No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Scattering of thermal He beams by crossed atomic and molecular beams. II. The He–Ar van der Waals potential
1.For recent reviews, see (a) U. Buck, Adv. Chem. Phys. 30, 313 (1975);
1.(b) J. P. Toennies, in Physical Chemistry: an Advanced Treatise, Vol. 6A, edited by H. Eyring, D. Henderson, and W. Jost (Academic, New York, 1974), p. 227;
1.(c) G. C. Maitland and E. B. Smith, Chem. Soc. Rev. 2, 181 (1973).
2.I. Amdur and J. E. Jordan, Adv. Chem. Phys. 10, 29 (1966).
3.A. A. Abrahamson, Phys. Rev. 130, 693 (1963).
4.J. O. Hirschfelder and W. J. Meath, Adv. Chem. Phys. 12, 3 (1967).
5.(a) Y. S. Kim and R. G. Gordon, J. Chem. Phys. 61, 1 (1974);
5.(b) J. S. Cohen and R. T. Pack, J. Chem. Phys. 61, 2372 (1974); , J. Chem. Phys.
5.(c) P. D. Dacre, Chem. Phys. Lett. 50, 147 (1977).
6.(a) A. L. J. Burgmans, J. M. Farrar, and Y. T. Lee, J. Chem. Phys. 64, 1345 (1976);
6.(b) J. M. Parson, P. E. Siska and Y. T. Lee, J. Chem. Phys. 56, 1511 (1972)., J. Chem. Phys.
7.D. E. Freeman, K. Yoshino, and Y. Tanaka, J. Chem. Phys. 61, 4880 (1974).
8.See also Y. Tanaka, K. Yoshino, and D. E. Freeman, J. Chem. Phys. 59, 5160 (1973).
9.See also G. L. Pollack, Rev. Mod. Phys. 36, 748 (1964).
10.J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).
11.For recently proposed combination rules, see for example (a) C. L. Kong and M. R. Chakrabarty, J. Phys. Chem. 77, 2668 (1973);
11.(b) F. T. Smith, Phys. Rev. A 5, 1708 (1972);
11.(c) H. L. Kramer and D. R. Herschbach, J. Chem. Phys. 53, 2792 (1970);
11.(d) P. T. Sikora, J. Phys. B 3, 1475 (1970); see alsc Ref. 10.
12.Ch. Schlier, Ann. Rev. Phys. Chem. 20, 191 (1969).
13.M. Keil and A. Kuppermann, J. Chem. Phys. 69, 3917 (1978).
14.C. H. Chen, P. E. Siska, and Y. T. Lee, J. Chem. Phys. 59, 601 (1973).
15.K. M. Smith, A. M. Rulis, G. Scoles, R. A. Aziz, and V. Nain, J. Chem. Phys. 67, 152 (1977).
16.K. M. Smith, A. M. Rulis, G. Scoles, R. A. Aziz, and G. Duquette, J. Chem. Phys. 63, 2250 (1975).
17.F. Pirani and F. Vecchiotcattivi, J. Chem. Phys. 66, 372 (1977).
18.R. Helbing, W. Gaide, and H. Pauly, Z. Phys. 208, 215 (1968).
19.D. E. Freeman, K. Yoshino, and Y. Tanaka, J. Chem. Phys. 67, 3462 (1977).
20.Our potential is somewhat similar to the MMSV part of the ESMMSV potential form pooposed in Ref. 6(a). Their choice of joining the two Morse functions at was not used here since the first Morse function would represent both the weakly repulsive wall and a significant part of the attractive region, and therefore would not have the desired flexibility for fitting the DCS. Furthermore, we felt that the second Morse parameter (for ) would then be used over too restricted a range of interatomic separations.
21.G. Simons, R. G. Parr, and J. M. Finlan, J. Chem. Phys. 59, 3229 (1973).
22.R. W. Bickes and R. B. Bernstein, Chem. Phys. Lett. 26, 457 (1974). Our SPF‐Dunham potential is actually a further variant of their modification to the SPF potential21 the major difference is the inclusion of dispersion terms of order higher than and in allowing these coeffiients to be treated as parameters.
23.J. W. Brewer and G. W. Vaughn, J. Chem. Phys. 50, 2960 (1969).
24.A. L. Blancett, K. R. Hall, and F. B. Canfield, Physica 47, 75 (1970).
25.N. K. Kalfoglou and John G. Miller, J. Phys. Chem. 71, 1256 (1967).
26.D. W. Gough, C. P. Matthews, and E. B. Smith, J. Chem. Soc. Faraday I 72, 645 (1976).
27.G. C. Maitland and E. B. Smith, J. Chem. Soc. Faraday I 70, 1191 (1974).
28.R. J. J. van Heijningen, J. P. Harpe, and J. J. M. Beenakker, Physica 38, 1 (1968).
29.W. Hogervorst, Physica 51, 59 (1971).
30.A. Kuppermann, R. J. Gordon, and M. J. Coggiola, Faraday Discuss. Chem. Soc. 55, 145 (1973);
30.R. J. Gordon, M. J. Coggiola, and A. Kupperman, Chem. Phys. Lett. 20, 493 (1973).
31.M. J. Coggiola, Ph.D. thesis, California Institute of Technology 1975.
32.J. B. Anderson and J. B. Fenn, Phys. Fluids 8, 780 (1965).
33.H. U. Hostettler and R. B. Bernstein, Rev. Sci. Instrum. 31, 872 (1960).
34.Galileo Electro‐Optics Corporation, Sturbridge, Massachusetts.
35.J. C. Johnson, A. T. Stair, and J. L. Pritchard, J. Appl. Phys. 37, 1551 (1966).
36.Wallace and Tiernan Company, Belleville, New Jersey.
37.Bendix Corporation, South Montrose, Pennsylvania.
38.Data Device Corporation, Bohemia, New York.
39.N. F. Ramsey, Molecular Beams (Oxford University, Oxford, 1956), pp. 16–19;
39.P. Kusch, J. Chem. Phys. 40, 1 (1964).
40.G. O. Brink, Rev. Sci. Instrum. 37, 857 (1966).
41.Extranuclear Laboratories Incorporated, P.O. Box 11512, Pittsburgh, Pennsylvania.
42.Princeton Applied Research Corporation, P.O. Box 2565, Princeton, New Jersey.
43.In addition to the primary and secondary beam angular divergence distribution function, a third one is needed to describe the overall apparatus angular resolution. Its FWHM is adjusted, as described in step 10 of Sec. III, and in Sec. IV. The calculated DCS is insensitive to the assumed shape of this apparatus angular resolution function; changing it from a cosine‐squared to a hyperbolic secant affects the adjusted FWHM but not the calculated DCS. Since the overall apparatus angular resolution contains significant contributions from the angular distributions of the primary and secondary beams, we assume that this insensitivity to the exact form of the angular resolution function also applies to the primary and secondary beam angular distribution functions.
44.Calculated by the method of R. T. Pack, J. Chem. Phys. 60, 633 (1974). For JWKB phase shifts could be calculated more conveniently and uniformly by a slightly different Gauss‐Mehler quadrature formula.
45.K. Smith, The Calculation of Atomic Collision Processes (Wiley, New York, 1971), p. 60.
45.It was found that for the present single‐channel case, the Numerov method was more accurate than that of R. G. Gordon, J. Chem. Phys. 51, 14 (1969); it was also about three times faster.
46.R. B. Bernstein, J. Chem. Phys. 33, 795 (1960).
47.M. Rosen and D. R. Yennie, J. Math. Phys. 5, 1505 (1964).
48.H. M. Seip, in Selected Topics in Structure Chemistry, edited by P. Andresen, O. Bastiansen and S. Furberg (Scandinavian University, Oslo, 1967), p. 25.
49.N. R. Draper and H. Smith, Applied Regression Analysis (Wiley, New York, 1966), Chaps. 2 and 9.
50.D. W. Marquardt, J. Soc. Indust. Appl. Math. 11, 431 (1963).
51.R. B. Bernstein, Adv. Chem. Phys. 10, 75 (1966).
52.J. M. Parson and Y. T. Lee, Entropie 42, 146 (1971). Modifications to their MSV potential concern the placement of the spline points; we have generally found that the spline region can best be freed of “wiggles” for a wide variety of β, and values if is chosen as in the text.
53.The dispersion coefficients are written in reduced form as
54.K. T. Tang, J. M. Norbeck, and P. R. Certain, J. Chem. Phys. 64, 3063 (1976).
55.P. E. Siska, J. M. Parson, T. P. Schafer, and Y. T. Lee, Chem. Phys. 55, 5762 (1971). The ESMSV parameterization produces calculated DCS’s which are almost identical to the corresponding MSV potentials.
56.Other potential forms investigated in Paper I were the LJ12‐6, Kihara Klein‐Hanley, Buckingham‐Corner, and double‐LJ families, as well as the Barker‐Pompe expansion model; see Paper I for their explicit parametrizations.
57.For additional functional forms that look interesting, see (a) A. J. Thakkar, J. Chem. Phys. 62, 1693 (1975);
57.(b) G. C. Maitland and E. B. Smith, Chem. Phys. Lett. 22, 443 (1973);
57.(c) V. H. Smith and A. J. Thakkar, Chem. Phys. Lett. 17, 274 (1972)., Chem. Phys. Lett.
58.We note that although neither of the potentials obtained separately were given any preference in this study, the out‐of‐plane potential may actually be slightly preferred, primarily for two reasons. Firstly, angular spacings between the diffraction oscillations are greater for the out‐of‐plane DCS than for the in‐plane one, allowing a better characterization of these oscillations. Secondly, the fits to the out‐of‐plane data are consistently of higher quality than are the in‐plane fits (see Fig. 4 and Table II). This difference may be related to small residual errors in the apparatus alignment (Sec. II). See also E. F. Greene, M. H. Lau, and J. Ross, J. Chem. Phys. 50, 3122 (1969).
59.(a) J. H. Dymond and B. J. Alder, J. Chem. Phys. 51, 309 (1969);
59.(b) J. H. Dymond and B. J. Alder, Chem. Phys. Lett. 2, 54 (1968).
60.J. Hepburn, G. Scoles, and R. Penco, Chem. Phys. Lett. 36, 451 (1975).
61.R. Ahlrichs, R. Penco, and G. Scoles, Chem. Phys. 19, 119 (1977).
62.J. A. Barker and A. Pompe, Aust. J. Chem. 21, 1683 (1968).
63.R. Duren, R. Feltgen, W. Gaide, R. Helbing, and H. Pauly, Phys. Lett. 18, 282 (1965).
64.M. V. Bobetic and J. A. Barker, J. Chem. Phys. 64, 2367 (1976).
65.To integrate the radial wavefunction, we use the Numerov propagator instead of the Gordon method45 of Ref. 64; this introduces only a small change in the resulting values
66.(a) G. E. Ewing, Can. J. Phys. 54, 487 (1976);
66.(b) G. E. Ewing, Accts. Chem. Res. 8, 185 (1975).
67.Y. Tanaka and K. Yoshino, J. Chem. Phys. 53, 2012 (1970).
68.F. J. Smith and R. J. Munn, J. Chem. Phys. 41, 3560 (1964).
69.S. O. Colgate, J. E. Jordan, I. Amdur, and E. A. Mason, J. Chem. Phys. 51, 968 (1969).
70.I. Amdur, E. A. Mason, and A. L. Harkness, J. Chem. Phys. 22, 1071 (1954).
71.A. B. Kamnev and V. B. Leonas, Dokl. Akad. Nauk SSSR [Sov. Phys.‐Doklady] 10, 529 (1965).
72.H. Kreek, Y. H. Pan, and W. J. Meath, Mol. Phys. 19, 513 (1970).
73.J. M. Finlan and G. Simons, J. Mol. Spectrosc. 57, 1 (1975).
74.(a) T. T. Warnock and R. B. Bernstein, J. Chem. Phys. 49, 1878 (1968);
74.(b) R. K. B. Helbing, J. Chem. Phys. 48, 472 (1968); , J. Chem. Phys.
74.(c) F. A. Morse and R. B. Bernstein, J. Chem. Phys. 37, 2019 (1962)., J. Chem. Phys.
Article metrics loading...
Full text loading...
Most read this month
Most cited this month