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Polarization effects in metastable neon atom (Ne* (3P2)) on ground state neon atom collision at thermal energy
ChemicalPhysics 145 (1990) 153-161 North-Holland
Polarization effects in metastable neon atom (Ne* ( 3P2) ) on ground state neon atom collision at thermal energy J. Baudon, F. Perales, Ch. Miniatura, J. Robert, G. Vassilev, J. Reinhardt Laboraloire de Physique des LUSTS ‘, UniversitPParis-Nerd, Avenue J.B. CMment, 93430 Villetaneuse, France
and H. Haberland Fakultiitfir Physik, Albert-Ludwigs Universitiit, Hermann Herder Strasse 3, 7800 Freiburg/B, FRG Received 28 December 1989; in final form 22 March 1990
The difference A between the differential cross sections for Ne*( sPz) atoms polarized either in state lj= 2, m = + 2) or lj=2, m = - 2), colliding at thermal energy with a groundstate target (Ne, Or), is measured. In the symmetric case Ne*-Ne, direct and exchange contributions are observed. General properties of A, derived from symmetry considerations, are established; in particular: (i ) the interference character of A, (ii) the role played by the azimuthal dependence of the scattering amplitudes, (iii) the property A( 0) = A( 180” ) ~0. The relationships between the Fourier harmonics introduced in this discussion and the scattering amplitudes used in standard collision treatments are given.
1. Intruductlon The collision of an atom with spin 0’) with a spherically symmetric target atom is governed by an anisotropic interaction. In a molecular description, using for instance the adiabatic Born-Oppenheimer basis set (,4 (0) states, where L!(62) is the projection of L (j) on the internuclear axis l? ) , the dynamics are complex especially because the atomic spin couples with the angular momentum I of the relative motion, to give the (constant ) total angular momentum (J) . This coupling results in long range rotational couplings between molecular states dissociating into a specific lj, m) atomic state, referred to a fixed axis 2. As a consequence, the collision treatment leads to a set of several coupled radial equations for each J value [ 11. Most of the difficulties in this problem arise from the change in the character of the diatomic system as the collision evolves: on the one hand, a purely atomic character, referred to 2, at infinite dis’ Associe au CNRS (URA No. 282). 0301-0104/90/$03.50
tance, where the collision channels arc defined; on the other hand a molecular character, referred to the rotating axis R, at short distances. When this change is suffkiently abrupt, the introduction of a so-called locking radius is justified [ 2 1. When a collision of a heavy rare gas metastable atom (Ne*, AP, ...) is considered at thermal energy, the problem is even more complicated by the spin-orbit interaction, which leads to energy splittings at infinite R, comparable to or even larger than the collision energy [ 3 1. In most of the differential scattering experiments of heavy particles, the initial internal state ]j, m) is not prepared, and the final one, IjO), m' ) , is not analyzed: only total differential cross sections (DCS ) are measured. This total DCS contains implicitly all potential energies corresponding to different molecular states. However, it does not exhibit clearly either the anisotropy of the interaction nor the rotational coupling effects. Let us assume that tine-structure transitions have a small probability to occur, whi.ch is generally true in the Ne*-Ne collision [ 41. To get complete information about the anisotropy and cou-
Q 1990 - Elsevier Science Publishers B.V. (North-Holland)
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J. Baudon et al. /Polarization effects in me&stable neon atom
plings would require a “perfect” experiment, in which a monokinetic and completely polarized 1j, m) Ne* beam crosses a monokinetic beam of ground state atoms, the atoms scattered at a given direction (0, 0) being analyzed ( Ij, m’ ) states) after the collision. In principle, it would be possible to measure not solely specific DCSs, such as Ifmm,(0, p) 12, where the f,,, are the scattering amplitudes, but also the relative phases between these amplitudes [ 5 1. Such an experiment is obviously difficult to realize, and it must be undertaken step by step. A first possible step is the type of experiment already performed by Dilren and Hasselbrink [ 6 ] on collisions between an excited alkali atom and a heavy rare gas atom. The excited atoms are prepared with their spin either up or down with respect to the collision plane, and the difference between the two corresponding angular distributions is measured as a function of the scattering angle. In the case of Ne* ( ‘P2 ) , this experiment consists of two measurements using polarized beams of metastables, in states lj=2, m= +2) and 12, -2), with respect to a quantization axis 2 perpendicular to the collision plane. The difference between the two DCSs is d(O)= c (If+2,m(f3,9=0) m
12- If-2.m(&
0) 12) ,
shown in fig. 1, will be discussed. Two supersonic nozzle beams (velocity spread WY= 6%, angular aperture 68x0.8” fwhm) are crossed at right angle. Metastable atoms are produced within one of the beams (the “primary” beam) by means of a coaxial counter-propagating electron beam, at an energy x 100 eV, which is well above the excitation threshold. The efficiency of the electron bombardment is improved by a coaxial magnetic field (few hundred G); with this configuration, the velocity spread of the metastable atoms is kept almost equal to the initial one (6v/v= 7%). The metastable atom flux, estimated from the secondary electronic emission current ( xnA), is of the order of lo9 at/s. It has been previously verified [ 91 that metastable levels 3Po, 3P2 are populated proportionally to their statistical weights (1:5). Scattered metastable atoms are detected by a rotatable electron multiplier. The overall angular spread is A& 2.5 ‘. A fixed detector (channel electron multiplier), set at 20 mm above the collision volume, is used as a monitor. In order to eliminate the background gas contribution, the secondary beam is chopped periodically ( 153 Hz). Counts are added during the open time (shifted by the time of flight from the chopper to the collision volume), and sub-
where m is the projection of the j=2 electronic angular momentum ajler the scattering event. It is expected that, in contrast to excited (P) alkali atoms, metastable Ne* atoms will exhibit only small anisotropy or “polarization” effects, because the 2p hole, which is responsible for these effects, is screened by the outer 3s orbital. Nevertheless, significant polarization effects in rare gas collisions have been already predicted for instance in Ne*-He collisions [ 7 1. In the special case of the Ne*-Ne collisions, direct and exchange polarization effects can be expected, together with interference effects arising from u-g and nuclear symmetry.
Ne
cw dye her
externel
ltelon
eeturated
ebecrptlon
2. Experiment 2.1. The crossed beam apparatus The scattering apparatus used here has been described in detail elsewhere [ 8 1. The main features,
Fig. 1. Scheme of the experiment. Nfl, Ne and L indicate respeotively the metasW& atombeam,the groundstate atombeamand the laser beam, F is an optical fiber, P is a linear polarizer, Q is a 1/4 plate; D is the metastable atom detector. A 15 G magnetic field is applied to preserve the atomic polarization from L to the collision volume.
.I. Baudon et al. /Polarization effecls in metastable neon atom
tracted when the secondary beam is stopped (up/ down counting). The collision energy can be varied either by heating the secondary beam source or by the seeded beam technique [ lo]. The velocity distributions of both beams are measured by time-of-flight. 2.2. Optical excitation. Polarization of the Ne* beam Laser excitation is used to prepare the electronic state of the *we* ( 3P2) atoms. A tunable cw laser is stabilized in frequency by means of an external Fabry-Perot etalon. In order to avoid any frequency drift during the long period ( x 1 h) needed for DCS measurements, the etalon frequency is locked to one of the Zeeman components of the 1s5( ‘P2)-2p,( ‘D2) saturated-absorption line (A= 6 14.3 nm ) , observed in an auxillary low pressure discharge [ 111. The laser power is stabilized to a value ( 15-20 mW) large enough to get a stationary regime of the laser excitation, and low enough to avoid any saturation effect. The laser light is directed into the scattering chamber by a single mode ( TEMoo ), polarization-preserving optical fiber. A parallel laser beam is finally recovered by means of a spherical lens. Its direction (2) is perpendicular to that of the Ne* beam. A linear dichroic polarizer followed by a 1/4 plate permits the production of any polarization (o+, R, o- ). In the experiments in this paper we have only used circularly polarized IS+, o- light. In contrast to the expcriments of ref. [ 61 where the laser is used to produce the excited atoms within the collision volume and at the same time to orient their spin, in the present case the laser is used only to prepare the internal state, e.g. 12, + 2 ) , at a distance of 4 mm before the collision point. In such conditions one has to be careful about the precession of the prepared spin state around the earth magnetic field. In the present case the precession frequency is about 1 MHz, which means that j makes a complete revolution every 1 us, i.e. one revolution for every 1 mm of path. To avoid this effect, a uniform magnetic field of about 1O- 15 G, parallel to the laser beam, is applied over the whole path of the atoms from the crossing point with the laser beam, to the collision point. If a definite polarization (o*, n) is used the laser “connects” each lower Zeeman sublevel (3P2) to a single upper sublevel ( ‘D2) and no coherence is directly induced between the sublevels. Therefore the
155
evolution of the metastable atoms during their transit across the laser beam is described satisfactorily by rate equations. The upper radiative level ( ‘D2) has a width y = 40.1 MHz and it can either decay to the initial level ( 3P2) or cascade to the ground state. As the Zeeman splittings due to the magnetic field present in this experiment are small compared to the effective width (including Doppler effect) of the laser and to y, all Zeeman sublevels can be considered as degenerate. For example, if o+ light is used, only Am = 1 transitions are allowed, and all mj levels save mj= + 2 are depopulated. The population of the mj= + 2 state is further enhanced by radiative decay from the up per mj= 1 state. Under such conditions, the rate equations can be solved analytically. The basic parameters are: a constant 1 characterizing the laser pumping, y the total width of the upper level, and r ( = 28.5 MHz) the partial width for the ‘D2-3P2 transition. The rate equations have been solved for several reasonable values of 1, ranging from 0.5 to 5 MHz. In fig. 2a, the time evolution of the populations are shown, for cr+ polarization. The transit time in the laser beam (+ 1 mm ) is about 1.3 us. Fig. 2b shows the total population of the metastable level at this time. Experimentally, the depopulated fraction of the metastable atom flux, after the laser action is 0.39 + 0.06. Neither **Ne*( 3P0,2)atoms ( 10% of the total flux) nor **,*“Ne*( ‘PO) atoms ( 15% of the total flux) are affected by the laser light. This means that the laser induced depopulation effect represents a fraction 0.39/0.75 =0.52 k 0.08 of the initial *‘Ne( ‘P2) population. This value is sufficiently close to the calculated asymptotic value to conclude that the stationary regime is indeed achieved and that the pumping coefficient is 1> 3 MHz. For the o+ polarization, 80% at least of the meastable level population corresponds to the m = + 2 sublevel. 2.3. Measurement of the diflerence between the m=+2andm=-2DCSs As mentioned above, the prepared atoms, *we* ( ‘P2), represent only 75% of all the metastable atoms. As the detector detects all metastables with about the same efficiency, the measurement of state selected m = + 2 or m = - 2 DCSs requires some further corrections, while in contrast, the difference
J. Baudon et al. /Polarization effects in metastable neon atom
156
is directly obtained in the lab frame and easily transformed in the c.m. frame *I. The experimental procedure is as follows: in a first run, the o+ polarization is used and for each angle 0 two (up/down) countings are made, one with the laser on (L + (0) ), the other one with the laser off (N + (6) ). In a second run this is repeated with the o- polarization, giving countings L - ( 0)) N - ( 0). If all experimental parameters were strictly constant, one would have N + ( 0) = N - ( 6). Actually, during the acquisition time ( x 1 h) some drift is likely to occur and the difference d needs to be calibrated:
0
‘h x=2
I u 1
A=(L+/N+ +I
0 1
0
x=1 I<
tot
0 0
-L-IN-)(N++N-)/2.
-2,-l ,o
t (us)
5
a .
1 (MHz)
b Fig. 2. (a) Time evolution of me&stable Zeeman sublevel (0, f 1, k 2) populations. Values of 1 (in MHz) are proportional to the laser power (see text). tot is the total metastable population. The vertical broken line, at t= 1.3 ps, corresponds to a laser beam effective diameter of 1 mm. (b) Total metastable population as a function of parameter 1 The two horizontal broken lines give the range of the experimental values.
The same arbitrary units are used for A and the DCS. As it wilI be seen further, the difference is relatively small ( 1 / 10 of the DCS or less) and difficult to measure with a good accuracy, over the whole angularrange (5”~&~~100”).1natirstrunthisrange has been explored with steps of lo. In a second run, angular intervals of 20” lab have been explored, with a reduced angular step (0.5” ), and better statistics. Fig. 3a shows the difference A as a function of the c.m. angle, for the Ne*-Ne collision at a collision energy of 64 meV. It exhibits a rather simple oscillatory structure with a mean value zero. The amplitude of oscillation decreases rapidly in the angular range 10‘40” c.m. and then increases, with a maximum at 180” (see fig. 3b). As can be seen in fig. 3, A behaves very differently from the total DCS especially around 180”. At 8= 180”, Ax 0; this important point (cf. section 3) has been confvmed by a more accurate measurement in the range 176”-184” c.m. Another example of the difference A is shown in fg 4, for the Ne*-O2 collision at 74 meV. It is known that Penning ionization occurs in this collision, which is further complicated by the ionic-covalent coupling [ 12 1. Previous differential measurements [ 13 ] have shown #I
It may be noticed that the lXS (da/dQ),,o which can be obtained in principle by use of a 1cpolarization, would need to be corrected for the contribution of non-prepared metastable atoms. An easier method would be to use a laser induced fluorescence detector, working on the same ‘Pr’D2 transition, which detects only rc’Ne*(-‘Pr ) atoms.
J. Baudon et al. /Polarization effects in metastable neon atom
157
Fig. 3. (a) Difference A between differential cross sections (da/@) fZ, for the Ne*-Ne collision at 64 meV, as a function of the c.m. scattering angle. Note the change in scale at 42”, and the passage through zero at & 180”. (b) Comparison of the total differential cross section (points) to the amplitude of oscillation of A (vertical bars). The same arbitraryunit is used for both quantities.
that the elastic DCS is a rapidly decreasing function of the angle. For this reason the measurement of A has been carried out only within a limited angular range ( 5 ‘- 15 ’ lab). The behaviour of A is qualitatively similar to that of the previous one at small angles. The ratio A/ (a), where (a) is the total DCS is 0.29 at 5” lab.
3. Discussion A complete calculation of A requires the solution of a set of coupled equations in an appropriate basis [ 11. This procedure itself requires a knowledge of the
interaction matrix and, in particular, terms u,,(R), y (R ) which appear in the expansion of the potential in terms of Legendre polynomials. In the Ne*-Ne case, the treatment is complicated by: (i) the u-g symmetry (nevertheless the interaction matrix is blockdiagonal in u-g), (ii) the multiplicity of the atomic level ( ‘*‘P); (iii) the spin-orbit interaction. On the other hand, general properties of A( 8) can be derived by a simple consideration of the symmetries. In the present discussion, we shall concentrate on this point, especially for the Ne*-Ne collision. Let us consider (see fg 5), in the c.m. frame, the collision of a polarized Ne* beam (state 12, + 2 ) for example), parallel to axis z, with a beam of ground state
158
J. Baudon et al. /Polarization @Ects in metastable neon atom
where 1=0, 1, .... co; p= -A, -A+ 1, .... +L The direct and exchange contributions to the o+ DCS are then =t
2 In=-2
If5,,(e,o)~f~*,(e,o)12
(2) where Y2,m.a.p -4.103
I 0
1
ld
2@
‘lab Fig. 4. Same as fig. 3a, for NC*-0, collision at 74 meV.
a
b
C
Fig. 5. (a) Ne*-Ne collision experiment in the c.m. frame. Ne? atoms are initially polarized ( + 2 ) and finally analyzed (m) by a filter (F),with respect toquantizationaxis2. (b) As (a), after a 1~rotation of the whole figure about z (same experiment, with the same setup). (c) As (b), except that the quantization axis is reversed (different experiment: Ne* polarized ( -2), detector at 0, B)=x, with the same setup).
Ne atoms. The detector moves in a plane perpendicular to the quantization axis 2. This particular collision plane consists of two half-planes, the azimuthal angles of which are I= 0 and Q= IL.In a perfect experiment, the final state 12, m) is analyzed. For the sake of clarity we shall assume that final states are referred to the same quantization axis 2. Because of the u-g decoupling, the collision is entirely described by the set of scattering amplitudes: f s;“2,m (6,~). These amplitudes can be expanded in terms of spherical harmonics or equivalently of the products P$(x) eiwp,wherex=cos& (1)
=2-“2
c%?lJ,,
+%%.a*,)
.9 2,m.A.p =2-“2(%n,A,p
-sf,m,,)
7 *
Rigorously, for indistinguishable atoms, one must take into account the interference between the direct contribution at (8, e) and the exchange one at (n - 0, p+x). In fact this will not be really necessary here, insofar as the experiment gives very small values of A around 90” (c.m. ), where this interference has its biggest effect. Finally we shall assume that dd dominates at small angles ( 8 < 40 o ) whereas A” dominates at large angles (e> 130”). To calculate A, one has to calculate also the DCS (da/d,@ _2 which is expressed in terms of the scattering amplitudesf k$,, (6,~). These amplitudes are readily deduced from the previous ones by symmetry considerations. By rotating as a whole fig. 5a, by an angle Aabout axis z, one gets fig. 5b which represents the same experiment made with the same experimental device. Now if we reverse the quantization axis (fg. 5c), we get a different experiment made with the same device, namely a polarized 12, - 2 ) Ne* beam impinging on a Ne beam along z, and a detector positioned in the direction (6, x) instead of (8, 0). The scattering amplitude remains unchanged, while the quantum numbers + 2, rn are changed into - 2, - m. Consequently, fy,_,(e,
x)=f$;,m(6,
0) .
(3)
This leads to the following expressions for the direct and exchange differences: Ad*==4C [ If!M@
m
- lf5,,ux
0) kf2,AR
70 +f2,,e3
n) 121.
0) I2 (4)
This result is equivalent to that given by Dilren and Hasselbrink for asymmetric systems [ 6 1. Using eqs.
J. Baudonet al./Polarizationeffzrt in metastableneonatom
dence of the scattering amplitudes is small, i.e. terms ,uu=0 strongly dominate the other ones. In such conditions, the differences are approximated by
( 1) and (4), one gets the following expansion: &Xc- m&P .
*’
t1-(-1)““‘l
xY(~),,~,,~(~*)sm~,.r,~~(x)~~‘(x)
Adz2 1 +&,,-,@&,,+c.c.,
*
m
(5)
As these sums contain no contribution from fl=p’, Ad,” are purely interference term quantities, in the sense that they contain only crossed terms which will finally behave as cosines of some phases. This. property explains why A oscillates around zero, as observed experimentally. In order to get simpler and more amenable expressions, it is convenient to consider explicitly the azimuthal dependence, by expanding the amplitudes as f %A(& CP)=2-“*Lfs,A@ =
E p=--a,
.W
or
3)2,m.J~)
v) +f &?I(&e)l eiw,
159
(6)
~1~x2 C %,m.o&n +c.c. ,
m
(9)
where C.C.is the complex conjugate and
r 2.m= pc,d %J?w *
A third general property of A can be obtained by means of symmetry considerations: A( 0) = A( IC)= 0. This is readily deduced from eq. (6): as the directions (6= 0 or II, g) are identical for any value of p, one has
where
(7) The quantities 9 or Q are simply the Fourier harmonics of the scattering amplitudes, considered as periodic functions of q. Using eq. ( 6 ) in expansion (4 ) or ( 5 ) gives
Therefore,A(O)=A(x)=O.ThevalueofAat8=0is difficult to observe because of the large forward peak of elastic scattering, but the property A( IC)= 0 is well verified experimentally. The various quantities introduced in the previous discussion (the basic ones being the scattering amplitudes f $g or f $ ) correspond to collision channels of the type 12, m)zI~,PL),,
A’= 2 C m
C
S,m,p
%n,,,
.
(8)
p’-_podd
As expected, Ads’ are different from zero if and only if the scattering amplitudes have an azimuthal dependence. Otherwise, only the harmonics f (or 9)2,nr,0differ from zero, which leads to dd,”E 0. Such a dependence implies: (i) an anisotropy of the interaction, (ii) rotational couplings between adiabatic 61 states (otherwise each Q state can be treated independently from the other ones, which leads to a set of scattering amplitudes independent of p). Anisotropy, and thus polarization effects, expected from metastable heavy rare gas atoms are small, in so far as their p character is screened by the excited outer s orbital. As a consequence, the azimuthal depen-
where the subscripts indicate the quantization axes. On the other hand, in the treatment of the collision, it is convenient to take in account in the invariance of J* and Jz, i.e. to use the angular basis: I(2, A), JM) z to which refer the standard scattering amplitudes Fjo,2n [ 11. The relationships between these amplitudes and the previous quantities (S, Y, 9, etc.) are obtained using straightforward angular momentum algebra, with the following transformations: before the collision, l~,mo~zl~o,~~,~l~,mo~zl~o,~,), + I (2,&)>
JW.
and after the collision,
J. Baudon et al. /Polarization effects in metastable neon atom
160
I (2,~),JWz+l2,
m>zlAcl>z
This allows us introduce the angular coefficient, 5$“k;dfl=[4x(2&+
l)]“’
Terms ( I ) are Clebsch-Gordan coefficients. Using coefficients W,one obtains for instance
etc. It may be observed that if the collision cannot change lo into il# Lo, then the transformations made after the collision are exactly the inverse of those made before. As a consequence, only &,,,. (or $,m,o) differ from zero, which leads to As 0.
4. Conclusion The difference A between DCSs for atomic polarizations (j=2, m=+2), and 12, -2)z, where the quantization axis 2 is perpendicular to the collision plane, has been measured as a function of the scattering angle, in spite of the fact that anisotropy and polarization effects manifested by metastable rare gas atoms are generally small. The interference character of this difference is a help in the measurement, since it consists only of crossed terms, essentially between strong amplitudes which are independent of p, and small dependent ones. As an example for Ne* collisions, the squared modulus of the dependent part is I%, or less, of the total DCS. The general symmetry properties of A have been verified experimentally. Surprisingly, the oscillatory structure of A( 0) is rather simple, particulary at large angles (exchange contribution). This is propably due to the fact that, for each m value, there are few significant crossed terms, maybe even only one, namely ( $A?&, +c.c. ). A priori, this term represents the interference of four amplitudes, since the Q are differences of g and u am-
plitudes. Only a complete calculation will provide a detailed interpretation of the phase of this oscillation. Obviously, fast oscillations can be damped by the limited angular resolution of the experiment. It is worthwhile noting that the angular spread has very different effects on A and on a standard DCS: A itself is smeared out, because its mean value is zero, whereas a DCS is averaged around some positive value. This can explain the very low value of A in the “undistinguishability” region (8~ 90” c.m. ). Many further developements of this type of experiment can be imagined. The tint simply consist of improvements and extensions of the present experiment: (i) measurement of A at a higher energy, by use of the seeded beam technique (e.g., 5% Ne in Hz gives a Ne*-Ne collision energy of 254 meV), (ii) use of a laser-induced-fluorescence detector, working on the transition 1s5-2p,, which detects only ‘ONe*( 3P2) atoms and then improves the contrast A/DCS. Other developements are more fundamental: (i) measurement of the final populations of the different Zeeman sublevels (i.e. If$!$, I’), by use of a laser-induced-fluorescence detector operating within a magnetic field ( z IO2 G) collinear to the laser beam; (ii) measurement of the relative phases between the scattering amplitudes f2,m; this can be achieved by using interference effects induced in a non-adiabatic transformer, or “spin-flipper” [ 14 1.
References [l]H.F.Mies,Phys.Rev.A7(1973)957; R.H.G. Reid, J. Phys. B 6 (1973) 2018; J. Grosser, Z. Physik D 3 (1986) 39. [ 2 ] LV. Hertel, H. Schmidt, A. Bahring and E. Meyer, Rept. Progr. Phys. 48 (1985) 375; J. Grosser, J. Phys. B 14 (1981) 1449. [3] J.S. Cohen and B. Schneider, J. Chem. Phys. 61 ( 1974) 3230. [4]C.O.Akoshile,J.D.ClarkandA.J.Cunningham,J.Phys.B 18 (1985) 2793. [ 51Ch. Miniatura, F. Pet-ales, G. Vassilev, J. Reinhardt, J. Robert and J. Baudon, J. Phys. (Paris), submitted. [6] R. Diiren and E. Hasselbrink, J. Chem. Phys. 85 (1986) 1880; 91 (1987) 5455. [7] B. Stem and J. Baudon, Z. Physik D 8 (1988) 359. [8] B. Brutschy and H. Haberland, Phys. Rev. A 19 (1979) 2232. [9] I. Colomb de Daunant, G. Vassilev, M. Dumont and J. Baudon, Phys. Rev. Letters 46 ( 198 1) 1322.
J. Baudon et al. /Polarization effits in metmtable neon atom [lo] P. Feron, A. Lagreze, J. Robert, Ch. Lerminiaux, J. Reinhardt, J. Baudon, W. Beyer, H.P. Ludescher and H. Haberland, Z. Physik D IO (1988) 221. [ 111 N. Courtier and M. Dumont, Rev. Phys. Appl. 16 ( 198 1) 601. [ 121 J.M. Alvarino, C. kkpp, M. Kreinensen, B. Staudenmayer, F. Vecchiocattivi and V. Tempter, J. Chem. Phys. 80 ( 1984) 765.
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[ 131 J. Baudon, P. Feron, J. Robert, B. Brunetti and F. Vecchiocattivi, MOLEC VII, Assisi, 1988, book of abstracts, 126. [14]R.D.HightandR.T.Robiscne,Phys.Rev.A17 (1977) 561; W. SchrUer and G. Baum, J. Phys. E 16 ( 1983) 52. Q.
Polarization effects in metastable neon atom (Ne* ( 3P2) ) on ground state neon atom collision at thermal energy J. Baudon, F. Perales, Ch. Miniatura, J. Robert, G. Vassilev, J. Reinhardt Laboraloire de Physique des LUSTS ‘, UniversitPParis-Nerd, Avenue J.B. CMment, 93430 Villetaneuse, France
and H. Haberland Fakultiitfir Physik, Albert-Ludwigs Universitiit, Hermann Herder Strasse 3, 7800 Freiburg/B, FRG Received 28 December 1989; in final form 22 March 1990
The difference A between the differential cross sections for Ne*( sPz) atoms polarized either in state lj= 2, m = + 2) or lj=2, m = - 2), colliding at thermal energy with a groundstate target (Ne, Or), is measured. In the symmetric case Ne*-Ne, direct and exchange contributions are observed. General properties of A, derived from symmetry considerations, are established; in particular: (i ) the interference character of A, (ii) the role played by the azimuthal dependence of the scattering amplitudes, (iii) the property A( 0) = A( 180” ) ~0. The relationships between the Fourier harmonics introduced in this discussion and the scattering amplitudes used in standard collision treatments are given.
1. Intruductlon The collision of an atom with spin 0’) with a spherically symmetric target atom is governed by an anisotropic interaction. In a molecular description, using for instance the adiabatic Born-Oppenheimer basis set (,4 (0) states, where L!(62) is the projection of L (j) on the internuclear axis l? ) , the dynamics are complex especially because the atomic spin couples with the angular momentum I of the relative motion, to give the (constant ) total angular momentum (J) . This coupling results in long range rotational couplings between molecular states dissociating into a specific lj, m) atomic state, referred to a fixed axis 2. As a consequence, the collision treatment leads to a set of several coupled radial equations for each J value [ 11. Most of the difficulties in this problem arise from the change in the character of the diatomic system as the collision evolves: on the one hand, a purely atomic character, referred to 2, at infinite dis’ Associe au CNRS (URA No. 282). 0301-0104/90/$03.50
tance, where the collision channels arc defined; on the other hand a molecular character, referred to the rotating axis R, at short distances. When this change is suffkiently abrupt, the introduction of a so-called locking radius is justified [ 2 1. When a collision of a heavy rare gas metastable atom (Ne*, AP, ...) is considered at thermal energy, the problem is even more complicated by the spin-orbit interaction, which leads to energy splittings at infinite R, comparable to or even larger than the collision energy [ 3 1. In most of the differential scattering experiments of heavy particles, the initial internal state ]j, m) is not prepared, and the final one, IjO), m' ) , is not analyzed: only total differential cross sections (DCS ) are measured. This total DCS contains implicitly all potential energies corresponding to different molecular states. However, it does not exhibit clearly either the anisotropy of the interaction nor the rotational coupling effects. Let us assume that tine-structure transitions have a small probability to occur, whi.ch is generally true in the Ne*-Ne collision [ 41. To get complete information about the anisotropy and cou-
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J. Baudon et al. /Polarization effects in me&stable neon atom
plings would require a “perfect” experiment, in which a monokinetic and completely polarized 1j, m) Ne* beam crosses a monokinetic beam of ground state atoms, the atoms scattered at a given direction (0, 0) being analyzed ( Ij, m’ ) states) after the collision. In principle, it would be possible to measure not solely specific DCSs, such as Ifmm,(0, p) 12, where the f,,, are the scattering amplitudes, but also the relative phases between these amplitudes [ 5 1. Such an experiment is obviously difficult to realize, and it must be undertaken step by step. A first possible step is the type of experiment already performed by Dilren and Hasselbrink [ 6 ] on collisions between an excited alkali atom and a heavy rare gas atom. The excited atoms are prepared with their spin either up or down with respect to the collision plane, and the difference between the two corresponding angular distributions is measured as a function of the scattering angle. In the case of Ne* ( ‘P2 ) , this experiment consists of two measurements using polarized beams of metastables, in states lj=2, m= +2) and 12, -2), with respect to a quantization axis 2 perpendicular to the collision plane. The difference between the two DCSs is d(O)= c (If+2,m(f3,9=0) m
12- If-2.m(&
0) 12) ,
shown in fig. 1, will be discussed. Two supersonic nozzle beams (velocity spread WY= 6%, angular aperture 68x0.8” fwhm) are crossed at right angle. Metastable atoms are produced within one of the beams (the “primary” beam) by means of a coaxial counter-propagating electron beam, at an energy x 100 eV, which is well above the excitation threshold. The efficiency of the electron bombardment is improved by a coaxial magnetic field (few hundred G); with this configuration, the velocity spread of the metastable atoms is kept almost equal to the initial one (6v/v= 7%). The metastable atom flux, estimated from the secondary electronic emission current ( xnA), is of the order of lo9 at/s. It has been previously verified [ 91 that metastable levels 3Po, 3P2 are populated proportionally to their statistical weights (1:5). Scattered metastable atoms are detected by a rotatable electron multiplier. The overall angular spread is A& 2.5 ‘. A fixed detector (channel electron multiplier), set at 20 mm above the collision volume, is used as a monitor. In order to eliminate the background gas contribution, the secondary beam is chopped periodically ( 153 Hz). Counts are added during the open time (shifted by the time of flight from the chopper to the collision volume), and sub-
where m is the projection of the j=2 electronic angular momentum ajler the scattering event. It is expected that, in contrast to excited (P) alkali atoms, metastable Ne* atoms will exhibit only small anisotropy or “polarization” effects, because the 2p hole, which is responsible for these effects, is screened by the outer 3s orbital. Nevertheless, significant polarization effects in rare gas collisions have been already predicted for instance in Ne*-He collisions [ 7 1. In the special case of the Ne*-Ne collisions, direct and exchange polarization effects can be expected, together with interference effects arising from u-g and nuclear symmetry.
Ne
cw dye her
externel
ltelon
eeturated
ebecrptlon
2. Experiment 2.1. The crossed beam apparatus The scattering apparatus used here has been described in detail elsewhere [ 8 1. The main features,
Fig. 1. Scheme of the experiment. Nfl, Ne and L indicate respeotively the metasW& atombeam,the groundstate atombeamand the laser beam, F is an optical fiber, P is a linear polarizer, Q is a 1/4 plate; D is the metastable atom detector. A 15 G magnetic field is applied to preserve the atomic polarization from L to the collision volume.
.I. Baudon et al. /Polarization effecls in metastable neon atom
tracted when the secondary beam is stopped (up/ down counting). The collision energy can be varied either by heating the secondary beam source or by the seeded beam technique [ lo]. The velocity distributions of both beams are measured by time-of-flight. 2.2. Optical excitation. Polarization of the Ne* beam Laser excitation is used to prepare the electronic state of the *we* ( 3P2) atoms. A tunable cw laser is stabilized in frequency by means of an external Fabry-Perot etalon. In order to avoid any frequency drift during the long period ( x 1 h) needed for DCS measurements, the etalon frequency is locked to one of the Zeeman components of the 1s5( ‘P2)-2p,( ‘D2) saturated-absorption line (A= 6 14.3 nm ) , observed in an auxillary low pressure discharge [ 111. The laser power is stabilized to a value ( 15-20 mW) large enough to get a stationary regime of the laser excitation, and low enough to avoid any saturation effect. The laser light is directed into the scattering chamber by a single mode ( TEMoo ), polarization-preserving optical fiber. A parallel laser beam is finally recovered by means of a spherical lens. Its direction (2) is perpendicular to that of the Ne* beam. A linear dichroic polarizer followed by a 1/4 plate permits the production of any polarization (o+, R, o- ). In the experiments in this paper we have only used circularly polarized IS+, o- light. In contrast to the expcriments of ref. [ 61 where the laser is used to produce the excited atoms within the collision volume and at the same time to orient their spin, in the present case the laser is used only to prepare the internal state, e.g. 12, + 2 ) , at a distance of 4 mm before the collision point. In such conditions one has to be careful about the precession of the prepared spin state around the earth magnetic field. In the present case the precession frequency is about 1 MHz, which means that j makes a complete revolution every 1 us, i.e. one revolution for every 1 mm of path. To avoid this effect, a uniform magnetic field of about 1O- 15 G, parallel to the laser beam, is applied over the whole path of the atoms from the crossing point with the laser beam, to the collision point. If a definite polarization (o*, n) is used the laser “connects” each lower Zeeman sublevel (3P2) to a single upper sublevel ( ‘D2) and no coherence is directly induced between the sublevels. Therefore the
155
evolution of the metastable atoms during their transit across the laser beam is described satisfactorily by rate equations. The upper radiative level ( ‘D2) has a width y = 40.1 MHz and it can either decay to the initial level ( 3P2) or cascade to the ground state. As the Zeeman splittings due to the magnetic field present in this experiment are small compared to the effective width (including Doppler effect) of the laser and to y, all Zeeman sublevels can be considered as degenerate. For example, if o+ light is used, only Am = 1 transitions are allowed, and all mj levels save mj= + 2 are depopulated. The population of the mj= + 2 state is further enhanced by radiative decay from the up per mj= 1 state. Under such conditions, the rate equations can be solved analytically. The basic parameters are: a constant 1 characterizing the laser pumping, y the total width of the upper level, and r ( = 28.5 MHz) the partial width for the ‘D2-3P2 transition. The rate equations have been solved for several reasonable values of 1, ranging from 0.5 to 5 MHz. In fig. 2a, the time evolution of the populations are shown, for cr+ polarization. The transit time in the laser beam (+ 1 mm ) is about 1.3 us. Fig. 2b shows the total population of the metastable level at this time. Experimentally, the depopulated fraction of the metastable atom flux, after the laser action is 0.39 + 0.06. Neither **Ne*( 3P0,2)atoms ( 10% of the total flux) nor **,*“Ne*( ‘PO) atoms ( 15% of the total flux) are affected by the laser light. This means that the laser induced depopulation effect represents a fraction 0.39/0.75 =0.52 k 0.08 of the initial *‘Ne( ‘P2) population. This value is sufficiently close to the calculated asymptotic value to conclude that the stationary regime is indeed achieved and that the pumping coefficient is 1> 3 MHz. For the o+ polarization, 80% at least of the meastable level population corresponds to the m = + 2 sublevel. 2.3. Measurement of the diflerence between the m=+2andm=-2DCSs As mentioned above, the prepared atoms, *we* ( ‘P2), represent only 75% of all the metastable atoms. As the detector detects all metastables with about the same efficiency, the measurement of state selected m = + 2 or m = - 2 DCSs requires some further corrections, while in contrast, the difference
J. Baudon et al. /Polarization effects in metastable neon atom
156
is directly obtained in the lab frame and easily transformed in the c.m. frame *I. The experimental procedure is as follows: in a first run, the o+ polarization is used and for each angle 0 two (up/down) countings are made, one with the laser on (L + (0) ), the other one with the laser off (N + (6) ). In a second run this is repeated with the o- polarization, giving countings L - ( 0)) N - ( 0). If all experimental parameters were strictly constant, one would have N + ( 0) = N - ( 6). Actually, during the acquisition time ( x 1 h) some drift is likely to occur and the difference d needs to be calibrated:
0
‘h x=2
I u 1
A=(L+/N+ +I
0 1
0
x=1 I<
tot
0 0
-L-IN-)(N++N-)/2.
-2,-l ,o
t (us)
5
a .
1 (MHz)
b Fig. 2. (a) Time evolution of me&stable Zeeman sublevel (0, f 1, k 2) populations. Values of 1 (in MHz) are proportional to the laser power (see text). tot is the total metastable population. The vertical broken line, at t= 1.3 ps, corresponds to a laser beam effective diameter of 1 mm. (b) Total metastable population as a function of parameter 1 The two horizontal broken lines give the range of the experimental values.
The same arbitrary units are used for A and the DCS. As it wilI be seen further, the difference is relatively small ( 1 / 10 of the DCS or less) and difficult to measure with a good accuracy, over the whole angularrange (5”~&~~100”).1natirstrunthisrange has been explored with steps of lo. In a second run, angular intervals of 20” lab have been explored, with a reduced angular step (0.5” ), and better statistics. Fig. 3a shows the difference A as a function of the c.m. angle, for the Ne*-Ne collision at a collision energy of 64 meV. It exhibits a rather simple oscillatory structure with a mean value zero. The amplitude of oscillation decreases rapidly in the angular range 10‘40” c.m. and then increases, with a maximum at 180” (see fig. 3b). As can be seen in fig. 3, A behaves very differently from the total DCS especially around 180”. At 8= 180”, Ax 0; this important point (cf. section 3) has been confvmed by a more accurate measurement in the range 176”-184” c.m. Another example of the difference A is shown in fg 4, for the Ne*-O2 collision at 74 meV. It is known that Penning ionization occurs in this collision, which is further complicated by the ionic-covalent coupling [ 12 1. Previous differential measurements [ 13 ] have shown #I
It may be noticed that the lXS (da/dQ),,o which can be obtained in principle by use of a 1cpolarization, would need to be corrected for the contribution of non-prepared metastable atoms. An easier method would be to use a laser induced fluorescence detector, working on the same ‘Pr’D2 transition, which detects only rc’Ne*(-‘Pr ) atoms.
J. Baudon et al. /Polarization effects in metastable neon atom
157
Fig. 3. (a) Difference A between differential cross sections (da/@) fZ, for the Ne*-Ne collision at 64 meV, as a function of the c.m. scattering angle. Note the change in scale at 42”, and the passage through zero at & 180”. (b) Comparison of the total differential cross section (points) to the amplitude of oscillation of A (vertical bars). The same arbitraryunit is used for both quantities.
that the elastic DCS is a rapidly decreasing function of the angle. For this reason the measurement of A has been carried out only within a limited angular range ( 5 ‘- 15 ’ lab). The behaviour of A is qualitatively similar to that of the previous one at small angles. The ratio A/ (a), where (a) is the total DCS is 0.29 at 5” lab.
3. Discussion A complete calculation of A requires the solution of a set of coupled equations in an appropriate basis [ 11. This procedure itself requires a knowledge of the
interaction matrix and, in particular, terms u,,(R), y (R ) which appear in the expansion of the potential in terms of Legendre polynomials. In the Ne*-Ne case, the treatment is complicated by: (i) the u-g symmetry (nevertheless the interaction matrix is blockdiagonal in u-g), (ii) the multiplicity of the atomic level ( ‘*‘P); (iii) the spin-orbit interaction. On the other hand, general properties of A( 8) can be derived by a simple consideration of the symmetries. In the present discussion, we shall concentrate on this point, especially for the Ne*-Ne collision. Let us consider (see fg 5), in the c.m. frame, the collision of a polarized Ne* beam (state 12, + 2 ) for example), parallel to axis z, with a beam of ground state
158
J. Baudon et al. /Polarization @Ects in metastable neon atom
where 1=0, 1, .... co; p= -A, -A+ 1, .... +L The direct and exchange contributions to the o+ DCS are then =t
2 In=-2
If5,,(e,o)~f~*,(e,o)12
(2) where Y2,m.a.p -4.103
I 0
1
ld
2@
‘lab Fig. 4. Same as fig. 3a, for NC*-0, collision at 74 meV.
a
b
C
Fig. 5. (a) Ne*-Ne collision experiment in the c.m. frame. Ne? atoms are initially polarized ( + 2 ) and finally analyzed (m) by a filter (F),with respect toquantizationaxis2. (b) As (a), after a 1~rotation of the whole figure about z (same experiment, with the same setup). (c) As (b), except that the quantization axis is reversed (different experiment: Ne* polarized ( -2), detector at 0, B)=x, with the same setup).
Ne atoms. The detector moves in a plane perpendicular to the quantization axis 2. This particular collision plane consists of two half-planes, the azimuthal angles of which are I= 0 and Q= IL.In a perfect experiment, the final state 12, m) is analyzed. For the sake of clarity we shall assume that final states are referred to the same quantization axis 2. Because of the u-g decoupling, the collision is entirely described by the set of scattering amplitudes: f s;“2,m (6,~). These amplitudes can be expanded in terms of spherical harmonics or equivalently of the products P$(x) eiwp,wherex=cos& (1)
=2-“2
c%?lJ,,
+%%.a*,)
.9 2,m.A.p =2-“2(%n,A,p
-sf,m,,)
7 *
Rigorously, for indistinguishable atoms, one must take into account the interference between the direct contribution at (8, e) and the exchange one at (n - 0, p+x). In fact this will not be really necessary here, insofar as the experiment gives very small values of A around 90” (c.m. ), where this interference has its biggest effect. Finally we shall assume that dd dominates at small angles ( 8 < 40 o ) whereas A” dominates at large angles (e> 130”). To calculate A, one has to calculate also the DCS (da/d,@ _2 which is expressed in terms of the scattering amplitudesf k$,, (6,~). These amplitudes are readily deduced from the previous ones by symmetry considerations. By rotating as a whole fig. 5a, by an angle Aabout axis z, one gets fig. 5b which represents the same experiment made with the same experimental device. Now if we reverse the quantization axis (fg. 5c), we get a different experiment made with the same device, namely a polarized 12, - 2 ) Ne* beam impinging on a Ne beam along z, and a detector positioned in the direction (6, x) instead of (8, 0). The scattering amplitude remains unchanged, while the quantum numbers + 2, rn are changed into - 2, - m. Consequently, fy,_,(e,
x)=f$;,m(6,
0) .
(3)
This leads to the following expressions for the direct and exchange differences: Ad*==4C [ If!M@
m
- lf5,,ux
0) kf2,AR
70 +f2,,e3
n) 121.
0) I2 (4)
This result is equivalent to that given by Dilren and Hasselbrink for asymmetric systems [ 6 1. Using eqs.
J. Baudonet al./Polarizationeffzrt in metastableneonatom
dence of the scattering amplitudes is small, i.e. terms ,uu=0 strongly dominate the other ones. In such conditions, the differences are approximated by
( 1) and (4), one gets the following expansion: &Xc- m&P .
*’
t1-(-1)““‘l
xY(~),,~,,~(~*)sm~,.r,~~(x)~~‘(x)
Adz2 1 +&,,-,@&,,+c.c.,
*
m
(5)
As these sums contain no contribution from fl=p’, Ad,” are purely interference term quantities, in the sense that they contain only crossed terms which will finally behave as cosines of some phases. This. property explains why A oscillates around zero, as observed experimentally. In order to get simpler and more amenable expressions, it is convenient to consider explicitly the azimuthal dependence, by expanding the amplitudes as f %A(& CP)=2-“*Lfs,A@ =
E p=--a,
.W
or
3)2,m.J~)
v) +f &?I(&e)l eiw,
159
(6)
~1~x2 C %,m.o&n +c.c. ,
m
(9)
where C.C.is the complex conjugate and
r 2.m= pc,d %J?w *
A third general property of A can be obtained by means of symmetry considerations: A( 0) = A( IC)= 0. This is readily deduced from eq. (6): as the directions (6= 0 or II, g) are identical for any value of p, one has
where
(7) The quantities 9 or Q are simply the Fourier harmonics of the scattering amplitudes, considered as periodic functions of q. Using eq. ( 6 ) in expansion (4 ) or ( 5 ) gives
Therefore,A(O)=A(x)=O.ThevalueofAat8=0is difficult to observe because of the large forward peak of elastic scattering, but the property A( IC)= 0 is well verified experimentally. The various quantities introduced in the previous discussion (the basic ones being the scattering amplitudes f $g or f $ ) correspond to collision channels of the type 12, m)zI~,PL),,
A’= 2 C m
C
S,m,p
%n,,,
.
(8)
p’-_podd
As expected, Ads’ are different from zero if and only if the scattering amplitudes have an azimuthal dependence. Otherwise, only the harmonics f (or 9)2,nr,0differ from zero, which leads to dd,”E 0. Such a dependence implies: (i) an anisotropy of the interaction, (ii) rotational couplings between adiabatic 61 states (otherwise each Q state can be treated independently from the other ones, which leads to a set of scattering amplitudes independent of p). Anisotropy, and thus polarization effects, expected from metastable heavy rare gas atoms are small, in so far as their p character is screened by the excited outer s orbital. As a consequence, the azimuthal depen-
where the subscripts indicate the quantization axes. On the other hand, in the treatment of the collision, it is convenient to take in account in the invariance of J* and Jz, i.e. to use the angular basis: I(2, A), JM) z to which refer the standard scattering amplitudes Fjo,2n [ 11. The relationships between these amplitudes and the previous quantities (S, Y, 9, etc.) are obtained using straightforward angular momentum algebra, with the following transformations: before the collision, l~,mo~zl~o,~~,~l~,mo~zl~o,~,), + I (2,&)>
JW.
and after the collision,
J. Baudon et al. /Polarization effects in metastable neon atom
160
I (2,~),JWz+l2,
m>zlAcl>z
This allows us introduce the angular coefficient, 5$“k;dfl=[4x(2&+
l)]“’
Terms ( I ) are Clebsch-Gordan coefficients. Using coefficients W,one obtains for instance
etc. It may be observed that if the collision cannot change lo into il# Lo, then the transformations made after the collision are exactly the inverse of those made before. As a consequence, only &,,,. (or $,m,o) differ from zero, which leads to As 0.
4. Conclusion The difference A between DCSs for atomic polarizations (j=2, m=+2), and 12, -2)z, where the quantization axis 2 is perpendicular to the collision plane, has been measured as a function of the scattering angle, in spite of the fact that anisotropy and polarization effects manifested by metastable rare gas atoms are generally small. The interference character of this difference is a help in the measurement, since it consists only of crossed terms, essentially between strong amplitudes which are independent of p, and small dependent ones. As an example for Ne* collisions, the squared modulus of the dependent part is I%, or less, of the total DCS. The general symmetry properties of A have been verified experimentally. Surprisingly, the oscillatory structure of A( 0) is rather simple, particulary at large angles (exchange contribution). This is propably due to the fact that, for each m value, there are few significant crossed terms, maybe even only one, namely ( $A?&, +c.c. ). A priori, this term represents the interference of four amplitudes, since the Q are differences of g and u am-
plitudes. Only a complete calculation will provide a detailed interpretation of the phase of this oscillation. Obviously, fast oscillations can be damped by the limited angular resolution of the experiment. It is worthwhile noting that the angular spread has very different effects on A and on a standard DCS: A itself is smeared out, because its mean value is zero, whereas a DCS is averaged around some positive value. This can explain the very low value of A in the “undistinguishability” region (8~ 90” c.m. ). Many further developements of this type of experiment can be imagined. The tint simply consist of improvements and extensions of the present experiment: (i) measurement of A at a higher energy, by use of the seeded beam technique (e.g., 5% Ne in Hz gives a Ne*-Ne collision energy of 254 meV), (ii) use of a laser-induced-fluorescence detector, working on the transition 1s5-2p,, which detects only ‘ONe*( 3P2) atoms and then improves the contrast A/DCS. Other developements are more fundamental: (i) measurement of the final populations of the different Zeeman sublevels (i.e. If$!$, I’), by use of a laser-induced-fluorescence detector operating within a magnetic field ( z IO2 G) collinear to the laser beam; (ii) measurement of the relative phases between the scattering amplitudes f2,m; this can be achieved by using interference effects induced in a non-adiabatic transformer, or “spin-flipper” [ 14 1.
References [l]H.F.Mies,Phys.Rev.A7(1973)957; R.H.G. Reid, J. Phys. B 6 (1973) 2018; J. Grosser, Z. Physik D 3 (1986) 39. [ 2 ] LV. Hertel, H. Schmidt, A. Bahring and E. Meyer, Rept. Progr. Phys. 48 (1985) 375; J. Grosser, J. Phys. B 14 (1981) 1449. [3] J.S. Cohen and B. Schneider, J. Chem. Phys. 61 ( 1974) 3230. [4]C.O.Akoshile,J.D.ClarkandA.J.Cunningham,J.Phys.B 18 (1985) 2793. [ 51Ch. Miniatura, F. Pet-ales, G. Vassilev, J. Reinhardt, J. Robert and J. Baudon, J. Phys. (Paris), submitted. [6] R. Diiren and E. Hasselbrink, J. Chem. Phys. 85 (1986) 1880; 91 (1987) 5455. [7] B. Stem and J. Baudon, Z. Physik D 8 (1988) 359. [8] B. Brutschy and H. Haberland, Phys. Rev. A 19 (1979) 2232. [9] I. Colomb de Daunant, G. Vassilev, M. Dumont and J. Baudon, Phys. Rev. Letters 46 ( 198 1) 1322.
J. Baudon et al. /Polarization effits in metmtable neon atom [lo] P. Feron, A. Lagreze, J. Robert, Ch. Lerminiaux, J. Reinhardt, J. Baudon, W. Beyer, H.P. Ludescher and H. Haberland, Z. Physik D IO (1988) 221. [ 111 N. Courtier and M. Dumont, Rev. Phys. Appl. 16 ( 198 1) 601. [ 121 J.M. Alvarino, C. kkpp, M. Kreinensen, B. Staudenmayer, F. Vecchiocattivi and V. Tempter, J. Chem. Phys. 80 ( 1984) 765.
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[ 131 J. Baudon, P. Feron, J. Robert, B. Brunetti and F. Vecchiocattivi, MOLEC VII, Assisi, 1988, book of abstracts, 126. [14]R.D.HightandR.T.Robiscne,Phys.Rev.A17 (1977) 561; W. SchrUer and G. Baum, J. Phys. E 16 ( 1983) 52. Q.