The velocity dependence of the integral cross sections for the scattering of H atoms and normal‐H2 molecules from the rare gases has been measured for primary beam velocities from 300 m/sec (Ec.m.=0.5 meV) to about 3000 m/sec (Ec.m.=100 meV). Three distinct resonance maxima were observed in each of the systems H–Xe, H–Kr, H2–Kr, and H2–Ar. At least one resonance maximum was found in H2–Xe and H–Ar, while H–Ne showed no maxima. The H2–Ar cross sections were also measured with a cold beam of pure para‐H2 consisting entirely of spherically symmetric j=0 molecules. No noticeable difference was found when compared to the n‐H2 cross sections indicating that the observed resonances depend only on the spherical symmetric potential. Extensive comparisons with spherical symmetric model potentials showed that all the observed resonances are due to temporary capture in the well of the effective potential. This phenomenon is usually referred to as ’’orbiting.’’ The energetic location of the observed orbiting resonances and glory maxima were found to be very sensitive to the potential shapes and parameters. Only models which included at least two terms in the long range dispersion potential C6/R6 and C8/C8 could describe the data in a satisfactory way. For H–Ar the data are in very good agreement with the experimental potential of Bassi etal. and in reasonable agreement with the abinitio MCSF potential of Wagner etal. For H2–Ar, –Kr, –Xe good agreement is found with the potentials recently determined from infrared spectra by Le Roy and co‐workers. For all the other systems new best fit potentials have been determined. The best fit values of ε and Rm are for H–Ne: 1.90 meV and 3.15 Å; H–Ar: 4.16 meV and 3.62 Å; H–Kr: 5.90 meV and 3.57 Å; H–Xe: 7.08 meV and 3.82 Å; H2–Ar: 6.30 meV and 3.57 Å; H2–Kr: 7.19 meV and 3.72 Å, and H2–Xe: 8.10 meV and 3.92 Å.

1.
L. Boltzmann, Vorlesung über Gastheorie, Vol. II (J. A. Barth, Leipzig, 1898), p. 186.
2.
K. F.
Herzfeld
,
Z. Phys.
8
,
132
(
1922
).
3.
W.
Steiner
,
Z. Phys. Chem. B
15
,
249
(
1932
).
4.
R. C. Tolman, Statistical Mechanics with Applications to Physics and Chemistry (Oxford University, London, 1927), p. 245–297.
5.
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).
6.
K. W.
Ford
,
D. L.
Hill
,
M.
Wakano
, and
J. A.
Wheeler
,
Ann. Phys.
7
,
239
(
1959
).
See also
B. C.
Eu
and
J.
Ross
,
J. Chem. Phys.
44
,
2467
(
1966
).
7.
D. L.
Bunker
,
J. Chem. Phys.
32
,
1001
(
1960
).
8.
R. E.
Roberts
,
B. B.
Bernstein
, and
C. F.
Curtiss
,
J. Chem. Phys.
50
,
5163
(
1969
);
P. A.
Whitlock
,
J. T.
Muckerman
, and
R. E.
Roberts
,
J. Chem. Phys.
60
,
3658
(
1974
).
9.
See for example
R. T.
Pack
,
R. L.
Snow
, and
W. D.
Smith
,
J. Chem. Phys.
56
,
926
(
1972
).
10.
M.
von Seggern
and
J. P.
Toennies
,
Z. Phys.
218
,
341
(
1969
).
11.
V. H.
Shui
and
J. P.
Appleton
,
J. Chem. Phys.
55
,
3126
(
1971
).
12.
(a)
D. W.
Trainor
,
D. O.
Ham
,
F.
Kaufman
,
J. Chem. Phys.
58
,
4599
(
1973
);
(b)
D. N.
Mitchell
and
D. J.
LeRoy
,
J. Chem. Phys.
67
,
1042
(
1977
).,
J. Chem. Phys.
13.
D. E.
Stogryn
and
J. O.
Hirschfelder
,
J. Chem. Phys.
31
,
1531
(
1958
);
D. E.
Stogryn
and
J. O.
Hirschfelder
,
31
,
1545
(
1959
).,
J. Chem. Phys.
14.
(a)
W.
Erlewein
,
M.
von Seggern
, and
J. P.
Toennies
,
Z. Phys.
211
,
35
(
1968
);
(b)
L.
Monchik
,
S.
Green
,
J. Chem. Phys.
63
,
2000
(
1975
);
(c) J. Schaefer, private communication.
15.
G. Herzberg, Molecular Spectra and Molecular Structure, I. Spectra of Diatomic Molecules (Van Nostrand Reinhold, New York, 1950).
16.
(a)
A. R. W.
McKellar
and
H. L.
Welsh
,
J. Chem. Phys.
55
,
595
(
1971
);
(b)
A. R. W.
McKellar
and
H. L.
Welsh
,
Can. J. Phys.
50
,
1458
(
1972
);
(c)
A. R. W.
McKellar
and
H. L.
Welsh
,
Can. J. Phys.
52
,
1082
(
1974
);
(d)
R. J.
Le Roy
and
J.
van Kranen‐donk
,
J. Chem. Phys.
61
,
4750
(
1974
).
17.
For reviews see (a) R. J. Le Roy in Specialist Periodical Reports on Molecular Spectroscopy, Vol. 1 (The Chemical Society, Burlington House, London, 1973), p. 113,
(b) M. S. Child in Specialist Periodical Reports on Molecular Spectroscopy, Vol. 2 (The Chemical Society, Burlington House, London, 1974), p. 466.
18.
(a)
R. B.
Bernstein
,
Phys. Rev. Lett.
16
,
385
(
1966
);
(b)
O.
Goscinski
and
O.
Tapia
,
Mol. Phys.
24
,
641
(
1972
);
(c)
L.
Gottdiener
and
J. N.
Murrell
,
Mol. Phys.
25
,
1041
(
1975
).,
Mol. Phys.
19.
Orbiting or complex formation with and without chemical reactions has been detected in a large number of atom‐molecule collision partners by the observation of angular distributions with large backward peaks. However no serious attempts were made to study these distributions as a function of energy, See, for example: (a)
W. B.
Miller
,
S. A.
Safron
, and
D. R.
Herschbach
,
Discuss. Faraday Soc.
44
,
108
(
1967
);
(b)
D. O.
Ham
and
J. L.
Kinsey
,
J. Chem. Phys.
53
,
285
(
1970
);
(c)
D.
Beck
and
H.
Förster
,
Z. Phys.
240
,
136
(
1970
);
(d)
J. M.
Parson
and
Y. T.
Lee
,
J. Chem. Phys.
56
,
4658
(
1972
).
20.
The ionic fragments of predissociating orbiting states of molecular ions such as HeH+ have also been recently observed. See, for example:
J.
Schopman
and
J.
Los
,
Physica
48
,
190
(
1970
);
J.
Schopman
,
P. G.
Fournier
, and
J.
Los
,
Physica
63
,
518
(
1973
).,
Physica (Amsterdam)
21.
See, for example: W. C. Stwalley, A. Niehaus, and D. R. Herschbach, Abstracts of Papers of the VIth. International Conference on the Physics of Electronic and Atomic Collisions (Nauka Press, Leningrad, 1967), p. 639;
F. G.
Collins
and
F. C.
Hurlbut
,
J. Chem. Phys.
56
,
2609
(
1972
).
22.
(a)
W. C.
Stwalley
,
A.
Niehaus
, and
D. R.
Herschbach
,
J. Chem. Phys.
63
,
3081
(
1975
);
(b)
A.
Schulte
,
D.
Bassi
,
F.
Tommasini
, and
G.
Scoles
,
J. Chem. Phys.
62
,
600
(
1975
); ,
J. Chem. Phys.
(c)
K. A.
Köhler
,
R.
Feltgen
, and
H.
Pauly
,
Phys. Rev. A
15
,
1407
(
1977
).
23.
W. C.
Stwalley
,
J. Chem. Phys.
63
,
3062
(
1975
).
24.
Preliminary reports on these measurements are (a) H;Xe:
J. P.
Toennies
,
W.
Welz
and
G.
Wolf
,
J. Chem. Phys.
61
,
2461
(
1974
);
(b) H‐Ar, Kr, Xe: J. P. Toennies, W. Welz, and G. Wolf, Abstracts of Papers of the IXth International Conference on the Phvsics of Electronic and Atomic Collisions, edited by J. S. Risley and R. Geballe (University of Washington, Seattle, 1975), p. 1007;
(c) H2Ar, Kr, Xe:
J. P.
Toennies
,
W.
Welz
, and
G.
Wolf
,
J. Chem. Phys.
64
,
5305
(
1976
);
(d) HCF4,SF6:
R.
Grover
,
J. P.
Toennies
,
W.
Welz
, and
G.
Wolf
,
Chem. Phys. Lett.
48
,
24
(
1977
).
25.
R. S.
Grace
,
D. L.
Johnson
, and
J. G.
Skofronick
,
J. Chem. Phys.
67
,
2443
(
1977
).
26.
(a)
F. T.
Smith
,
Phys. Rev.
118
,
349
(
1960
);
Erratum:
F. T.
Smith
,
Phys. Rev.
119
,
2098
(
1960
);
(b)
R. J.
Le Roy
and
R. B.
Bernstein
,
J. Chem. Phys.
54
,
5114
(
1971
).
27.
(a)
J. N. L.
Connor
,
Mol. Phys.
15
,
621
(
1968
);
J. N. L.
Connor
,
16
,
525
(
1969
); ,
Mol. Phys.
J. N. L.
Connor
,
23
,
717
(
1972
); ,
Mol. Phys.
(b)
R. R.
Herm
,
J. Chem. Phys.
47
,
4290
(
1967
);
(c) R. J. LeRoy and W.‐K. Lin, J. Chem. Phys. (to be published).
28.
W. C. Stwalley, Abstracts of the VIII International Conference on the Physics of Electronic and Atomic Collisions, Vol. 1, Belgrade, 1973, p. 40.
29.
At 2000 m/sec the correction amounts to ≲1.5% of σ0, see page 287ff of H. Pauly and J. P. Toennies in Methods of Experimental Physics, Vol. 7A (Academic, New York, 1968), pp. 227–360.
30.
See p. 283ff of Ref. 29.
31.
G.
Clausnitzer
,
W.
Dürr
,
R.
Fleischmann
,
G.
Graw
,
W.
Hammon
,
G.
Hartmann
,
W.
Kretschmer
,
H.
Nahr
,
A.
Neufert
,
E.
Salzborn
,
H.
Wilsch
, and
J.
Witte
,
Nucl. Instrum. Methods
80
,
245
(
1970
).
32.
H.
Wilsch
,
J. Chem. Phys.
56
,
1412
(
1974
).
33.
Similar discharge sources for H atoms have been described by: (a)
R. T.
Brackmann
and
W. L.
Fite
,
J. Chem. Phys.
34
,
1572
(
1961
);
(b)
G. O.
Brink
,
R. A.
Fluegge
, and
R. J.
Hull
,
Rev. Sci. Instrum.
39
,
1171
(
1968
);
(c)
V.
Aquilanti
,
G.
Liuti
,
E.
Luzzatti
,
F.
Vecchio‐Cattivi
, and
G. G.
Volpi
,
Z. Phys. Chem.
79
,
200
(
1972
);
(e)
T. M.
Miller
,
J. Appl. Phys.
45
,
1713
(
1974
);
(f)
A.
Schalk
,
D.
Bassi
,
F.
Tommasini
, and
G.
Scoles
,
J. Chem. Phys.
62
,
600
(
1975
);
(g) K. A. Köhler, Dissertation, Bonn (1975).
34.
H.
Wise
and
B. J.
Wood
,
Adv. At. Mol. Phys.
3
,
291
(
1967
).
35.
The resonator is similar to one described by
W. W.
Mac Alpine
and
R. O.
Schildknecht
,
Proc. IRE
2099
(
1959
).
36.
This was confirmed by several independent measurements in our laboratory carried out by U. Borkenhagen, R. David, M. Faubel, H. MaLthan, and K. Winkelmann.
37.
We are grateful to G. Brusdeylins and H. D. Meyer of our laboratory for performing these measurements for us.
38.
W.
Bauer
,
L. Y.
Rusin
, and
J. P.
Toennies
,
J. Chem. Phys.
68
,
4490
(
1978
).
39.
E. V.
Kornelsen
and
B.
Domeij
,
J. Vac. Sci. Tech.
3
,
20
(
1966
).
40.
Page 284 of Ref. 29.
41.
W. B. Miller, Dissertation Harvard University, Cambridge, MA, 1969.
42.
F. W. Dustmann, Max‐Planck‐Institut für Strömungsforschung, Report No. 114/1975, 1975.
43.
“See AIP document No. PAPS JCPSA‐71‐614‐11 for 11 pages of measured relative integral cross sections with errors for different primary beam velocities in the sequential order of the measurements for all systems.
Order by PAPS number and journal reference from American Institute of Physics, Physics Auxiliary Publication Service, 335 East 45th Street, New York, NY 10017. The price is $1.50 for each microfiche (98 pages), or $5 for photocopies of up 30 pages with: $0.15 for each additional page over 30 pages. Airmail additional. Make checks payable to the American Institute of Physics. This material also appears in Current Physics Microform, the monthly microfilm edition of the complete set of journals published by AIP, on the frames immediately following this journal article.”
44.
R. W.
Bickes
, Jr.
,
B.
Lantzsch
,
J. P.
Toennies
, and
K.
Walaschewski
,
Faraday Discuss. Chem. Soc.
55
,
167
(
1973
).
45.
See, for example, N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Clarendon Press, Oxford, 1965), p. 39.
46.
L.
Zandee
and
J.
Reuss
,
Chem. Phys.
26
,
345
(
1977
).
47.
Strictly speaking this assertion is only valid if transitions to energetically forbidden states (closed channels) are neglected. In order to explore the effect of closed channels J. Schaefer has carried out close‐coupling calculations for H2Ar with and without closed channels using a realistic anisotropic potential. The results indicate that at the lowest energies probed in these experiments the closed channels have no effect on the cross sections confirming our assertion. However at lower collision energies closed channels do lead to a shift and broadening of the resonances.
48.
M. Faubel and J. P. Toennies, J. Chem. Phys. (to be published).
49.
G. Herzberg, Molecular Spectra and Molecular Structure, I. Spectrn of Diatomic Molecules (Van Nostrand, New York, 1950).
50.
H. D. Meyer and J. P. Toennies (to be published).
51.
W. Welz, Max‐Planck‐Institut für Strömungsforschung, Report No. 107/1976, 1976.
52.
F. Calogero, Variable Phase Approach to Potential Scattering (Academic, New York, 1968).
53.
D.
Bassi
,
M. G.
Dondi
,
F.
Tommasini
,
F.
Torello
, and
U.
Valbusa
,
Phys. Rev. A
13
,
584
(
1976
).
54.
(a)
G.
Das
,
A. F.
Wagner
, and
A. C.
Wahl
, private communication; (b)
J. Chem. Phys.
68
,
4917
(
1978
).
55.
W. C.
Stwalley
,
J. Chem. Phys.
61
,
3840
(
1974
).
56.
Ch. Hahn, Max‐Planck‐Institut für Strömungsforschung, Report No. 118/1972, 1972.
57.
A. F.
Wagner
,
G.
Das
, and
C.
Wahl
,
J. Chem. Phys.
60
,
1885
(
1974
).
58.
(a)
J. P.
Toennies
,
Chem. Phys. Lett.
20
,
238
(
1973
);
(b)
R.
Ahlrichs
,
R.
Penco
, and
G.
Scoles
,
Chem. Phys.
19
,
119
(
1977
);
(c)
K. T.
Tang
and
J. P.
Toennies
,
J. Chem. Phys.
66
,
1496
(
1977
).
59.
G.
Starkschall
,
J. Chem. Phys.
56
,
5729
(
1972
).
60.
W. C.
Stwalley
,
J. Chem. Phys.
61
,
3840
(
1974
).
61.
The critical value of B was determined by trial and error.
62.
R.
Helbing
,
W.
Gaide
, and
H.
Pauly
,
Z. Phys.
208
,
215
(
1968
).
63.
(a)
R. W.
Bickes
,Jr.
,
G.
Scoles
, and
K. M.
Smith
,
Can. J. Phys.
53
,
435
(
1975
);
(b)
A. M.
Rulis
,
K. M.
Smith
, and
G.
Scoles
,
Can. J. Phys.
56
,
753
(
1978
).
64.
(a)
A. R. W.
McKellar
and
H. L.
Welsh
,
J. Chem. Phys.
55
,
595
(
1971
);
(b)
A. R. W.
McKellar
and
H. L.
Welsh
,
61
,
4636
(
1974
); ,
J. Chem. Phys.
(c) H. L. Welsh in Spectroscopy (Butterworths, London, 1972);
M. T. P. International Reviews of Science, Physical Chemistry, Vol. 3, p. 83.
65.
R. J.
LeRoy
and
J.
van Kranendonk
,
J. Chem. Phys.
61
,
4750
(
1974
).
66.
(a)A. M. Dunker, Ph.D. thesis, Harvard University, Cambridge, MA, 1974. Results from this thesis yielded 5%‐8% larger well depths for H2Ar, Kr, and Xe than those found in Refs. 22 and 23 and in the present work. For this reason no detailed comparison with this work was made;
(b)
A. M.
Dunker
and
R. G.
Gordon
,
J. Chem. Phys.
68
,
700
(
1978
).
67.
R. J.
LeRoy
,
J.
Carley
, and
J. E.
Grabenstetter
,
Faraday Discuss. Chem. Soc.
62
,
169
(
1977
).
68.
J. S.
Carley
,
Faraday Discuss. Chem. Soc.
62
,
303
(
1977
).
69.
J. Schäfer, private communication.
70.
R. M.
Jonkman
,
G. J.
Prangsma
,
I.
Erlas
,
H. F. P.
Knaap
, and
J. J. M.
Beenakker
,
Physica
38
,
441
(
1968
).
71.
L.
Zandee
and
J.
Reuss
,
Chem. Phys.
26
,
345
(
1977
).
72.
H. J. M. Hanley and M. Klein, Technical Note 628, National Bureau of Standards (USA), 1972.
73.
C8 and C10 coefficients have recently been estimated for H2Ar, Kr, and Xe; K. T. Tang and J. P. Toennies (to be published).
74.
(a)
C. H.
Chen
,
P. E.
Siska
, and
Y. T.
Lee
,
J. Chem. Phys.
59
,
601
(
1973
);
(b)
K. M.
Smith
,
A. M.
Rulis
,
G.
Scoles
,
R. A.
Aziz
, and
V.
Nain
,
J. Chem. Phys.
67
,
152
(
1977
).,
J. Chem. Phys.
75.
For references to the original literature and a compilation of the theoretical and experimental potential parameters see Ref. 74.
76.
For calculations of Ne‐Ne see
J. P.
Toennies
and
K.
Winkelmann
,
J. Chem. Phys.
66
,
3965
(
1977
).
77.
U.
Schwalm
and
J. P.
Toennies
,
Chem. Phys. Lett.
63
,
17
(
1979
).
78.
Lev. Y. Rusin and J. P. Toennies, Abstracts of Papers XIth International Conference on Physics of Electronic and Atomic Collisions (Commissariat à l’ Energie Atomique, Paris, 1977), p. 88.
This content is only available via PDF.

Supplementary Material

You do not currently have access to this content.