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Two-photon detachment from the negative ions F− and I−: angular distributions with elliptically polarised light
Nuclear Instruments and Methods in Physics Research B79 (1993) 156-158
North-Holland
NOMB
Beam Interactions with Materials&Atoms
Two-photon detachment from the negative ions F- and I-: angular distributions with elliptically polarised light C. Blonde1 and C. Delsart Luboratoire Aim&Cotton, CNRS II, ba^timent505, F-91405 Orsay cedex, France
Angular distributions of multiphoton detached electrons enable the determination of the relative amplitudes of the different channels allowed in the photodetachment process. Though detachment from a negative ion can be represented in the plane-wave approximation with real amplitudes, there are some unknown phases that can only be measured through multiphoton excitation with elliptically polarised light. The experiment is performed using an ion beam of either F- or I- with light of various ellipticities (A = 532 nm). Four real parameters can be extracted from the angular distributions. Their measured values show a qualitative difference between fluorine and iodine.
1. Principle Angular distributions of photoelectrons give a good insight into the processes of photoionisation or photodetachment. This is especially useful when dealing with multiphoton excitation, because many angular momentum states can be reached, and only angular measurements give access to the corresponding branching ratios. Multiphoton ionisation or detachment is usually produced experimentally with linearly polarised light. Measuring the angular distribution then only requires varying the angle 6 between the electric field of the light, i.e. the polarisation direction, and the detector. If the atom or ion is initially in a spherically symmetric state (J = O), the differential cross-section obeys the formula da _=-
u
do
4~
1+
5 ~~~p&os
0)
k=l
with N the number of photons used for the excitation and Pzk the Legendre polynomials of even order [l]. The case we have studied experimentally is twophoton detachment from halogen negative ions, which are initially in a ‘S, state, and detach to produce a p 5P neutral atom. This very simple case already gives insight into very general properties of a multiphoton transition to the continuum, especially when angular distributions are considered, as will be shown below. Application of the selection rules for coherent twophoton excitation in our example shows that the final state can be either J= 0, the outgoing electron necessarily being a p one, or J = 2, with either a p or an f outgoing electron (the same conclusion would hold for 0168-583X/93/$06.00
two-photon ionisation of a rare-gas atom). There are thus three atomic channels and, correspondingly, three unknown transition amplitudes. Because we measure angular distributions only, and no absolute cross-sections, only normalised amplitudes are relevant. Taking the normalisation condition into account, the number of unknowns reduces to two meaning that any angular distribution is determined by two independent amplitudes only. Formula (1) shows that angular distribution measurements with linearly polarised light actually yield two real “asymmetry parameters” & and p4, so what is the need to go to more complicated polarisation schemes? The problem comes from the fact that & and p4 are real numbers, whereas the amplitudes can be considered as real only in two very particular cases: i) the pure Coulomb problem, i.e. ionisation of the hydrogen atom (only at low energies above threshold); ii) photodetachment, provided it is well described by the plane-wave approximation, which completely neglects interaction of the outgoing electron with the residual core. In the general case, scattering by the residual core creates phase-shifts which must be considered, and the transition amplitudes to the three independent final states are complex numbers. We thus have four independent real parameters to measure (two amplitude moduli and two relative phases). The aim of this paper is to show that we can actually extract four real parameters from the angular distributions, provided we use elliptically polarised light, and vary its ellipticity. Explicit formulae for angular distributions after multiphoton excitation with elliptically polarised light have been published for two-photon ionisation of hydrogen only [2]. Calculations done explicitly in the
0 1993 - Elsevier Science Publishers B.V. All rights reserved
C. Blondel, C. Delsart / Two-photon detachment from F - and I -
157
‘S+p’P cas e [3I show that we can still write the differential cross-section in the polarisation plane as ~=C[l+ocos2~+cosS(buX20 +c sin 5 sin 20 + d cost cos 40)],
(2)
with 5 the elliptic&y angle, 5 = 0 and 5 = 7~/2 describing linearly and circularly polarised light, respectively, C a normahsation coefficient, that we do not measure, and a, 6, c and d the coefficients which relate to the unknown relative amplitudes. Making 6 = 0 in eq. (2) and comparing with eq. (1) shows that the asymmetry parameters of the linear polarisation case can be expressed as 7b-4d
p$!
7 5[3(1+a)-61-d
(3)
and 192
d
B4=~5[3(1+a)-b]-de
(4)
Asymmetry in the angular distribution (with respect to 0 = 0) appears only through the term c cos 5 sin 5 sin 20, which vanishes in linear polarisation for obvious symmetry reasons, and vanishes as well if the amplitude phase differences are integer multiples of r, for c is a linear combination of the sines of these phase differences [31. There is no asymmetry term at the highest order (no sin 40 term), which seems to be a very general property. As an illustration, in the particular case of singlephoton excitation, there is no asymmetry term at all [4]. One really must use multiphoton excitation to measure transition amplitude phase shifts by looking at the asymmetry of the angular distributions.
2. Experiment and results The experiment is performed on an ion beam, with a frequency doubled single-mode Nd: YAG laser. A complete description and a scheme of the experimental setup were given with the results obtained in linear polarisation [5]. The ion beam is produced from a hot cathode discharge source under an acceleration voltage of 1200 V. The current which crosses the interaction region is typically 50 nA. The laser beam, orthogonal to the ion beam, is focused by a 0.3 m plano-convex lens. Laser pulses are shot at a rate of 10 Hz, with a PWHM duration of 12 ns, greater than the transit time of ions across the light beam (a few nanoseconds). Roughly one thousand ions are illuminated for each laser shot. Electrons are detected at the top of a time-of-flight tube. Angular selection (typically 4” of angular aper-
Fig. 1. Angular distribution of two-photon detachment (532 nm) from I- at four different values of ellipticity angle 5. Abscissa is with respect to the major axis of the ellipse, in the sense where it is described. The continuous curves show the result of fitting all four recordings with one common set of parameters (a, b, c, d) (see formula (2) and text). Kinetic energy selection of the outgoing electron makes sure that I is left in its lower (‘Ps,r) fine-structure state. I. ATOMIC/MOLECULAR
PHYSICS
C. Blondel, C. Delsart / Two-photon detachment from F - and I -
158
Table 1 Asymmetry parameters of the two-photon detachment angular distributions of F- and I-, either with elliptically polarised light (parameters a, b, c, d) or with linearly polarised light (&, p4). Here /3r and p4 are deduced from the former parameters according to formulae (3) and (41 (see text). a Fluorine Iodine
0.14 0.15
b
C
- 0.01 0.19
0.57 0.09
ture) makes the average number
of electrons detected per laser shot smaller than 1. The situation is thus ideal for electron counting. The ellipticity of the light is adjusted by means of a quarter-wave plate. The angle 8 between the major axis of the ellipse and the detection direction is varied by rotating a half-wave plate. Results obtained for different ellipticities are shown in fig. 1, for the case of I-, the neutral atom I being left in its lower 2P,,2 fine structure state. The four angular distributions displayed have been
fitted by formula (2) with four different values of the normalisation coefficient but only one set of (n, b, c, d) parameters. The corresponding numerical results are given in table 1, together with similar results obtained for fluorine. Classical asymmetry parameters p2 and p4 have also been calculated, according to eqs. (3) and (4). They appear to be quite consistent with the ones already published for fluorine [5], but they have significantly increased absolute values for iodine, probably meaning that, in this case, the background signal was severely underestimated in the former measurement
El. More precise measurements are still to be done. Nevertheless it is already clear that coefficient c, which is nearly zero in the case of fluorine, has a significant nonzero value in iodine. The corresponding asymmetry is clearly visible in fig. 1. We already had some indications that iodine should exhibit large discrepancies with the simplified picture given by the plane-wave approximation [5]. It is now clear that its detachment amplitudes are far from being real numbers. On the other hand fluorine, which is a comparatively much smaller and lighter ion, still seems to obey the model of real amplitudes. The same kind of asymmetry has also been observed in the case of multiphoton ionisation of the rare gases [6], but the problem is physically different. Asymmetries observed in ionisation of neutral atoms reveal how far these atoms lie from the hydrogenic
model.
Indeed
d
- 0.31 - 0.54
I32
1.03 0.46
P4
- 0.59 - 0.85
rare gas atoms are far from being hydrogenic, for they have appreciable quantum defects. Moreover, as pointed out by Lambropoulos and Tang [7], the test [6] was done in a case of excess-photon absorption, where amplitudes are expected to be complex anyway. Obtaining asymmetries in the elliptical polarisation case was thus not really a surprise. The case of detachment of negative ions is different. Quantum defects do not exist there, and the plane-wave approximation is usually thought of as a good one. The asymmetry observed for two-photon detachment of I- clearly shows that this approximation does not tell the whole story. The next question is whether the intermediate halogen ions, Cl- and Br-, enter the symmetric or asymmetric case.
Acknowledgement It is a pleasure to acknowledge many fruitful discussions with Michele Crance, both about theoretical problems of multiphoton detachment, and about the manuscript.
References [l] S.J. Smith and G. Leuchs, Adv. Atom. Mol. Phys. 24 (1988) 157. [2] A. Kassaee, M.L. Rustgi and S.A.T. Long, Phys. Rev. A37 (1988) 999, and erratum Phys. Rev. A46 (1992) 4453. [3] C. Blonde1 and C. Delsart (19921, unpublished. [4] JAR. Samson and A.F. Starace, J. Phys. B8 (1975) 1806, with corrigendum J. Phys. B12 (1979) 3993. [5] C. Blondel, M. Crance, C. Delsart and A. Giraud, J. Phys. II France 2 (1992) 839. [6] M. Bashkansky, P.H. Buckabaum and D.W. Schumacher, Phys. Rev. Lett. 60 (1988) 2458. [7] P. Lambropoulos and X. Tang, Phys. Rev. Lett. 61 (1988) 2506.
North-Holland
NOMB
Beam Interactions with Materials&Atoms
Two-photon detachment from the negative ions F- and I-: angular distributions with elliptically polarised light C. Blonde1 and C. Delsart Luboratoire Aim&Cotton, CNRS II, ba^timent505, F-91405 Orsay cedex, France
Angular distributions of multiphoton detached electrons enable the determination of the relative amplitudes of the different channels allowed in the photodetachment process. Though detachment from a negative ion can be represented in the plane-wave approximation with real amplitudes, there are some unknown phases that can only be measured through multiphoton excitation with elliptically polarised light. The experiment is performed using an ion beam of either F- or I- with light of various ellipticities (A = 532 nm). Four real parameters can be extracted from the angular distributions. Their measured values show a qualitative difference between fluorine and iodine.
1. Principle Angular distributions of photoelectrons give a good insight into the processes of photoionisation or photodetachment. This is especially useful when dealing with multiphoton excitation, because many angular momentum states can be reached, and only angular measurements give access to the corresponding branching ratios. Multiphoton ionisation or detachment is usually produced experimentally with linearly polarised light. Measuring the angular distribution then only requires varying the angle 6 between the electric field of the light, i.e. the polarisation direction, and the detector. If the atom or ion is initially in a spherically symmetric state (J = O), the differential cross-section obeys the formula da _=-
u
do
4~
1+
5 ~~~p&os
0)
k=l
with N the number of photons used for the excitation and Pzk the Legendre polynomials of even order [l]. The case we have studied experimentally is twophoton detachment from halogen negative ions, which are initially in a ‘S, state, and detach to produce a p 5P neutral atom. This very simple case already gives insight into very general properties of a multiphoton transition to the continuum, especially when angular distributions are considered, as will be shown below. Application of the selection rules for coherent twophoton excitation in our example shows that the final state can be either J= 0, the outgoing electron necessarily being a p one, or J = 2, with either a p or an f outgoing electron (the same conclusion would hold for 0168-583X/93/$06.00
two-photon ionisation of a rare-gas atom). There are thus three atomic channels and, correspondingly, three unknown transition amplitudes. Because we measure angular distributions only, and no absolute cross-sections, only normalised amplitudes are relevant. Taking the normalisation condition into account, the number of unknowns reduces to two meaning that any angular distribution is determined by two independent amplitudes only. Formula (1) shows that angular distribution measurements with linearly polarised light actually yield two real “asymmetry parameters” & and p4, so what is the need to go to more complicated polarisation schemes? The problem comes from the fact that & and p4 are real numbers, whereas the amplitudes can be considered as real only in two very particular cases: i) the pure Coulomb problem, i.e. ionisation of the hydrogen atom (only at low energies above threshold); ii) photodetachment, provided it is well described by the plane-wave approximation, which completely neglects interaction of the outgoing electron with the residual core. In the general case, scattering by the residual core creates phase-shifts which must be considered, and the transition amplitudes to the three independent final states are complex numbers. We thus have four independent real parameters to measure (two amplitude moduli and two relative phases). The aim of this paper is to show that we can actually extract four real parameters from the angular distributions, provided we use elliptically polarised light, and vary its ellipticity. Explicit formulae for angular distributions after multiphoton excitation with elliptically polarised light have been published for two-photon ionisation of hydrogen only [2]. Calculations done explicitly in the
0 1993 - Elsevier Science Publishers B.V. All rights reserved
C. Blondel, C. Delsart / Two-photon detachment from F - and I -
157
‘S+p’P cas e [3I show that we can still write the differential cross-section in the polarisation plane as ~=C[l+ocos2~+cosS(buX20 +c sin 5 sin 20 + d cost cos 40)],
(2)
with 5 the elliptic&y angle, 5 = 0 and 5 = 7~/2 describing linearly and circularly polarised light, respectively, C a normahsation coefficient, that we do not measure, and a, 6, c and d the coefficients which relate to the unknown relative amplitudes. Making 6 = 0 in eq. (2) and comparing with eq. (1) shows that the asymmetry parameters of the linear polarisation case can be expressed as 7b-4d
p$!
7 5[3(1+a)-61-d
(3)
and 192
d
B4=~5[3(1+a)-b]-de
(4)
Asymmetry in the angular distribution (with respect to 0 = 0) appears only through the term c cos 5 sin 5 sin 20, which vanishes in linear polarisation for obvious symmetry reasons, and vanishes as well if the amplitude phase differences are integer multiples of r, for c is a linear combination of the sines of these phase differences [31. There is no asymmetry term at the highest order (no sin 40 term), which seems to be a very general property. As an illustration, in the particular case of singlephoton excitation, there is no asymmetry term at all [4]. One really must use multiphoton excitation to measure transition amplitude phase shifts by looking at the asymmetry of the angular distributions.
2. Experiment and results The experiment is performed on an ion beam, with a frequency doubled single-mode Nd: YAG laser. A complete description and a scheme of the experimental setup were given with the results obtained in linear polarisation [5]. The ion beam is produced from a hot cathode discharge source under an acceleration voltage of 1200 V. The current which crosses the interaction region is typically 50 nA. The laser beam, orthogonal to the ion beam, is focused by a 0.3 m plano-convex lens. Laser pulses are shot at a rate of 10 Hz, with a PWHM duration of 12 ns, greater than the transit time of ions across the light beam (a few nanoseconds). Roughly one thousand ions are illuminated for each laser shot. Electrons are detected at the top of a time-of-flight tube. Angular selection (typically 4” of angular aper-
Fig. 1. Angular distribution of two-photon detachment (532 nm) from I- at four different values of ellipticity angle 5. Abscissa is with respect to the major axis of the ellipse, in the sense where it is described. The continuous curves show the result of fitting all four recordings with one common set of parameters (a, b, c, d) (see formula (2) and text). Kinetic energy selection of the outgoing electron makes sure that I is left in its lower (‘Ps,r) fine-structure state. I. ATOMIC/MOLECULAR
PHYSICS
C. Blondel, C. Delsart / Two-photon detachment from F - and I -
158
Table 1 Asymmetry parameters of the two-photon detachment angular distributions of F- and I-, either with elliptically polarised light (parameters a, b, c, d) or with linearly polarised light (&, p4). Here /3r and p4 are deduced from the former parameters according to formulae (3) and (41 (see text). a Fluorine Iodine
0.14 0.15
b
C
- 0.01 0.19
0.57 0.09
ture) makes the average number
of electrons detected per laser shot smaller than 1. The situation is thus ideal for electron counting. The ellipticity of the light is adjusted by means of a quarter-wave plate. The angle 8 between the major axis of the ellipse and the detection direction is varied by rotating a half-wave plate. Results obtained for different ellipticities are shown in fig. 1, for the case of I-, the neutral atom I being left in its lower 2P,,2 fine structure state. The four angular distributions displayed have been
fitted by formula (2) with four different values of the normalisation coefficient but only one set of (n, b, c, d) parameters. The corresponding numerical results are given in table 1, together with similar results obtained for fluorine. Classical asymmetry parameters p2 and p4 have also been calculated, according to eqs. (3) and (4). They appear to be quite consistent with the ones already published for fluorine [5], but they have significantly increased absolute values for iodine, probably meaning that, in this case, the background signal was severely underestimated in the former measurement
El. More precise measurements are still to be done. Nevertheless it is already clear that coefficient c, which is nearly zero in the case of fluorine, has a significant nonzero value in iodine. The corresponding asymmetry is clearly visible in fig. 1. We already had some indications that iodine should exhibit large discrepancies with the simplified picture given by the plane-wave approximation [5]. It is now clear that its detachment amplitudes are far from being real numbers. On the other hand fluorine, which is a comparatively much smaller and lighter ion, still seems to obey the model of real amplitudes. The same kind of asymmetry has also been observed in the case of multiphoton ionisation of the rare gases [6], but the problem is physically different. Asymmetries observed in ionisation of neutral atoms reveal how far these atoms lie from the hydrogenic
model.
Indeed
d
- 0.31 - 0.54
I32
1.03 0.46
P4
- 0.59 - 0.85
rare gas atoms are far from being hydrogenic, for they have appreciable quantum defects. Moreover, as pointed out by Lambropoulos and Tang [7], the test [6] was done in a case of excess-photon absorption, where amplitudes are expected to be complex anyway. Obtaining asymmetries in the elliptical polarisation case was thus not really a surprise. The case of detachment of negative ions is different. Quantum defects do not exist there, and the plane-wave approximation is usually thought of as a good one. The asymmetry observed for two-photon detachment of I- clearly shows that this approximation does not tell the whole story. The next question is whether the intermediate halogen ions, Cl- and Br-, enter the symmetric or asymmetric case.
Acknowledgement It is a pleasure to acknowledge many fruitful discussions with Michele Crance, both about theoretical problems of multiphoton detachment, and about the manuscript.
References [l] S.J. Smith and G. Leuchs, Adv. Atom. Mol. Phys. 24 (1988) 157. [2] A. Kassaee, M.L. Rustgi and S.A.T. Long, Phys. Rev. A37 (1988) 999, and erratum Phys. Rev. A46 (1992) 4453. [3] C. Blonde1 and C. Delsart (19921, unpublished. [4] JAR. Samson and A.F. Starace, J. Phys. B8 (1975) 1806, with corrigendum J. Phys. B12 (1979) 3993. [5] C. Blondel, M. Crance, C. Delsart and A. Giraud, J. Phys. II France 2 (1992) 839. [6] M. Bashkansky, P.H. Buckabaum and D.W. Schumacher, Phys. Rev. Lett. 60 (1988) 2458. [7] P. Lambropoulos and X. Tang, Phys. Rev. Lett. 61 (1988) 2506.