At ejected photoelectron energies below 20 eV the present experimental results are seen to be in good agreement with both sets’, 9 of theoretical calculations. At higher energies the calculations, for both Ar and Kr, predict that the value of /? passes through a maximum followed by a Cooper minimum at still higher energies. This behaviour is shown by the experimental points. Although there is obvious qualitative agreement between both sets of calculations and the measured data points, there are major discrepancies in the energy range in which the value of p is decreasing to the Cooper minimum. For Ar it may be readily seen from Figure 1 that the calculations of Amusia et al.’ are in much better agreement with the experimental data than are the calculations of Kennedy and Manson ‘. However, even for the calculations of Amusia there are significant discrepancies between the theory and experiment. The theory predicts that p should start to decrease in value in the region of 24 eV above threshold, whereas the experimental data indicates that this decrease starts at about 18-21 eV above threshold (due to the error bars on the experimental data, it is not-possible to set an accurate value for the energy at which p starts to decrease in value). This decrease in p is apparent from the last few data points of the end of the energy range of the existing electron synchrotron experiments. The calculations of Amusia et ah9 also predict that the Cooper minimum should occur at an energy of approximateIy 37 eV above threshold. Due to the experimental uncertainties it is not possible to locate this minimum from the present data. As discussed earlier the values of /?, at the highest energies investigated, may well be too low, because of a contribution to N(O”,E) from s-shell ionisation, which may start to become significant at 30-35 eV
127 above the threshold
for p-shell ionisation*.
Thus from the data the Cooper
minimum
may well occur at as low an energy as 35 eV above threshold, which is in fairly good agreement with the calculated value of Amusia et al. For Kr, in the energy range covered, both sets of calculations are very similar, except that the calculations of Amusia et aL9 again predict a lower value for the energy at which /3 starts to decrease. The calculations of Amusia are thus again in closer agreement with the experimental data, except that large discrepancies do exist in that the experimental value for the energy of the maximum is clearly much less than the value predicted by the calculations. The rate at which p subsequently decreases also appears to be faster than predicted by theory. The experimental data and theory do agree in that the shape of the curve in the region of the maximum value of p is much more shallow than in the case of Ar. The contribution from 4s ionisation is expected to be negligible in this energy range (see earlier discussion). CONCLUSIONS
The energy variations of the photoelectron angular distribution parameters for Ar 3p and Kr 4p electrons obtained in the present study are in excellent agreement with earlier experimental data. The energy range of the variation is extended sufficiently such that a decrease in the value of p is observed for both Ar and Kr. The behavior at lower energies is in good agreement with both sets of theoretical calculations. At higher energies, the data for Ar is in closer agreement with the RPAE calculations of Amusia et aL9 in which many-electron correlations are taken into account. In the case of Kr the lower energy for the maximum in fl as predicted by the RPAE calculation is more in accord with experiment than is the value from HartreeFock theory. ACKNOWLEDGEMENl-
Financial cil of Canada.
support for this work was provided by the National
Research
Coun-
REFERENCES 1 2 3
P. Mitchell and K. Codling, Phys. Letf., 38A (1972) 31. M. J. Lynch, K. Codling and A. B. Gardner, Phys. Lett., 43A (1973) J. Berkowitz and H. Ehrhardt, Whys. Lett., 21 (1966) 531; J. Berkowitz, H. Ehrhardt and T. Tekaat, Z. P~>?.Y., 200 (1967) 69.
213.
* From approximate calculations based on the relative cross-sections for s-shell and p-shell ionisation given by both Kennedy and Mansons and Amusia et aL13* l4 indicate that for the highest data point measured, the true value of @ for 3p-shell ionisation in Ar at 54 eV above threshold, could be as high as 1.2, on the basis of the present data.
128 4
7 8 9 10 11 12 13 14
D. A. Vroom, A. R. Comeaux and J. W. McGowan, Chem. Phys. Lett., 3 (1969) 476; J. W. McGowan, D. A. Vroom and A. R. Comeaux, J. Chem. Phys., 51 (1969) 5626. J. A. R. Samson, Phil. Trans. Roy. Sot. London, A268 (1970) 141. R. Morgenstern, A, Niehaus and M. W. Ruf, Chem. Phys. Lett., 4 (1970) 635; A. Niehaus and M. W. Ruf, Z. Phys., 252 (1972) 84. T. A. Carlson and A. E. Jonas, J. Chem. Phys., 55 (1971) 4913. D. J. Kennedy and S. T. Manson, Phys. Rev., A5 (1972) 227. M. Ya. Amusia, N. A. Cherepkov and L. V. Chernysheva, Phys. Left., 4OA (1972) 15. M. J. van der Wiel and C. E. &ion, J. Electron Spectrosc., 1 (1972/1973) 309. M. J. van der Wiel and C. E. &ion, J. Erectron Specfrosc., 1 (1972/1973) 443. M. J. van der Wiel and C. E. &ion, J. Ekctron Spectrosc., 1 (1972/1973) 439. M. Ya. Amusia, V. K. Ivanov, N. A. Cherepkov and L. V. Chernysheva, P&s. Lett., 40A (1972) 361. M. Ya. Amusia, N. A. Cherepkov and L. V. Chernysheva, Sov. Phys. JEEP, 33 (1971) 90.
MEASUREMENT OF THE ENERGY DEPENDENCES ELECTRON ANGULAR DISTRIBUTION PARAMETERS Kr 4p ELECTRONS USING AN ELECTRON-ELECTRON EXPERIMENT
G. R. BRANTON
OF THE PHOTOFOR Ar 3p AND COINCIDENCE
* and C. E. BRION
Department of Chemisby,
University of British Columbia, Vancouver 8, B.C. (Canada)
(First received 21 September 1973; in final form 5 October 1973)
ABSTRACT
The energy dependence of the photoelectron angular distribution parameter (p) has been measured for Ar 3p and Kr 4p electrons in the energy ranges 4-54 eV and 4-40 eV above threshold respectively, using 3.5 keV electron impact with coincidence detection of the scattered and ejected electrons. This energy range is considerably greater than that covered in previous experiments. The data over the whole energy range are compared with the Hartree-Fock calculations of Kennedy and Manson and with those of Amusia et al., using the random phase approximation with exchange method. For Ar the calculations of Amusia et al., which take into account many-electron correlations, are shown to agree more closely with the present data. The data are also shown to be in very good agreement with earlier experimental data obtained over a more limited energy range using electron synchrotron radiation. INTRODUCTION
Experimental data on the energy dependence of the photoelectron angular distribution parameter, #?, in the energy range O-23 eV above threshold have been determined for both Arl and Kr’, using electron synchrotron radiation. In addition, there have been several determinations of isolated values of B for Ar and Kr using He T and Ne I resonance radiations 3 - 7 _ These data generally support the validity of both the length and velocity formulation Hartree-Fock calculations of Kennedy and Manson’ and the calculations of Amusia et a1.9 in which many-electron correlations are taken into account in the random phase approximation with exchange * Permanent Canada.
address:
Department
of Chemistry,
University
of Victoria,
Victoria,
B.C.,
124 (RPAE). The data of Codling et al.” ‘, using electron synchrotron radiation, cover only a limited range of energies (O-23 eV above threshold), and in this energy range differences between the calculations are not sufficiently large that it is experimentally possible to distinguish between them (taking into account the error limits of the experimental data). At higher energies both sets of calculations predict that the value of p should pass through a maximum and fall to a Cooper minimum, before rising again to a constant value at even higher energies. In the region of the Cooper minimum and where the value of p is decreasing, relatively large differences between the theoretical calculations do exist. The present study was undertaken to extend the experimenta1 data into this energy range, in order to make a comparison with the differing theoretical models. EXPERIMENTAL
The technique used in the present study involved fast (3.5 keV) electron impact with coincidence detection of the energy analysed scattered and ejected electrons in order to simulate the conditions of photoelectron spectroscopy (in this technique the electron energy loss is equivalent to the photon energy). The validity of this simulation technique has been demonstrated in earlier experiments by van der Wiel and Brionr ’9 1 ’ and the method has been used to determine /I for neon12. The experimental arrangement has been described in detail elsewhere” and was employed in the present study without major modification. The application of this technique to the determination of p has been examined previously119 r2. The parameter, /I, may be determined from the expression”’ I2
Nminc(E,E) B(E) =(v(E) N(O”, E)a9-l1 1
[
where E is the energy loss (“photon energy”), E (= E - IP) the energy of the ejected electron, iV (0”, E) the number of forward scattered electrons, Nc,i”JE,E) the number of true coincidences, C(E) a known” simple function of the energy loss and T(E) a transmission factor for the ejected electron energy analyser. T(E) was determined as previously l1 from expression (1) using He 1s ionisation for which /? = 2. The above expression strictly only applies for the energies between the first ionization potential (removal of an outer p electron) and the ionization energy of the outer s electron (with the exception of the energy range where autoionizing levels contribute12). However, in tests conducted at energies above the outer s electron ionisation potential it was found (as was the case for Ne12) that the number of electrons ejected from the s-orbitals were so few in number, relative to the number from the p-orbitals, that eqn. (1) may be applied at energies greater than the s electron ionisation potentials. (Because of the length of time involved these tests were not conducted at energy losses greater than 40 eV.) Theoretical calculationsg9 13, l4
125 indicate
that this assumption
is certainly
valid up to an ejected photoelectron
energy
of 30-35 eV for Ar and greater than 40 eV for Kr. At larger energies there may be a significant contribution from s ionisation, thereby making the values of p determined in the present study to low (since the value of N(O”, E) used in eqn. (1) will contain significant contributions from both s and p ionisation). Our method, as with the method using electron synchrotron radiation yields the relative shape of the energy variation of p and thus the data require normalisation. For both the Ar and Kr data the low energy points (4-7 eV) were used for normalisation to the Hartree-Fock calculations of Kennedy and Manson’. (This arbitrary choice facilitates comparison with the data of Codling et al.” ‘.) RESULTS
AND DISCUSSION
The data for the Ar 3p and Kr 4p subshells are shown in Figures 1 and 2 respectively. Also shown are the data points obtained from the electron synchrotron experiments l, 2 as well as a few isolated values obtained using resonance line radiation sources3-7. The lengths of the error bars shown for the present data reflect the statistical uncertainties in the determination of both Ncoinc(&a) and in T(e), but do not include any contribution from possible systematic errors. For both Ar and Kr the present data and the data obtained using electron synchrotron radiation agree to within the error bars of the work. The only points which do not agree within these error bars are the points obtained in the present study which lie in the region of autoionising states just below the threshold for s ionisation. As discussed previouslyll, the energy resolution (1.3 eV FWHM) employed in the present study was insufficient to avoid some contribution from these
-1.0
0
IO
El&n
EnZ&
50
%
(eV)
Figure 1. Argon 3p shell b values: present study (0) normalised to theory8 at 4 eV. Included are the measurements of Codling et a1.l (a) and the values of Carlson and Jonas’ (I); Vroom et a1.4 (0); Berkowitz et al.3 (0); Sampson5 (A): Niehaus et al.8 (X); the theoretical results of Kennedy and Mansons () and of Amusia et al.9 (- - -).
126
Figure 2. Krypton 4p shell j3 values: present study (0) normalised to theory* at 5 eV. Included are the measurements of Codling et a1.2 (e) and the values of Carlson and Jonas’ (I); and Niehaus et aL6 (x); the theoretical results of Kennedy and Mansons () and of Amusia et aLg (- - -1.
levels,
and
as in the case of neon1 2, this
leads to an anomalously
low value for B
at these energies. At ejected photoelectron energies below 20 eV the present experimental results are seen to be in good agreement with both sets’, 9 of theoretical calculations. At higher energies the calculations, for both Ar and Kr, predict that the value of /? passes through a maximum followed by a Cooper minimum at still higher energies. This behaviour is shown by the experimental points. Although there is obvious qualitative agreement between both sets of calculations and the measured data points, there are major discrepancies in the energy range in which the value of p is decreasing to the Cooper minimum. For Ar it may be readily seen from Figure 1 that the calculations of Amusia et al.’ are in much better agreement with the experimental data than are the calculations of Kennedy and Manson ‘. However, even for the calculations of Amusia there are significant discrepancies between the theory and experiment. The theory predicts that p should start to decrease in value in the region of 24 eV above threshold, whereas the experimental data indicates that this decrease starts at about 18-21 eV above threshold (due to the error bars on the experimental data, it is not-possible to set an accurate value for the energy at which p starts to decrease in value). This decrease in p is apparent from the last few data points of the end of the energy range of the existing electron synchrotron experiments. The calculations of Amusia et ah9 also predict that the Cooper minimum should occur at an energy of approximateIy 37 eV above threshold. Due to the experimental uncertainties it is not possible to locate this minimum from the present data. As discussed earlier the values of /?, at the highest energies investigated, may well be too low, because of a contribution to N(O”,E) from s-shell ionisation, which may start to become significant at 30-35 eV
127 above the threshold
for p-shell ionisation*.
Thus from the data the Cooper
minimum
may well occur at as low an energy as 35 eV above threshold, which is in fairly good agreement with the calculated value of Amusia et al. For Kr, in the energy range covered, both sets of calculations are very similar, except that the calculations of Amusia et aL9 again predict a lower value for the energy at which /3 starts to decrease. The calculations of Amusia are thus again in closer agreement with the experimental data, except that large discrepancies do exist in that the experimental value for the energy of the maximum is clearly much less than the value predicted by the calculations. The rate at which p subsequently decreases also appears to be faster than predicted by theory. The experimental data and theory do agree in that the shape of the curve in the region of the maximum value of p is much more shallow than in the case of Ar. The contribution from 4s ionisation is expected to be negligible in this energy range (see earlier discussion). CONCLUSIONS
The energy variations of the photoelectron angular distribution parameters for Ar 3p and Kr 4p electrons obtained in the present study are in excellent agreement with earlier experimental data. The energy range of the variation is extended sufficiently such that a decrease in the value of p is observed for both Ar and Kr. The behavior at lower energies is in good agreement with both sets of theoretical calculations. At higher energies, the data for Ar is in closer agreement with the RPAE calculations of Amusia et aL9 in which many-electron correlations are taken into account. In the case of Kr the lower energy for the maximum in fl as predicted by the RPAE calculation is more in accord with experiment than is the value from HartreeFock theory. ACKNOWLEDGEMENl-
Financial cil of Canada.
support for this work was provided by the National
Research
Coun-
REFERENCES 1 2 3
P. Mitchell and K. Codling, Phys. Letf., 38A (1972) 31. M. J. Lynch, K. Codling and A. B. Gardner, Phys. Lett., 43A (1973) J. Berkowitz and H. Ehrhardt, Whys. Lett., 21 (1966) 531; J. Berkowitz, H. Ehrhardt and T. Tekaat, Z. P~>?.Y., 200 (1967) 69.
213.
* From approximate calculations based on the relative cross-sections for s-shell and p-shell ionisation given by both Kennedy and Mansons and Amusia et aL13* l4 indicate that for the highest data point measured, the true value of @ for 3p-shell ionisation in Ar at 54 eV above threshold, could be as high as 1.2, on the basis of the present data.
128 4
7 8 9 10 11 12 13 14
D. A. Vroom, A. R. Comeaux and J. W. McGowan, Chem. Phys. Lett., 3 (1969) 476; J. W. McGowan, D. A. Vroom and A. R. Comeaux, J. Chem. Phys., 51 (1969) 5626. J. A. R. Samson, Phil. Trans. Roy. Sot. London, A268 (1970) 141. R. Morgenstern, A, Niehaus and M. W. Ruf, Chem. Phys. Lett., 4 (1970) 635; A. Niehaus and M. W. Ruf, Z. Phys., 252 (1972) 84. T. A. Carlson and A. E. Jonas, J. Chem. Phys., 55 (1971) 4913. D. J. Kennedy and S. T. Manson, Phys. Rev., A5 (1972) 227. M. Ya. Amusia, N. A. Cherepkov and L. V. Chernysheva, Phys. Left., 4OA (1972) 15. M. J. van der Wiel and C. E. &ion, J. Electron Spectrosc., 1 (1972/1973) 309. M. J. van der Wiel and C. E. &ion, J. Erectron Specfrosc., 1 (1972/1973) 443. M. J. van der Wiel and C. E. &ion, J. Ekctron Spectrosc., 1 (1972/1973) 439. M. Ya. Amusia, V. K. Ivanov, N. A. Cherepkov and L. V. Chernysheva, P&s. Lett., 40A (1972) 361. M. Ya. Amusia, N. A. Cherepkov and L. V. Chernysheva, Sov. Phys. JEEP, 33 (1971) 90.