A calculation of symmetric resonant charge exchange cross sections has been made for a selection of atoms in the velocity range where the impact parameter method is applicable. Cross sections for other atoms can be estimated by interpolating in terms of their ionization potentials. The results are in fair agreement with experiment. A similar calculation has been attempted for asymmetric nonresonant charge exchange processes. The approximations used are more restrictive in this calculation, the calculations being only semiquantitative in nature. The cross section of an asymmetric charge exchange process is determined in terms of the ΔE of the reaction and the ``average'' ionization potential of the two atoms. The results are qualitatively in agreement with experiment. A very brief discussion of approaches for extrapolating data to lower velocities, where the rectilinear orbit impact parameter method is not applicable, is given.

1.
This proposal was made by J. L. Magee and D. Rapp, Proc. 2nd Intern. Symp. on Electronic and Atomic Impact Phenomena, Boulder, Colorado, June 1961.
2.
D. R.
Bates
,
H. S. W.
Massey
, and
A. L.
Stewart
,
Proc. Roy. Soc. (London)
A216
,
437
(
1953
).
3.
E. F.
Gurnee
and
J. L.
Magee
,
J. Chem. Phys.
26
,
1237
(
1957
).
4.
K.
Takayanagi
,
Repts. Progr. Saitama Univ.
AII
,
33
(
1955
).
5.
D. R.
Bates
and
R.
McCarrol
,
Proc. Roy. Soc. (London)
A245
,
175
(
1958
).
6.
R. McCarrol, reference 1.
7.
References 2–4 are but a few of the many available papers in this connection.
8.
D.
Rapp
and
I. B.
Ortenburger
,
J. Chem. Phys.
33
,
1230
(
1960
).
9.
D. R.
Bates
,
K.
Ledsham
, and
A. L.
Stewart
,
Phil. Trans. Roy. Soc.
A246
,
215
(
1953
).
10.
B. L.
Moisevitch
,
Proc. Phys. Soc. (London)
A69
,
653
(
1956
).
11.
T. J. M.
Boyd
and
A.
Dalgarno
,
Proc. Phys. Soc. (London)
A72
,
694
(
1958
).
12.
A.
Dalgarno
,
Phil. Trans. Roy. Soc.
A250
,
426
(
1958
).
13.
I. Popescu
Iovitsu
and
N.
Ionescu‐Pallas
,
Soviet Phys.‐Tech. Phys.
4
,
781
(
1960
).
14.
A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, Bateman Manuscript Project (McGraw‐Hill Book Company, Inc., New York, 1954), Vol. I, p. 86.
15.
E. A.
Mason
and
J. T.
Vanderslice
,
J. Chem. Phys.
29
,
361
(
1958
);
E. A.
Mason
and
J. T.
Vanderslice
,
30
,
599
(
1959
).,
J. Chem. Phys.
16.
W. H.
Cramer
and
J. H.
Simons
,
J. Chem. Phys.
26
,
1272
(
1957
).
17.
W. H.
Cramer
,
J. Chem. Phys.
28
,
688
(
1958
).
18.
The equilibrium constant for reaction (21) is f1/f2e−ΔE/RT, where in more usual terms f1/f2 = (gAgB+/gA+gB), and the g’s are statistical weights of the atoms.
19.
D. R.
Bates
and
N.
Lynn
,
Proc. Roy. Soc. (London)
A253
,
141
(
1959
).
20.
T.
Holstein
,
J. Phys. Chem.
56
,
832
(
1952
).
21.
L. Pauling and E. B. Wilson, Jr., Introduction to Quantum Mechanics (McGraw‐Hill Book Company, Inc., New York, 1935), pp. 138–139.
22.
In the limit ω1 = ω2,η1−η2 = 0 by this assumption. However, use of more realistic orbitals would lead to η1−η2≠0 when A and B are different even though ω1 = ω2. This case of “accidental resonance” is important in the reaction O+(4S)+H(2S)→O(3P)+H+ for which ω1−ω2 is very small.8,19 The contribution of η1−η2 to Ω in such a process is difficult to ascertain accurately. At very large impact parameters Ω≅ω since η1−η2→0 as b→∞. Whether η1−η2 is still negligible at the finite impact parameters involved in charge transfer, is subject to question.19 In our approximate calculation we put Ω = ω for all ω and b.
23.
Bates and Lynn19 have pointed out that in processes of the type
A++B+A+++B
, η1−η2 may be very large compared to ω, leading to Ω≠ω. We do not consider such processes in this paper.
24.
In general, the smaller the nonresonance, and the higher the ion velocity, the better the present theory should be.
25.
A recent examination of the available data in terms of this conclusion leads to a “best” value of about 7 Å for a. [J. B. Hasted and A. R. Lee, University College, London (personal communication of a preprint to be published)].
26.
H. S. W.
Massey
,
Rept. Progr. Phys.
12
,
248
(
1949
).
27.
N.
Rosen
and
C.
Zener
,
Phys. Rev.
40
,
502
(
1932
).
28.
B. G.
Skinner
,
Proc. Phys. Soc. (London)
A77
,
551
(
1961
).
29.
The various functions |aA(∞)|2 oscillate with b with different frequencies, so that comparison at identical (b, v) combinations is not as meaningful as a comparison of the integrals obtained from Eq. (4).
30.
See the discussion immediately following Eq. (11).
31.
Although there is some ambiguity in the choice of I in a nonresonant process, σ is not usually very dependent on this choice. For extreme nonresonances such as
Cs+He+He+Cs+
, the choice of I is both important and dubious, and the present method is inadequate.
32.
Excepting He+, which is a S2 state.
33.
J. B.
Hasted
,
Proc. Roy. Soc. (London)
A212
,
235
(
1952
).
34.
W. L.
Fite
,
R. F.
Stebbings
,
D. G.
Hummer
, and
R. T.
Brackmann
,
Phys. Rev.
119
,
663
(
1960
);
D. G.
Hummer
,
R. F.
Stebbins
,
W. L.
Fite
, and
L. M.
Branscomb
,
Phys. Rev.
119
,
668
(
1960
).,
Phys. Rev.
35.
D. P.
Stevenson
and
G.
Gioumousis
,
J. Chem. Phys.
29
,
294
(
1958
).
36.
The charge exchange probability may be roughly taken as P(o,υ) in a direct encounter, despite the curved orbit.
37.
J. L. Franklin and F. H. Field, Proc. ASTM Mass Spectrometry Conference, Chicago, Illinois, June 1961.
This content is only available via PDF.
You do not currently have access to this content.