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Non-spherical potentials and molecular scattering at thermal energies. Nitrogen and the noble gases
volume 10, nilmba 1
CHEhnCALPHYSICSLETTERS
1 Jllly-IS171
NON-S~HERICAL POTENTIALS AND MOLECULAR SCATTERING AT THERMAL ENERGIES. NITROGEN AND THE NOBLE GASES *
M. CAVALUNl
**, M.G. DONDI, G. SCOLES and U. VALBUSA istituto di S&me FL&he delWiiiversi?~. 16132 Geneva, Ita@
Received7 June 1971
High resolution differential collision cross sxtion measurements far the systems F$z-Ar, NP-Kr and Nz -N2 are presented and compared with equal resolution Ar-Ax data. Tke quenching of the amplitude of the rainbow oscilb tion in the cross section is consistent with theoretical predictkns.
Recently a great deal of attention has been given to eidatic scattering experiments with n&-alkali systems in order to obtain unambiguous information on intermolecular potentials [l-7 ] . The first rainbow peak has been resolved for the Ar--Nz system by Bickes and Bernstein [i) . Its energy dependence was then measured by Kales and Grosser [2]. Later, high resolution data for spherical identical or non-identical partners were obtained at the Universities of Chicago [4,5] and Geneva [3,7]. Recently Anlauf et al. [6] obtained improved data on the systemAr-N2 showingevidence of the quenching effect of the potential anisotropy on the rainbow structure. in the present paper we present the results of high resolution Nz-Ar, Nz-Kr and Nz-N, differential collision cross section measurements and compare them with similar resoluticn Ar-A.r data in order to
show the influence of ths potential anisotropy. A theory on this subject has been presented by Cross [8]. The apparatus, which has been briefly described [7] previously and whose modifications are reported in ref. 131, is a crossed beam scattering machine with a supersonic primary beam, a liquid N, cooled multicha&el
l
Work a;pported by the Italian Nnticnsl Rezarch Council tbroq& the GmppoNazkmak di Strutha della Mat&a.
l + Pmcnt
-bddlcss: Labimtorio Ricerchc di Baoe, SNAM
Progetti, Montuotondo, Roma, Italy.
22.
vertical secondary beam and an out-of-plane rotatable, fiquid He cooled, Ge bolometer detector 191. Results for the Ar-N, and N+r systems are reported in fig. la. The velocities in the lab system are such as to give tile same relative:energy (630°K). Excellent agree-
ment between the two cross sections is apparent and shows the Hod internal consistency of the data. For comparison we report also the Ar-Ar cross section (E = 750%) which shows the rainbow at about the same position. A quenching of about 50% in the rainbow amplitude is found for the asymmetrical systems in qualitative agreement with Cross’s predictions [8]. In fig. lb results for the N,-Kr system arc compared with Ar-Ar data obtained at about thl: same relative energy. This comparison is particularly significant since
tic reduced masses, and hence the wave numbers at the same energy, are, within IO%, the same. The relative quenching of the rainbow amplitude is almost
quantitatively the same as in the Nz-Ar system. It is useful to notice, at this point, that energy resolution is comparable in all measured systems
@E/E = 20% fwhm) while angular resolution due to
ec.m.+ elab transformation increases in the sequence Ar-N2, Ar-Ar, N2-Ar, N2-Kr (A8,b = lo fwhm in aU cases). In order to show the rainbow amplitude quenching
due to finite apparatus resolution we report in fig. 2a. the Ar-As differential collision cross section along
Volume 10, nlmlhcr 1
1 July 1971
Qs-uM.icAL PHYSICS IEiTERs
r;-
c
2
Fig.
4
5
8
10
1. Differential collision
PO
9e.m.
30
.
-
-
.
.
2
4
6
6
10
cross section data for various
spherical and non-qherical Systems. (a) b AI-&, 0 NyAr,
E = 750%. E/e = k =.5.3. E = 630?, k=5.1. l Ar-N2, & = 630 K, k = 5.1. (b) 0 Ar-Ar, E = 750% k = 5.3. 9 N2-Kr, E= 780%, k = 5.1.
(a) D -
0
with values calculated from a potential recently pm posed by Parson and Lee [IO] with and withmt the averaging procedure consistent with the given relative velocity dispersion and f-tite angular resolution of the detector. As can be verified in fig. 1, the rainbow maximum is, for N2 -AI and N2 -K.r with respect to Ar-Ar, shifted about 4.5% to wider angles. Keeping in mind that to a fmt approximation the
6c.m.
30
Fig. 2. Ar-Aa experiment, E = 750%. (same energy) calculated from Parson and Lee potential [ml) no aueregiag. - As-Ar (same energy, same potentfal) fully everaged Ar-AI
rir
03’
20
- data, E = 65S°K. data, E = S&L
N2-N2
rainbow shifts are inversely proportional to relative energy, with the rather arbitrary assumption that the rainbow position knot ~fected by the anisotropy, and assuming for the weff depth E of Ar-Ar the value of 141”K\[lo,1 If, we-obtain %+Ar
= 124%.
and
%Z_Kr = 152%
23
imne10, numbex 1
CIiEhIlCAL PHYSICS LEI-IERS
Y .:.
1 JuIy 1971
‘___’
= 197S’K [12] gd we assume take *,-KC the combination rule Ex_Y =.(exe,,) to be valid, we obtain if ~8
%4*-N* =
(EN - “6, )2= e;r
iOg°K I
which is quite near the value calculated in the equivalent way:
It is a pleasure to acknowlkiige the cooperation of Dr. Lucia Meneghetti in the early stage of the experi. ment and Mr. Giovanni Badinella in the final measurements. We thank JM. Parson and Y.T. Lee for communicating to us their results before publication. For the same reason we are indebted to KG. Anlauf, RW. Bickes and R.B. Bernstein.
References Both values bracket the number obtained by direct comparison of N2-N2 scattering data with Ar-Ar data Of fig. 2b which gives eNz _Nz = 114OK. z& eXpetted, the rainbow maximum is severely quenched iIlt.hiSCaSe. The agreement is closer than it appears since there ‘are two reasons to believe that for eKr_Kr the value of 197.5 is an underestimate. The first is that assum? mg eAr- Ar = 141°K [lo,1 11, ~ZA~_K~= 172% [5] and E.+~ = (E~E,)~ we obtain eKr_Kr = 21O’K. The second is that the VahIe of eKr_Kr higher than 197.5 “K is suggested by Kr-Kr differential collision cross sections recently measured in our laboratory [ 131. The vahre of 124°K obtained for e&_Ar is in agreement with the vaiue of 120 * 4 obtained in ref. [6]. This is not surprising since the Lennard-Jones (20,6) potential adopted for the analysis in ref. [6J, although not especially realistic, leads to a good estimate for the parameter E [3].
[ l] R-W_Bickes and R.B. Bernstein, Chem. Phys. Letters 4 (1969) 111. [2] F.Kalos and A.E. Grosser, Chem. Phys. Letters 6 (1970) 537. 13) M. CavaUni, G. GaL&uo, L. Menegbetti, G. S&es and U. VaItusa, Chem. Phys Letters 7 (1970) 303. 14) J.hiM. Parson, T.P. Schafer, P.E. Siska, F-9. TuBy, Y.C. Wang and Y.T. Lee, I. Chem. Phys. 53 (1970) 2123. (5 ] JM. Parson, T.P. Schafer, P.E. Siska, F.P. Tully, Y.C. Wangand Y.T. Lee, J. Chem. Phys 53 (1970) 3755. [6] KG. AnIauf, R.W. Bickes Jr. and R.B. Bernstein, J. Chem. Phys. 54 (1971) 3647. [?j M. CavalI& L. MeneghettI, G. Stoles and M. YeaBand, Phys. Rev. Letters 24 (1970) 1469. [S] R.J. Cxoss Jr., J. Chem. Phys. 52 (1970) 5703. (91 M. CavaUini,G. Gallinaro and G. Stoles, 2. Natuforsch. 22a (1967) 413. {IO] J.&I.Parson and Y.T. Lee, private communication [ 111 V.M. Bobetic and JA. Barker, Pbys. Rev. B2 (1970) 4169. [ 121 V.M. Bobetic, Thesis, University of Waterloo (1971). [ 13 ] M. CavalIini. MC. Dondi, G. Stoles and U. VaIbusa, submitted to the III Intern. Symp. on Molecular Beams, Cannes (1971).
CHEhnCALPHYSICSLETTERS
1 Jllly-IS171
NON-S~HERICAL POTENTIALS AND MOLECULAR SCATTERING AT THERMAL ENERGIES. NITROGEN AND THE NOBLE GASES *
M. CAVALUNl
**, M.G. DONDI, G. SCOLES and U. VALBUSA istituto di S&me FL&he delWiiiversi?~. 16132 Geneva, Ita@
Received7 June 1971
High resolution differential collision cross sxtion measurements far the systems F$z-Ar, NP-Kr and Nz -N2 are presented and compared with equal resolution Ar-Ax data. Tke quenching of the amplitude of the rainbow oscilb tion in the cross section is consistent with theoretical predictkns.
Recently a great deal of attention has been given to eidatic scattering experiments with n&-alkali systems in order to obtain unambiguous information on intermolecular potentials [l-7 ] . The first rainbow peak has been resolved for the Ar--Nz system by Bickes and Bernstein [i) . Its energy dependence was then measured by Kales and Grosser [2]. Later, high resolution data for spherical identical or non-identical partners were obtained at the Universities of Chicago [4,5] and Geneva [3,7]. Recently Anlauf et al. [6] obtained improved data on the systemAr-N2 showingevidence of the quenching effect of the potential anisotropy on the rainbow structure. in the present paper we present the results of high resolution Nz-Ar, Nz-Kr and Nz-N, differential collision cross section measurements and compare them with similar resoluticn Ar-A.r data in order to
show the influence of ths potential anisotropy. A theory on this subject has been presented by Cross [8]. The apparatus, which has been briefly described [7] previously and whose modifications are reported in ref. 131, is a crossed beam scattering machine with a supersonic primary beam, a liquid N, cooled multicha&el
l
Work a;pported by the Italian Nnticnsl Rezarch Council tbroq& the GmppoNazkmak di Strutha della Mat&a.
l + Pmcnt
-bddlcss: Labimtorio Ricerchc di Baoe, SNAM
Progetti, Montuotondo, Roma, Italy.
22.
vertical secondary beam and an out-of-plane rotatable, fiquid He cooled, Ge bolometer detector 191. Results for the Ar-N, and N+r systems are reported in fig. la. The velocities in the lab system are such as to give tile same relative:energy (630°K). Excellent agree-
ment between the two cross sections is apparent and shows the Hod internal consistency of the data. For comparison we report also the Ar-Ar cross section (E = 750%) which shows the rainbow at about the same position. A quenching of about 50% in the rainbow amplitude is found for the asymmetrical systems in qualitative agreement with Cross’s predictions [8]. In fig. lb results for the N,-Kr system arc compared with Ar-Ar data obtained at about thl: same relative energy. This comparison is particularly significant since
tic reduced masses, and hence the wave numbers at the same energy, are, within IO%, the same. The relative quenching of the rainbow amplitude is almost
quantitatively the same as in the Nz-Ar system. It is useful to notice, at this point, that energy resolution is comparable in all measured systems
@E/E = 20% fwhm) while angular resolution due to
ec.m.+ elab transformation increases in the sequence Ar-N2, Ar-Ar, N2-Ar, N2-Kr (A8,b = lo fwhm in aU cases). In order to show the rainbow amplitude quenching
due to finite apparatus resolution we report in fig. 2a. the Ar-As differential collision cross section along
Volume 10, nlmlhcr 1
1 July 1971
Qs-uM.icAL PHYSICS IEiTERs
r;-
c
2
Fig.
4
5
8
10
1. Differential collision
PO
9e.m.
30
.
-
-
.
.
2
4
6
6
10
cross section data for various
spherical and non-qherical Systems. (a) b AI-&, 0 NyAr,
E = 750%. E/e = k =.5.3. E = 630?, k=5.1. l Ar-N2, & = 630 K, k = 5.1. (b) 0 Ar-Ar, E = 750% k = 5.3. 9 N2-Kr, E= 780%, k = 5.1.
(a) D -
0
with values calculated from a potential recently pm posed by Parson and Lee [IO] with and withmt the averaging procedure consistent with the given relative velocity dispersion and f-tite angular resolution of the detector. As can be verified in fig. 1, the rainbow maximum is, for N2 -AI and N2 -K.r with respect to Ar-Ar, shifted about 4.5% to wider angles. Keeping in mind that to a fmt approximation the
6c.m.
30
Fig. 2. Ar-Aa experiment, E = 750%. (same energy) calculated from Parson and Lee potential [ml) no aueregiag. - As-Ar (same energy, same potentfal) fully everaged Ar-AI
rir
03’
20
- data, E = 65S°K. data, E = S&L
N2-N2
rainbow shifts are inversely proportional to relative energy, with the rather arbitrary assumption that the rainbow position knot ~fected by the anisotropy, and assuming for the weff depth E of Ar-Ar the value of 141”K\[lo,1 If, we-obtain %+Ar
= 124%.
and
%Z_Kr = 152%
23
imne10, numbex 1
CIiEhIlCAL PHYSICS LEI-IERS
Y .:.
1 JuIy 1971
‘___’
= 197S’K [12] gd we assume take *,-KC the combination rule Ex_Y =.(exe,,) to be valid, we obtain if ~8
%4*-N* =
(EN - “6, )2= e;r
iOg°K I
which is quite near the value calculated in the equivalent way:
It is a pleasure to acknowlkiige the cooperation of Dr. Lucia Meneghetti in the early stage of the experi. ment and Mr. Giovanni Badinella in the final measurements. We thank JM. Parson and Y.T. Lee for communicating to us their results before publication. For the same reason we are indebted to KG. Anlauf, RW. Bickes and R.B. Bernstein.
References Both values bracket the number obtained by direct comparison of N2-N2 scattering data with Ar-Ar data Of fig. 2b which gives eNz _Nz = 114OK. z& eXpetted, the rainbow maximum is severely quenched iIlt.hiSCaSe. The agreement is closer than it appears since there ‘are two reasons to believe that for eKr_Kr the value of 197.5 is an underestimate. The first is that assum? mg eAr- Ar = 141°K [lo,1 11, ~ZA~_K~= 172% [5] and E.+~ = (E~E,)~ we obtain eKr_Kr = 21O’K. The second is that the VahIe of eKr_Kr higher than 197.5 “K is suggested by Kr-Kr differential collision cross sections recently measured in our laboratory [ 131. The vahre of 124°K obtained for e&_Ar is in agreement with the vaiue of 120 * 4 obtained in ref. [6]. This is not surprising since the Lennard-Jones (20,6) potential adopted for the analysis in ref. [6J, although not especially realistic, leads to a good estimate for the parameter E [3].
[ l] R-W_Bickes and R.B. Bernstein, Chem. Phys. Letters 4 (1969) 111. [2] F.Kalos and A.E. Grosser, Chem. Phys. Letters 6 (1970) 537. 13) M. CavaUni, G. GaL&uo, L. Menegbetti, G. S&es and U. VaItusa, Chem. Phys Letters 7 (1970) 303. 14) J.hiM. Parson, T.P. Schafer, P.E. Siska, F-9. TuBy, Y.C. Wang and Y.T. Lee, I. Chem. Phys. 53 (1970) 2123. (5 ] JM. Parson, T.P. Schafer, P.E. Siska, F.P. Tully, Y.C. Wangand Y.T. Lee, J. Chem. Phys 53 (1970) 3755. [6] KG. AnIauf, R.W. Bickes Jr. and R.B. Bernstein, J. Chem. Phys. 54 (1971) 3647. [?j M. CavalI& L. MeneghettI, G. Stoles and M. YeaBand, Phys. Rev. Letters 24 (1970) 1469. [S] R.J. Cxoss Jr., J. Chem. Phys. 52 (1970) 5703. (91 M. CavaUini,G. Gallinaro and G. Stoles, 2. Natuforsch. 22a (1967) 413. {IO] J.&I.Parson and Y.T. Lee, private communication [ 111 V.M. Bobetic and JA. Barker, Pbys. Rev. B2 (1970) 4169. [ 121 V.M. Bobetic, Thesis, University of Waterloo (1971). [ 13 ] M. CavalIini. MC. Dondi, G. Stoles and U. VaIbusa, submitted to the III Intern. Symp. on Molecular Beams, Cannes (1971).