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Integrated state multipoles and plane asymmetry
Volume 92A, number 9
PHYSICS LETTERS
13 December 1982
INTEGRATED STATE MULTIPOLES AND PLANE ASYMMETRY * T.T.GIEN Department of Physics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada AIB 3X7 Received 3 September 1982
The relationship between the integrated alignment and orientation coefficients and the polarizations of the decay photons measured in an experiment where the scattered electrons are not observed is expounded. The determination of some integrated state multipoles is shown to provide also a simple checking of the plane symmetry invariance of an atomic collision.
In recent work [1], we have shown that it would be more appropriate to analyze electron—photon coincidence measurements [2] with a more general version of the theory in which the symmetry invariance in the reflection through a plane (plane symmetry) is not assumed a priori for the collision process since (i) the more general theory is required to confirm whether an effect which was detected in previous correlation experiments [3] originates from the spin—orbit coupling effect [4] alone or from both spin—orbit coupling and plane asymmetry effects, (ii) it provides, besides, the means for checking the plane symmetry invariance which has customarily been assumed for an atomic collision process (speculation on parity violation due to the asymmetric distribution of a very complex collision target was also made recently by Farago [5]) and (iii) the possibility of extracting information from electron—photon coincidence experiments (or from superelastic scattering experiments [6]) does not reduce significantly in the extended theory. We have formulated this extended version of the theory of coincidence measurements in our recent publications [1] and have also suggested how the plane asymmetry invariance could be checked by an e—y coincidence (or superelastic scattering) experiment. In this letter, we wish to expound the relationship between the so-called integrated state multipoles [7] ~ Research work supported by the Natural Sciences and Engineering Research Council of Canada (Operating Grant A3962).
0 03l-9163/82/0000—0000/$02.75 © 1982 North-Holland
(or equivalently, the integrated alignment and orientation coefficients [1]) and the polarizations of the pho. tons which are measured in an e—atom (molecule) excitation experiment where the scattered electrons are not observed at all and then to propose how the plane asymmetry effect of an atomic collision (if this effect should exist) can be as well detected by such an experiment. The significance of the present proposal is that (i) the statistics of the new type of experiment would be much improved due to the non-requirement of observing the scattered electrons, (ii) exactly the same experiment which was performed by the MUnster group [7] (to measure the polarizations of the decay photons from the excited target) can be used here to record the plane asymmetry effect if this effect should exist (simply by locating the photon detector at a new position). In an e—atom excitation experiment where the scattered electrons are not observed, the “integrated” alignment and orientation coefficients [1] are defined in terms of the integrated state multipoles as (for simplicity, we limit our discussion to the case of J = I —~Jf= 0; the generalization to other cases is quite straightforward) (OCOI)
=
[(J~
1) +
<4
1)]/2ia
,
(Ia)
(A~?’)int = ~> + (ACO 22)1/2~~ ,
(ib) (ic)
—
col\ 3 1/2 + ~A0 ‘mt — (J20)ici fQcol\ — I J+ ) j+ 1 ‘2 ~ i+-’int 11 — < 1~1>1/ a, ,-
(~)
(ld) (le) 435
Volume 92A, number 9 =
/0
PHYSICS LETFERS
(lg)
lar momentum of the collision system. Let us first concentrate our attention to the atomic excitation by an unpolarized electron beam. Since the integration
(lh)
over the scattering angles of electrons suppresses the asymmetry ofthe the scattered coincidence system
(11)
,
1)~~t = i[
1)]/2u,
(A~ol) — ifl
=
i[(J~ — 2>
—
(J~2)]/2a,
a= is the integrated target excitation cross section. It should be cautioned ahead that in general not all the integrated state multipoles and integrated alignment and orientation coefficients so defined are non-vanishing. The corresponding “integrated” Stokes parameters of the decay photons can then be expressed in terms of the integrated alignment and orientation coefficients according to ‘I~0 ~‘ = co t’I + ~ 20 1\IAc0l\ ~. ‘P~jfl~ ns ~ c ~ — 1’ 0 flint + ~ sin 20 [(A~)~ 1)~ 0tcos p (A~° 11tsin p] 3 sin 2 0 [(A2+) col tcos 2p (A2col ) ts~~ +~ 2p]} 12a~ ‘0 ~‘ ~.
—
—
in
—
,
in
const{—~51fl20(A6°’)jnt col sin 20 [(A col 1÷ )lfl ~cosp
—
(A1 — ) ~
under rotation around the Oz-axis, the system should now be rotationally invariant around Oz (this would also imply the conservation of J~if Oz is, as usual, chosen to be the quantization axis). With the rotational invariance of the system around the quantization axis Oz, the rule of transformation of the integrated state multipoles under rotation around Oz would dictate the vanishing of all state multipoles <~~<-Q> which have a non-zero 1) value ofQ [8]. Thus, (~~~‘)jnt’ 1),~~ ~would (A~. 1~~, ~ (°~~)intand (Oj° identically vanish in this case regardless of whether plane containing Oz is respected or not.for Ifthrough one doesa the invariance in the reflection not symmetry assume plane symmetry invariance the colli. 0
sion process, then only (O~’)~~t, (A~0l)intand a =~/~ are different from zero. In this case the
(‘~3)int 3
13 December 1982
p]
non-vanishing integrated Stokes20parameters become, l)(A~0I)int1 (1(0,’PTh~t= const[l +~(3cos (3a) —
2’P
+ ~
+ (A~0l)~~tsin 2p]
,
(2b)
(‘~l)int= const{—3[sin 0 cos ‘P (A~0l)m~t
sin —
1) u
IACOI\flint sin ~p‘t’l+
—
L~ C05 L’P ‘) IACO1\ C05 t’ V1 2—flint
const[—~ sifl20(A~ol)int]
(In ). ‘~ 1 mt
0
=
(3b) (3c
,
‘
cos 0 sin 2’P (A~’) 1~~]},
~ 7?2ii~it
u
(‘~13)jnt=
cons
=
(2c)
2(Ocol\. ‘0 10 lint cos 0
1
tf_~3l2_l/
(‘n2)~nt= const[~i(O~)intcos0] (3d) Thus, the detection of the circular polarization ~2 .
(1712)intl(’)int of the photons decaying from the excited targets at any angle 0 ~ ir/2 means the deviation from the plane symmetry invariance of the collision The hermicity condition and plane symmetry condiprocess. Since the electrons are not required to be obtion should remain formally the same as those of the served in this type of experiment, the statistics of the state multipoles. Therefore, if plane symmetry invariresults would be much improved. To check the plane ance in the reflection through a plane containing the symmetry invariance, one only needs to find out incident electron direction Oz is respected, one should whether the circular polarizations of the photons dealso have (°~)int,(O?8’)~~~, (A~Ol)mntand (A~°’),~~ caying from the excited targets are different from identically equal to zero, zero or not. The method of determining the circular For the description of electron scattering from polarization of the photons has been well known. atoms (or molecules) the interaction is usually assumed In the case when a transversally polarized electron to be subject to certain conservation laws, such as inbeam is used to excite the target (say P = Pg), the variance under time reversal, rotation and spatial reflecrotational invariance around the Oz-axis again implies tion. Among these three, perhaps the rotational invari[7] <~~&un 0 for Q 0. Furthermore, since P is ance is the most “sacred” one, since the deviation from now perpendicular to Oz, the rotational invariance this invariance implies the non-conservation of anguaround Oz of the z-component of the angular momen—
436
sin 0 cos
p (O~°+’)jnt + sin
0 sin ‘P (O~0l)jnt]} (2d) .
Volume 92A, number 9
PHYSICS LETTERS
13 December 1982
turn still preserves and its conservation impliesM’ — M = rn’ 0 — rn0 (the notations of Bartschat et al. [7] are used here). Equivalently, Q = q where q = ±1 in this case. Note that the same conclusion was reached by Bartschat et al. [7] who used a somewhat more analytical reasoning. If the circular and linear polarizations of the decay photons are to be measured [7], the angular position of the photon detector should be chosen at 0 = ir/2 and ‘P = ii’/2. In this case, the circular polarization i~2 and the linear polarization ~i of the photons are = 3(0
)int![’ _~(A6Ol)int] ,
= _3(A~)intI[l
—
~(Ag0l)~~~] -
(4a) (4b)
Note that the asymmetric integrated alignment and orientation coefficients disappear from the formulae of the polarizations with this particular choice of the angular position for the photon detector. Thus, the experimental results ofBartschat et a!. should not be affected at all by the non-assumption ofplane symmetry invariance. On the other hand, if the asymmetric alignment and orientation coefficients ~ and (A1~)jntare to be determined (which we are interested in here), the photon detector should be placed at 0 = ir/2, ‘P = 0 (or ‘P = ir), i.e. along the Ox axis (which is perpendicular to both the incident electron direction Oz and its transverse polarization direction Oy, fig. 1). In this case, — col S col = ~~(~i+ )in~IU— ~(A0 )int = ~3 Re(J11).asym,m /a[l — ~
~
(5a) ,
and
IC
Fig. 1. Experimental arrangement to test plane symmetry invariance of an atomic collision. The photon detector is placed along Ox, while the polarization vector of the electron beam is in the Oy direction. Oz is the direction of the incident electron beam.
be repeated, now with its photon detector rotated by 900 from the previous position. If one finds that ~2 and i~ are different from zero with the new position of the photon detector, then one may have reason
to suspect the breakdown of the plane symmetry invariance of the collision process. Then, to confirm the existence of the plane asymmetry effect, one should check further to see whether or not the distributions of ~72(’P) and ~ii(‘P) are asymmetric through Ox, Besides, as was noted Bartschat et al. 1KQ>asyrn,rn (i.e., by (J~Q>pchanges sign[7], when the direction of the electron polarization is reversed. There‘~
fore, one may also check further the presence of
these circular and linear polarizations of the photons
at this particular position of the photon detector (and =_3(Acol\
/11 ~IrAc~~. 1 2’. 0 /int’ = ~3 Im(J~ 3)l/2 1) /a[l — ‘( 0—l(J±)] asym,m (Sb) +
‘0
1—/int’ I
.
hence the violation of plane symmetry invariance) by repeating the same experiment either with the polarization direction of the electron beam reversed or the position of the photon detector rotated by 180°
Thus, in order to check the plane symmetry invari-
around Oz. In both cases, the circular and linear polar-
ance, one simply has to try to verify the existence of the circular polarization ~2 or of the linear polarization i~ of the photons decaying in the direction specified above. Exactly the same experiment which was performed by Bartschat et al. [7] (to determine the circular 3P and linear 1S polarizations of the photons in the 6 1 —6 0 resonance radiation of mercury) can
izations of the decaying photons should change their sign if they are different from zero. Finally, one may also determine the circular polarizations ~2 and/or linear polarization ~i of the photons at different angular positions p (with 0 = ir/2) of the photon detector and if one finds that the distribution of either ~2 or ~i is in the form of a cos ‘P + 13 sin p (instead of 437
Volume 92A, number 9
PHYSICS LETTERS
13 sin’P), then one may also suspect the violation of plane symmetry of an atomic collision. Although the
question of plane asymmetry in an atomic collision is, admittedly, of a highly speculative nature at present, it is however worth pushing forward the proposed checking since, as was pointed out earlier [1], some
of the evidence for the existence of the spin—orbit coupling effect in correlation measurements may also be interpreted as evidence for the plane symmetry violation and since, furthermore, some kind of plane asymmetry effect might have been detected by the JPLgroup [9].
References [11 T.T. Gien, J. Phys. B15 (1982), to be published; see also T.T. Gien, papers presented at the 8th ICAP, Book of Abstracts, 8th ICAP, Goteborg, Sweden (1982). (2] See for instance K. Blum and H. Kleinpoppen, Phys. Rep. 52 (1979) 203, and references therein.
438
13 December 1982
(3] A.A. Zaidi, S.M. Khalid, I. McGregor and H. Klcinpoppen, J. Phys. B14 (1981) L503; D.F. Register, Electron scattering from laser excited Ba, private communication (1981). 141 K. Blum, F.J. da Paixao and G. Csanak, J. Phys. B13 (1980) L257; F.J. da Paixao, N.T. Padial, G. Csanak and K. Blum, Phys. Rev. Lett. 45 (1981) 1164. 151 P.S. Farago, J. Phys. B 13 (1980) L567. (6] I.V. Hertel and W. Stoll, Adv. At. Mol. Phys. 13 (1977) 113; J.H. Nacek and I.V. Hertel, J. Phys. B7 (1974) 2173. (71 K. Bartschat, K. Blum, G.F. 1-lanne and J. Kessler, J. Phys. B14 (1981) 3761. (81 K. Blum, in: Progress in atomic spectroscopy, eds. W. Hanle and H. Kleinpoppen (Plenum, New York, 1978) p. 71. [9] D.F. Register, S. Trajmar, G. Csanak, SW. Jensen and R.T. Poe, Reflection symmetry violation in low-energy electron scattering by laser excited barium, private communication (1982).
PHYSICS LETTERS
13 December 1982
INTEGRATED STATE MULTIPOLES AND PLANE ASYMMETRY * T.T.GIEN Department of Physics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada AIB 3X7 Received 3 September 1982
The relationship between the integrated alignment and orientation coefficients and the polarizations of the decay photons measured in an experiment where the scattered electrons are not observed is expounded. The determination of some integrated state multipoles is shown to provide also a simple checking of the plane symmetry invariance of an atomic collision.
In recent work [1], we have shown that it would be more appropriate to analyze electron—photon coincidence measurements [2] with a more general version of the theory in which the symmetry invariance in the reflection through a plane (plane symmetry) is not assumed a priori for the collision process since (i) the more general theory is required to confirm whether an effect which was detected in previous correlation experiments [3] originates from the spin—orbit coupling effect [4] alone or from both spin—orbit coupling and plane asymmetry effects, (ii) it provides, besides, the means for checking the plane symmetry invariance which has customarily been assumed for an atomic collision process (speculation on parity violation due to the asymmetric distribution of a very complex collision target was also made recently by Farago [5]) and (iii) the possibility of extracting information from electron—photon coincidence experiments (or from superelastic scattering experiments [6]) does not reduce significantly in the extended theory. We have formulated this extended version of the theory of coincidence measurements in our recent publications [1] and have also suggested how the plane asymmetry invariance could be checked by an e—y coincidence (or superelastic scattering) experiment. In this letter, we wish to expound the relationship between the so-called integrated state multipoles [7] ~ Research work supported by the Natural Sciences and Engineering Research Council of Canada (Operating Grant A3962).
0 03l-9163/82/0000—0000/$02.75 © 1982 North-Holland
(or equivalently, the integrated alignment and orientation coefficients [1]) and the polarizations of the pho. tons which are measured in an e—atom (molecule) excitation experiment where the scattered electrons are not observed at all and then to propose how the plane asymmetry effect of an atomic collision (if this effect should exist) can be as well detected by such an experiment. The significance of the present proposal is that (i) the statistics of the new type of experiment would be much improved due to the non-requirement of observing the scattered electrons, (ii) exactly the same experiment which was performed by the MUnster group [7] (to measure the polarizations of the decay photons from the excited target) can be used here to record the plane asymmetry effect if this effect should exist (simply by locating the photon detector at a new position). In an e—atom excitation experiment where the scattered electrons are not observed, the “integrated” alignment and orientation coefficients [1] are defined in terms of the integrated state multipoles as (for simplicity, we limit our discussion to the case of J = I —~Jf= 0; the generalization to other cases is quite straightforward) (OCOI)
=
[(J~
1) +
<4
1)]/2ia
,
(Ia)
(A~?’)int = ~> +
(ib) (ic)
—
col\ 3 1/2 + ~A0 ‘mt — (J20)ici fQcol\ — I J+ ) j+ 1 ‘2 ~ i+-’int 11 — < 1~1>1/ a, ,-
(~)
(ld) (le) 435
Volume 92A, number 9 =
PHYSICS LETFERS
(lg)
lar momentum of the collision system. Let us first concentrate our attention to the atomic excitation by an unpolarized electron beam. Since the integration
(lh)
over the scattering angles of electrons suppresses the asymmetry ofthe the scattered coincidence system
(11)
,
1)~~t = i[
1)]/2u,
(A~ol) — ifl
=
i[(J~ — 2>
—
(J~2)]/2a,
a= is the integrated target excitation cross section. It should be cautioned ahead that in general not all the integrated state multipoles and integrated alignment and orientation coefficients so defined are non-vanishing. The corresponding “integrated” Stokes parameters of the decay photons can then be expressed in terms of the integrated alignment and orientation coefficients according to ‘I~0 ~‘ = co t’I + ~ 20 1\IAc0l\ ~. ‘P~jfl~ ns ~ c ~ — 1’ 0 flint + ~ sin 20 [(A~)~ 1)~ 0tcos p (A~° 11tsin p] 3 sin 2 0 [(A2+) col tcos 2p (A2col ) ts~~ +~ 2p]} 12a~ ‘0 ~‘ ~.
—
—
in
—
,
in
const{—~51fl20(A6°’)jnt col sin 20 [(A col 1÷ )lfl ~cosp
—
(A1 — ) ~
under rotation around the Oz-axis, the system should now be rotationally invariant around Oz (this would also imply the conservation of J~if Oz is, as usual, chosen to be the quantization axis). With the rotational invariance of the system around the quantization axis Oz, the rule of transformation of the integrated state multipoles under rotation around Oz would dictate the vanishing of all state multipoles <~~<-Q> which have a non-zero 1) value ofQ [8]. Thus, (~~~‘)jnt’ 1),~~ ~would (A~. 1~~, ~ (°~~)intand (Oj° identically vanish in this case regardless of whether plane containing Oz is respected or not.for Ifthrough one doesa the invariance in the reflection not symmetry assume plane symmetry invariance the colli. 0
sion process, then only (O~’)~~t, (A~0l)intand a =~/~
(‘~3)int 3
13 December 1982
p]
non-vanishing integrated Stokes20parameters become, l)(A~0I)int1 (1(0,’PTh~t= const[l +~(3cos (3a) —
2’P
+ ~
+ (A~0l)~~tsin 2p]
,
(2b)
(‘~l)int= const{—3[sin 0 cos ‘P (A~0l)m~t
sin —
1) u
IACOI\flint sin ~p‘t’l+
—
L~ C05 L’P ‘) IACO1\ C05 t’ V1 2—flint
const[—~ sifl20(A~ol)int]
(In ). ‘~ 1 mt
0
=
(3b) (3c
,
‘
cos 0 sin 2’P (A~’) 1~~]},
~ 7?2ii~it
u
(‘~13)jnt=
cons
=
(2c)
2(Ocol\. ‘0 10 lint cos 0
1
tf_~3l2_l/
(‘n2)~nt= const[~i(O~)intcos0] (3d) Thus, the detection of the circular polarization ~2 .
(1712)intl(’)int of the photons decaying from the excited targets at any angle 0 ~ ir/2 means the deviation from the plane symmetry invariance of the collision The hermicity condition and plane symmetry condiprocess. Since the electrons are not required to be obtion should remain formally the same as those of the served in this type of experiment, the statistics of the state multipoles. Therefore, if plane symmetry invariresults would be much improved. To check the plane ance in the reflection through a plane containing the symmetry invariance, one only needs to find out incident electron direction Oz is respected, one should whether the circular polarizations of the photons dealso have (°~)int,(O?8’)~~~, (A~Ol)mntand (A~°’),~~ caying from the excited targets are different from identically equal to zero, zero or not. The method of determining the circular For the description of electron scattering from polarization of the photons has been well known. atoms (or molecules) the interaction is usually assumed In the case when a transversally polarized electron to be subject to certain conservation laws, such as inbeam is used to excite the target (say P = Pg), the variance under time reversal, rotation and spatial reflecrotational invariance around the Oz-axis again implies tion. Among these three, perhaps the rotational invari[7] <~~&un 0 for Q 0. Furthermore, since P is ance is the most “sacred” one, since the deviation from now perpendicular to Oz, the rotational invariance this invariance implies the non-conservation of anguaround Oz of the z-component of the angular momen—
436
sin 0 cos
p (O~°+’)jnt + sin
0 sin ‘P (O~0l)jnt]} (2d) .
Volume 92A, number 9
PHYSICS LETTERS
13 December 1982
turn still preserves and its conservation impliesM’ — M = rn’ 0 — rn0 (the notations of Bartschat et al. [7] are used here). Equivalently, Q = q where q = ±1 in this case. Note that the same conclusion was reached by Bartschat et al. [7] who used a somewhat more analytical reasoning. If the circular and linear polarizations of the decay photons are to be measured [7], the angular position of the photon detector should be chosen at 0 = ir/2 and ‘P = ii’/2. In this case, the circular polarization i~2 and the linear polarization ~i of the photons are = 3(0
)int![’ _~(A6Ol)int] ,
= _3(A~)intI[l
—
~(Ag0l)~~~] -
(4a) (4b)
Note that the asymmetric integrated alignment and orientation coefficients disappear from the formulae of the polarizations with this particular choice of the angular position for the photon detector. Thus, the experimental results ofBartschat et a!. should not be affected at all by the non-assumption ofplane symmetry invariance. On the other hand, if the asymmetric alignment and orientation coefficients ~ and (A1~)jntare to be determined (which we are interested in here), the photon detector should be placed at 0 = ir/2, ‘P = 0 (or ‘P = ir), i.e. along the Ox axis (which is perpendicular to both the incident electron direction Oz and its transverse polarization direction Oy, fig. 1). In this case, — col S col = ~~(~i+ )in~IU— ~(A0 )int = ~3 Re(J11).asym,m /a[l — ~
~
(5a) ,
and
IC
Fig. 1. Experimental arrangement to test plane symmetry invariance of an atomic collision. The photon detector is placed along Ox, while the polarization vector of the electron beam is in the Oy direction. Oz is the direction of the incident electron beam.
be repeated, now with its photon detector rotated by 900 from the previous position. If one finds that ~2 and i~ are different from zero with the new position of the photon detector, then one may have reason
to suspect the breakdown of the plane symmetry invariance of the collision process. Then, to confirm the existence of the plane asymmetry effect, one should check further to see whether or not the distributions of ~72(’P) and ~ii(‘P) are asymmetric through Ox, Besides, as was noted Bartschat et al. 1KQ>asyrn,rn (i.e., by (J~Q>pchanges sign[7], when the direction of the electron polarization is reversed. There‘~
fore, one may also check further the presence of
these circular and linear polarizations of the photons
at this particular position of the photon detector (and =_3(Acol\
/11 ~IrAc~~. 1 2’. 0 /int’ = ~3 Im(J~ 3)l/2 1) /a[l — ‘( 0—l(J±)] asym,m (Sb) +
‘0
1—/int’ I
.
hence the violation of plane symmetry invariance) by repeating the same experiment either with the polarization direction of the electron beam reversed or the position of the photon detector rotated by 180°
Thus, in order to check the plane symmetry invari-
around Oz. In both cases, the circular and linear polar-
ance, one simply has to try to verify the existence of the circular polarization ~2 or of the linear polarization i~ of the photons decaying in the direction specified above. Exactly the same experiment which was performed by Bartschat et al. [7] (to determine the circular 3P and linear 1S polarizations of the photons in the 6 1 —6 0 resonance radiation of mercury) can
izations of the decaying photons should change their sign if they are different from zero. Finally, one may also determine the circular polarizations ~2 and/or linear polarization ~i of the photons at different angular positions p (with 0 = ir/2) of the photon detector and if one finds that the distribution of either ~2 or ~i is in the form of a cos ‘P + 13 sin p (instead of 437
Volume 92A, number 9
PHYSICS LETTERS
13 sin’P), then one may also suspect the violation of plane symmetry of an atomic collision. Although the
question of plane asymmetry in an atomic collision is, admittedly, of a highly speculative nature at present, it is however worth pushing forward the proposed checking since, as was pointed out earlier [1], some
of the evidence for the existence of the spin—orbit coupling effect in correlation measurements may also be interpreted as evidence for the plane symmetry violation and since, furthermore, some kind of plane asymmetry effect might have been detected by the JPLgroup [9].
References [11 T.T. Gien, J. Phys. B15 (1982), to be published; see also T.T. Gien, papers presented at the 8th ICAP, Book of Abstracts, 8th ICAP, Goteborg, Sweden (1982). (2] See for instance K. Blum and H. Kleinpoppen, Phys. Rep. 52 (1979) 203, and references therein.
438
13 December 1982
(3] A.A. Zaidi, S.M. Khalid, I. McGregor and H. Klcinpoppen, J. Phys. B14 (1981) L503; D.F. Register, Electron scattering from laser excited Ba, private communication (1981). 141 K. Blum, F.J. da Paixao and G. Csanak, J. Phys. B13 (1980) L257; F.J. da Paixao, N.T. Padial, G. Csanak and K. Blum, Phys. Rev. Lett. 45 (1981) 1164. 151 P.S. Farago, J. Phys. B 13 (1980) L567. (6] I.V. Hertel and W. Stoll, Adv. At. Mol. Phys. 13 (1977) 113; J.H. Nacek and I.V. Hertel, J. Phys. B7 (1974) 2173. (71 K. Bartschat, K. Blum, G.F. 1-lanne and J. Kessler, J. Phys. B14 (1981) 3761. (81 K. Blum, in: Progress in atomic spectroscopy, eds. W. Hanle and H. Kleinpoppen (Plenum, New York, 1978) p. 71. [9] D.F. Register, S. Trajmar, G. Csanak, SW. Jensen and R.T. Poe, Reflection symmetry violation in low-energy electron scattering by laser excited barium, private communication (1982).