High‐Velocity Molecular Beam Scattering: Total Elastic Cross Sections for L‐J(n, 6) and Exp‐6(α) Potentials

Bernstein, Richard B.

High‐Velocity Molecular Beam Scattering: Total Elastic Cross Sections for L‐J(n, 6) and Exp‐6(α) Potentials

dc.contributor.author	Bernstein, Richard B.	en_US
dc.date.accessioned	2010-05-06T21:50:49Z
dc.date.available	2010-05-06T21:50:49Z
dc.date.issued	1963-01-15	en_US
dc.identifier.citation	Bernstein, Richard B. (1963). "High‐Velocity Molecular Beam Scattering: Total Elastic Cross Sections for L‐J(n, 6) and Exp‐6(α) Potentials." The Journal of Chemical Physics 38(2): 515-522. <http://hdl.handle.net/2027.42/70237>	en_US
dc.identifier.uri	https://hdl.handle.net/2027.42/70237
dc.description.abstract	Explicit expressions are derived for the total elastic scattering cross sections in the high‐velocity region for molecules interacting according to L‐J (n, 6) and exp‐6(α) potentials. Cross sections are presented in tabular and graphical form.	en_US
dc.format.extent	3102 bytes
dc.format.extent	513888 bytes
dc.format.mimetype	text/plain
dc.format.mimetype	application/pdf
dc.publisher	The American Institute of Physics	en_US
dc.rights	© The American Institute of Physics	en_US
dc.title	High‐Velocity Molecular Beam Scattering: Total Elastic Cross Sections for L‐J(n, 6) and Exp‐6(α) Potentials	en_US
dc.type	Article	en_US
dc.subject.hlbsecondlevel	Physics	en_US
dc.subject.hlbtoplevel	Science	en_US
dc.description.peerreviewed	Peer Reviewed	en_US
dc.contributor.affiliationum	Chemistry Department, University of Michigan, Ann Arbor	en_US
dc.description.bitstreamurl	http://deepblue.lib.umich.edu/bitstream/2027.42/70237/2/JCPSA6-38-2-515-1.pdf
dc.identifier.doi	10.1063/1.1733689	en_US
dc.identifier.source	The Journal of Chemical Physics	en_US
dc.identifier.citedreference	R. B. Bernstein, (a) J. Chem. Phys. 33, 795 (1960); (b) 34, 361 (1961); (c) 36, 1403 (1962); (d) 37, 1880 (1962).Errata are as follows: (1a) Table III: η1(3)η1(3) and η16(20)η16(20) should both be positive. Fig. 13: For the lowest curve, β′ = 3.3.β′=3.3. (lb) p. 365: BA4BA4 should be 2.00×107.2.00×107. (lc) Equation (5) was not in fact, obtained from Eq. (4), but rather was derived from the integral using an alternate boundary condition appropriate to this special case, i.e., η0 = −A.η0=−A. In example 3, for b∗>2,b∗>2, the sign of η∗η∗ should be positive. (1d) The symbol ηm ≡ ηmaxηm≡ηmax (i.e, the superscript m is not an exponent).	en_US
dc.identifier.citedreference	H. S. W. Massey and C. B. O. Mohr, Proc. Roy. Soc. (London) A144, 188 (1934).	en_US
dc.identifier.citedreference	A. Dalgarno and M. R. McDowell, Proc. Phys. Soc. (London) A69, 615 (1956); A. Dalgarno, M. R. McDowell, and A. Williams, Phil. Trans. Roy. Soc. (London) A250, 411 (1958).	en_US
dc.identifier.citedreference	E. A. Mason and J. T. Vanderslice, J. Chem. Phys. 29, 361 (1958).These authors employ a reduced velocity parameter υ∗υ∗ which is closely related to Dz:υ∗ = 2Dz−1Dz:υ∗=2Dz−1.	en_US
dc.identifier.citedreference	In reference 1 attention was limited to the L‐J (12, 6) potential, and the notation involved σ [the first zero of V(r)V(r)] and x ≡ r/σ;x≡r∕σ; for the purpose of generalizing to other potentials, it is advantageous to change to the notation which makes use of rmrm and z ≡ r/rm.z≡r∕rm.	en_US
dc.identifier.citedreference	N. F. Mott and H. S. W. Massey, Theory of Atomic Collisions (Clarendon Press, Oxford, England, 1949), 2nd ed.	en_US
dc.identifier.citedreference	Equation (14a) follows exactly from Eqs. (10a) and (6). However, in deriving Eq. (14b) from Eqs. (10b) and (6), an approximation was introduced, since the integral yielding the term in eα(1−βL)eα(1−βL) is not expressible in simple form. It was convenient to transform it to one involving Erf (x½),(x12), which was then expanded for large x in a semiconvergent series (the first few terms of which disappeared by cancellation). In computation, the series is terminated when the (n+1)th(n+1)th term exceeds the nth; a residue of half the nth; term is then applied. The error in X introduced by this procedure is <2%<2% for x>10,x>10, but increases to ∼ 30%∼30% at x = 5.x=5. Fortunately, this has a negligible influence on the resulting QB∗QB∗ since the entire second term in the braces of Eq. (14b) is in the range 5–10%, compared to unity. The principal factor governing Q∗Q∗ is the quantity 2βL2,2βL2, where βLβL is, of course, strongly dependent on Dz.Dz.	en_US
dc.identifier.citedreference	I. Amdur and H. Pearlman, J. Chem. Phys. 9, 503 (1941).I. Amdur, J. E. Jordan, and S. O. Colgate, 34, 1525 (1961)and other papers in the series.	en_US
dc.identifier.citedreference	E. A. Mason and J. T. Vanderslice, J. Chem. Phys. 27, 917 (1957).	en_US
dc.identifier.citedreference	G. N. Watson, Theory of Bessel Functions (Cambridge University Press, England, 1944), 2nd ed., pp.78, 79, 202.	en_US
dc.owningcollname	Physics, Department of

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