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Experimental determination of the mj distribution in inelastic scattering of Na2 by He
C’HEhllCAL
EXPERIMENTAL
IN INELASTIC
DETERhlIiVATION
SCATTERING
OF N+
PHYSICS
20 May 19s3
LETTERS
OF THE nzJ DISTRIBUTION BY He
i‘he orirnt.triorxA distrlburxm of h’a2 molrcule~ ScJIterCd by He has been determined in a molecular beam experiment. At large andc vxttcriw -_. \\hcre inelastic collisions are dominant. 3 high degree of alignment hss been observed. This alignment diepcnds \trcrngI\ on the rotational qu;lntum numberl after wzatterinp. TheJdependence can be explained by assummg thAt during collisions IJIJ iz consrrved uhen the quntiution x\is ic chosen parallel with the geometric apse.
rotational quantum numbers. We will report here on a beam experiment in which the spatial distribution of J can bc drtrnnincd for larger scattering angles and for relatively high rotational states. a situation which applies to most gsses. So far experimental results have been obtained for Naz backward scattering by He. Both orientation and magnitude of the alignment have been determined. To our knowledge this is the firsr observation of alignment produced in large-angle scattering.
3. Experimental
method
In this esperirnent the method of Visser [6] to determine alignment in a molecular bran1 is used. The configuration of sources. fields. laser beam and detection is shown in fig_ l_ The beml sources together with magnetic field B,,, cm be rotated to allow the study of alignment at different scattering angles. We keep the detection chamber fixed in order to prevent difficulties with alignment of the optics and to be able to reduce the background light, which mainly originates from scattering of the laser beam by optical elemenrs and windows. Na-, is chosen as molecule for studying angular momentum polarization because it is one of the few molecules that have a suitable transition in the part of the spectrum that can be easily reached with a tunable dye laser. Helium is the
0 009-X
14/S3/0000-0000/S
03.00
0 1983 North-Holland
Volume 97. number 3
CHEMICAL
20 hlay 1983
PHYSICS LETTERS
letter we will present the results of experiments with
molecules that are scattered over this maximum scat-
Fii. 1. The experimental apparatus. Both supersonic beam sources can be rotated together with Baus to allow analysis of different scattering angles. The analyzing magnetic field Ban is perpendicular to the plane of drawing. The molecules are excited by polarized laser-light propagating perpendicular to the collisionplane and with the electric vector & parallel with the molecular velocity_ The fluorescence ls detected by a photomultiplier.
chosen scattering partner because of the small maximum scattering angIe in the laboratory frame of reference as can be seen in the Newton diagram (fig. 2). This results in a high intensity of scattered molecules in the detector at the expense of the angular resolution. The maximum scattering angle in the laboratory frame is, for these specific circumstances, 14”. In this
tering angle. We have chosen this particular angle because at other angles, as can be seen in the Newton diagram, two groups of molecules with different velocities and different centre-ofmass scattering angles contribute to the flux of scattered particles_ The diagram shown in fig_ 2 is the Newton diagram for elastic scattering. For inelastic collisions dtab associated with a certain 0, is slightly different, but even for large AJ transitions this change in 9rti is of the same order of magnitude as our angular resolution_ The molecules are excited by a dye laser tuned to the transitions of the A r 3: u’ = 9, J’ + X 1 Zz Y” = 0. J” vibration rotation band. In order to measure the alignment of the scattered molecules we make use of the fact that the probability for excitation depends on the angle between the transition moment,p, and the electric vector, E, of the polarized laser beam. Since p is directly coupled with J. in fact p is perpendicular to J. the fluorescence intensity depends on the distribution of with respect to c:. As a first approximation we will describe the distribution ofJwith an ellipsoidal distribution niJ
N(J) = 1+ a,P,(J _ -
- i) ,
(III
where ii is the symmetry axis of the distribution_ A negative a-, results in a discus-like shape and a positive CI~in a s&-like shape with the preferential orlentat&t of J perpendicular and parallel with respect to 17 respectively_ Because of the plane symmetry exhibited by our experimental configuration ri is located in the scattering plane, defined by the beam sources and the point of detection_ The degree of alignment in the molecular beam can be measured by passing the molecules through a magnetic field (B, in fig. I). In this field the molecules will precess through an angle &, &
Es_ 2. Newtondiagram for elastic collisions of Naa and He_ The measurements have been performed at the scattereg ygje shown in the drawing. The geometric apse 4 = (kf ki) is shown;cg makes an angle = with the normal on the fmal Naz velocity (~f,~azl.
=
kJ!@/ZI)L/u
7
(3
where L/v is the flight time through the magnetic fdd_ Thus the angle between the preferential orientation of the molecules and & will be changed, leading to a subsequent change in fluorescence intensity_ If we take Q to be the angle between ii and &, the relative change in fluorescence intensity in our apparatus can be written, in first approximation, according to Visser [6] as 343
V0ltmc
97. number 3
[l(B) - f(O)]/I(O)
= $olsin&(sin&
CHEMICAL
PHYSICS
cos 29
+ ~0s~~ sin 2Q) _
(3)
It ml he seen from this formula that ~72and Q cannot be drrrrmined independently in this esperimental zippx.nus: the sign of oz is not determined and Q is determined modulo n/2. This is equivalent to the fact that the direction of G isonly determinedmodulo IT/?. The direction of thr preferential orientation ofJ howvewr is determined uniqurly. Such a result is not surprising JS one actually measures the relative distributton oiJ
in a plam perpendicular to B,. The situatherefore be clxified by performing also mcasnrenlcnts with the field B, turned over 90” into the p1.1~ of scattering to position Bk (see insert in fig. I ). Together with the results with the field in posltiou B,. both sign and magnitude of a2 as well as 1111:dIrectinn ofll can then be determined unambigu 011sl!‘. tion
cm
3. Results Xs .u~ cxtiiiplc we 5how the result for theJ = 28 lrvei (fig . 3 1. At 0” (no scattering) we se0 the small .111pruw11r (nortlc alignmtml) found previously by
LETTERS
20 May 1983
Visser [6]. At 14” a very large effect is found. The results are not symmetric in the magnetic field but show a small shift towards negative magnetic field. From this shift we determine that the preferential orientation ofJmakes a small angle with e [eq_ (3)]_ This angle is 12 2 2” and therefore 4 is 12” (modulo n/2). To determine the exact value of Q we have turned B, over 90°, to position BA. In this configuration the effect is very small and this means that u^is nearly parallel with B& and therefore Q = 102 2 +’ _ _ The difference in amplitude observed in fig. 3 beteween the effect with positive and negative field is caused by averaging over molecules with different
velocities since the precession angle depends on the molecular velocity [eq. (II)] _ The maximum of the effect shown in fig_ 3 is studied as a function of the value of J after scattering. The result is shown in fig. 4. Note the change of sign at J = 10. There is no influence of the small alignment which already e_xists in the molecular beam before scattering. This is verified by passing the primary beam before scattering through magnetic field B,,. In this way the nozzle-alignment is rotated out of the scattering plane. This rotation has no detectable in-
fluence on the results in fig. 4.
; 01
f
IL i
f
1
I=) IIO)
“_,
00 I
.._._ _..
r!_.. .__ ._..___ __ ____
i 3
. -\%
I ig 3 K~l~tr~2 chm~r to lluorescencr intensity as 9 function ~ri the m+mrttc field z:ratpth. 5. For excitntion the X ’ 5: Y’ = Y -3’ -- .\ ’ x; I.” = 0.J” tratsitiatt is used. The data for 13” sc_tttaxin~ m&c .tre rsprewtted by =. The drawn tune is the eiiwt 111~1could be e\pcctrd if the preferenti.tl orientation c*il ~sre p.trztllel\\ iflt the tnolwul.tr wlocify. For :! cotnpariwn tits data for 0’ tno sc.tttrrinp) ~irr also &own. X _ Here xce wz 111r ~~11 nozzle-induced .tltgttttatt in rbe Na2 bean.
f
f
t -07111,.1,1,,,,,,,,,,,I,,,..,,,,,1 0 Fig. 4. J-dependence Intensity.
3
10
of the ntsGtnutn
20
30
change in fluorexence
Volume 97, number 3
20 hlay 19s3
CHEMICAL PHYSICS LETTERS
4. Discussion
Acknowledgement
The measurements of Bergmann [7] show that the Na, -He system is dominated by inelastic collisions at angles greater than 4O in the laboratory system. At a rotational temperature of 50 K in the beam the level with the highest occupation isJ= lo-Hence statistically the molecules which are in J = 4 after collision have come from higher J levels, while the molecules in J = 28 have come from lower J levels_ From this result we can conclude that positive AJ transitions give a positive effect and that negative AJ transitions give a
We are indebted to Professor J .J &I_ Beenakker for his stimulating interest in this work_ This work is part of the research program of the Stichting voor Fundamenteel Ondelzoek der Materie (Foundation for Fundamental Research on Matter) and was made possible by financial support from the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (Netherlands Organization for the Advancement of Pure Research).
negative effect. This is equivalent with the statement that positive AJ transitions produce a preferential of J in the direction of the molecular velocity and that negative AJ transitions produce
References
orientation
a preferential orientation perpendicular to the molecular velocity _ This conclusion is in agreement with recent theoretical work of Khare et al. [S.9] who concluded that in impulsive inelastic collisions in the non-fonvard region, as is the case in our experinient,mJ will show a preserving propensity if the quantization axis is chosen along the geometric apse, Gi, = (k, - ii)-_ If this is true we expect to find a preferential orientation of J parallel with the geometric apse in the case of a negative AJ transition and perpendicular to this apse for a positive AJ transition. The geometric
apse
is shown in the Newton diagram (fig. 2). It makes an angle of = + 12” with the normal to the velocity_ This angle a is in good agreement with the shift found in the curve in fig. 3 and indeed sZ is the symmetry axis of the J distribution.
[l] J.J.M. Beenakker and T.R. McCourt, Ann. Rev. Phys. Cbem. 21 (1970) 47_ 131 R.AJ_ Keijser, KD_ van den Hour. 31. de Groat and H-F-P. Knaap, Physica 75 (19740 515. 13) H. Kate, S.R. Jeles. AJ. McCaffen and M.D. Ro~c. Chem. Phys. Letters 39 (1976) 573. [4] U. Borkenhagen. J. hlalthan and J-P. Toennies, J. Chem. Phw. 74 (1979) 1732. 151 L.-Zsndee, J. Verberne and J. Reuss. Chem. Phys. 16 (1977) I: H. Thuis. S. Stolte and J. Reuss, Chem. Phys. 43 (1979) 351.
161 i\.G.Visser,
J.P. lkkooy,
LXvander
B1eij.C. de Vreugd
and J. Korvinz. Chem. Phys. 20 (1977) 391. I71 I;. Bergmann, U. Hefter and J. Witt, J_ Chem. (1960)
Phys. 72
4777.
and D-1;. Hoffman. 1. Chsm. Phys. 74 (1981) 2275. r91 V. Share, D.J. Kouri and D.K. Hoffman, J. Chem. Ph)-s. 76 (1982) 4493.
IS1
V. Share, D-l. Kouri
EXPERIMENTAL
IN INELASTIC
DETERhlIiVATION
SCATTERING
OF N+
PHYSICS
20 May 19s3
LETTERS
OF THE nzJ DISTRIBUTION BY He
i‘he orirnt.triorxA distrlburxm of h’a2 molrcule~ ScJIterCd by He has been determined in a molecular beam experiment. At large andc vxttcriw -_. \\hcre inelastic collisions are dominant. 3 high degree of alignment hss been observed. This alignment diepcnds \trcrngI\ on the rotational qu;lntum numberl after wzatterinp. TheJdependence can be explained by assummg thAt during collisions IJIJ iz consrrved uhen the quntiution x\is ic chosen parallel with the geometric apse.
rotational quantum numbers. We will report here on a beam experiment in which the spatial distribution of J can bc drtrnnincd for larger scattering angles and for relatively high rotational states. a situation which applies to most gsses. So far experimental results have been obtained for Naz backward scattering by He. Both orientation and magnitude of the alignment have been determined. To our knowledge this is the firsr observation of alignment produced in large-angle scattering.
3. Experimental
method
In this esperirnent the method of Visser [6] to determine alignment in a molecular bran1 is used. The configuration of sources. fields. laser beam and detection is shown in fig_ l_ The beml sources together with magnetic field B,,, cm be rotated to allow the study of alignment at different scattering angles. We keep the detection chamber fixed in order to prevent difficulties with alignment of the optics and to be able to reduce the background light, which mainly originates from scattering of the laser beam by optical elemenrs and windows. Na-, is chosen as molecule for studying angular momentum polarization because it is one of the few molecules that have a suitable transition in the part of the spectrum that can be easily reached with a tunable dye laser. Helium is the
0 009-X
14/S3/0000-0000/S
03.00
0 1983 North-Holland
Volume 97. number 3
CHEMICAL
20 hlay 1983
PHYSICS LETTERS
letter we will present the results of experiments with
molecules that are scattered over this maximum scat-
Fii. 1. The experimental apparatus. Both supersonic beam sources can be rotated together with Baus to allow analysis of different scattering angles. The analyzing magnetic field Ban is perpendicular to the plane of drawing. The molecules are excited by polarized laser-light propagating perpendicular to the collisionplane and with the electric vector & parallel with the molecular velocity_ The fluorescence ls detected by a photomultiplier.
chosen scattering partner because of the small maximum scattering angIe in the laboratory frame of reference as can be seen in the Newton diagram (fig. 2). This results in a high intensity of scattered molecules in the detector at the expense of the angular resolution. The maximum scattering angle in the laboratory frame is, for these specific circumstances, 14”. In this
tering angle. We have chosen this particular angle because at other angles, as can be seen in the Newton diagram, two groups of molecules with different velocities and different centre-ofmass scattering angles contribute to the flux of scattered particles_ The diagram shown in fig_ 2 is the Newton diagram for elastic scattering. For inelastic collisions dtab associated with a certain 0, is slightly different, but even for large AJ transitions this change in 9rti is of the same order of magnitude as our angular resolution_ The molecules are excited by a dye laser tuned to the transitions of the A r 3: u’ = 9, J’ + X 1 Zz Y” = 0. J” vibration rotation band. In order to measure the alignment of the scattered molecules we make use of the fact that the probability for excitation depends on the angle between the transition moment,p, and the electric vector, E, of the polarized laser beam. Since p is directly coupled with J. in fact p is perpendicular to J. the fluorescence intensity depends on the distribution of with respect to c:. As a first approximation we will describe the distribution ofJwith an ellipsoidal distribution niJ
N(J) = 1+ a,P,(J _ -
- i) ,
(III
where ii is the symmetry axis of the distribution_ A negative a-, results in a discus-like shape and a positive CI~in a s&-like shape with the preferential orlentat&t of J perpendicular and parallel with respect to 17 respectively_ Because of the plane symmetry exhibited by our experimental configuration ri is located in the scattering plane, defined by the beam sources and the point of detection_ The degree of alignment in the molecular beam can be measured by passing the molecules through a magnetic field (B, in fig. I). In this field the molecules will precess through an angle &, &
Es_ 2. Newtondiagram for elastic collisions of Naa and He_ The measurements have been performed at the scattereg ygje shown in the drawing. The geometric apse 4 = (kf ki) is shown;cg makes an angle = with the normal on the fmal Naz velocity (~f,~azl.
=
kJ!@/ZI)L/u
7
(3
where L/v is the flight time through the magnetic fdd_ Thus the angle between the preferential orientation of the molecules and & will be changed, leading to a subsequent change in fluorescence intensity_ If we take Q to be the angle between ii and &, the relative change in fluorescence intensity in our apparatus can be written, in first approximation, according to Visser [6] as 343
V0ltmc
97. number 3
[l(B) - f(O)]/I(O)
= $olsin&(sin&
CHEMICAL
PHYSICS
cos 29
+ ~0s~~ sin 2Q) _
(3)
It ml he seen from this formula that ~72and Q cannot be drrrrmined independently in this esperimental zippx.nus: the sign of oz is not determined and Q is determined modulo n/2. This is equivalent to the fact that the direction of G isonly determinedmodulo IT/?. The direction of thr preferential orientation ofJ howvewr is determined uniqurly. Such a result is not surprising JS one actually measures the relative distributton oiJ
in a plam perpendicular to B,. The situatherefore be clxified by performing also mcasnrenlcnts with the field B, turned over 90” into the p1.1~ of scattering to position Bk (see insert in fig. I ). Together with the results with the field in posltiou B,. both sign and magnitude of a2 as well as 1111:dIrectinn ofll can then be determined unambigu 011sl!‘. tion
cm
3. Results Xs .u~ cxtiiiplc we 5how the result for theJ = 28 lrvei (fig . 3 1. At 0” (no scattering) we se0 the small .111pruw11r (nortlc alignmtml) found previously by
LETTERS
20 May 1983
Visser [6]. At 14” a very large effect is found. The results are not symmetric in the magnetic field but show a small shift towards negative magnetic field. From this shift we determine that the preferential orientation ofJmakes a small angle with e [eq_ (3)]_ This angle is 12 2 2” and therefore 4 is 12” (modulo n/2). To determine the exact value of Q we have turned B, over 90°, to position BA. In this configuration the effect is very small and this means that u^is nearly parallel with B& and therefore Q = 102 2 +’ _ _ The difference in amplitude observed in fig. 3 beteween the effect with positive and negative field is caused by averaging over molecules with different
velocities since the precession angle depends on the molecular velocity [eq. (II)] _ The maximum of the effect shown in fig_ 3 is studied as a function of the value of J after scattering. The result is shown in fig. 4. Note the change of sign at J = 10. There is no influence of the small alignment which already e_xists in the molecular beam before scattering. This is verified by passing the primary beam before scattering through magnetic field B,,. In this way the nozzle-alignment is rotated out of the scattering plane. This rotation has no detectable in-
fluence on the results in fig. 4.
; 01
f
IL i
f
1
I=) IIO)
“_,
00 I
.._._ _..
r!_.. .__ ._..___ __ ____
i 3
. -\%
I ig 3 K~l~tr~2 chm~r to lluorescencr intensity as 9 function ~ri the m+mrttc field z:ratpth. 5. For excitntion the X ’ 5: Y’ = Y -3’ -- .\ ’ x; I.” = 0.J” tratsitiatt is used. The data for 13” sc_tttaxin~ m&c .tre rsprewtted by =. The drawn tune is the eiiwt 111~1could be e\pcctrd if the preferenti.tl orientation c*il ~sre p.trztllel\\ iflt the tnolwul.tr wlocify. For :! cotnpariwn tits data for 0’ tno sc.tttrrinp) ~irr also &own. X _ Here xce wz 111r ~~11 nozzle-induced .tltgttttatt in rbe Na2 bean.
f
f
t -07111,.1,1,,,,,,,,,,,I,,,..,,,,,1 0 Fig. 4. J-dependence Intensity.
3
10
of the ntsGtnutn
20
30
change in fluorexence
Volume 97, number 3
20 hlay 19s3
CHEMICAL PHYSICS LETTERS
4. Discussion
Acknowledgement
The measurements of Bergmann [7] show that the Na, -He system is dominated by inelastic collisions at angles greater than 4O in the laboratory system. At a rotational temperature of 50 K in the beam the level with the highest occupation isJ= lo-Hence statistically the molecules which are in J = 4 after collision have come from higher J levels, while the molecules in J = 28 have come from lower J levels_ From this result we can conclude that positive AJ transitions give a positive effect and that negative AJ transitions give a
We are indebted to Professor J .J &I_ Beenakker for his stimulating interest in this work_ This work is part of the research program of the Stichting voor Fundamenteel Ondelzoek der Materie (Foundation for Fundamental Research on Matter) and was made possible by financial support from the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (Netherlands Organization for the Advancement of Pure Research).
negative effect. This is equivalent with the statement that positive AJ transitions produce a preferential of J in the direction of the molecular velocity and that negative AJ transitions produce
References
orientation
a preferential orientation perpendicular to the molecular velocity _ This conclusion is in agreement with recent theoretical work of Khare et al. [S.9] who concluded that in impulsive inelastic collisions in the non-fonvard region, as is the case in our experinient,mJ will show a preserving propensity if the quantization axis is chosen along the geometric apse, Gi, = (k, - ii)-_ If this is true we expect to find a preferential orientation of J parallel with the geometric apse in the case of a negative AJ transition and perpendicular to this apse for a positive AJ transition. The geometric
apse
is shown in the Newton diagram (fig. 2). It makes an angle of = + 12” with the normal to the velocity_ This angle a is in good agreement with the shift found in the curve in fig. 3 and indeed sZ is the symmetry axis of the J distribution.
[l] J.J.M. Beenakker and T.R. McCourt, Ann. Rev. Phys. Cbem. 21 (1970) 47_ 131 R.AJ_ Keijser, KD_ van den Hour. 31. de Groat and H-F-P. Knaap, Physica 75 (19740 515. 13) H. Kate, S.R. Jeles. AJ. McCaffen and M.D. Ro~c. Chem. Phys. Letters 39 (1976) 573. [4] U. Borkenhagen. J. hlalthan and J-P. Toennies, J. Chem. Phw. 74 (1979) 1732. 151 L.-Zsndee, J. Verberne and J. Reuss. Chem. Phys. 16 (1977) I: H. Thuis. S. Stolte and J. Reuss, Chem. Phys. 43 (1979) 351.
161 i\.G.Visser,
J.P. lkkooy,
LXvander
B1eij.C. de Vreugd
and J. Korvinz. Chem. Phys. 20 (1977) 391. I71 I;. Bergmann, U. Hefter and J. Witt, J_ Chem. (1960)
Phys. 72
4777.
and D-1;. Hoffman. 1. Chsm. Phys. 74 (1981) 2275. r91 V. Share, D.J. Kouri and D.K. Hoffman, J. Chem. Ph)-s. 76 (1982) 4493.
IS1
V. Share, D-l. Kouri