1974
DOI: 10.1063/1.1682492
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Semiclassical collision theory. Multidimensional integral method

Abstract: Numerical results on the integral expression for the semiclassical S matrix are compared with exact quantum results for a multidimensional problem. The collision of a rigid rotor with an atom is treated. The integral method proves to be easy to ·apply. Within its range of maximum validity (no sign changes in the pre-exponential factor of the semiclassical wavefunction) the agreement was typically within 20%. When sign changes occurred, the agreement was about a factor of 2 or better. Conditions affecting sign … Show more

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Cited by 33 publications
(13 citation statements)
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“…47 Historically, Eq. (11) is the starting point of the SCIVR, 45,46,48,49 remarkably accurate for direct inelastic collisions, 45,47,50 direct collinear reactions 51,52 and molecular spectroscopy. 53,54 The interested reader will find detailed developments on SCIVR in the previously mentioned references and references therein.…”
Section: Dynamical Methodsmentioning
confidence: 99%
“…47 Historically, Eq. (11) is the starting point of the SCIVR, 45,46,48,49 remarkably accurate for direct inelastic collisions, 45,47,50 direct collinear reactions 51,52 and molecular spectroscopy. 53,54 The interested reader will find detailed developments on SCIVR in the previously mentioned references and references therein.…”
Section: Dynamical Methodsmentioning
confidence: 99%
“…3,12,13,[17][18][19] At the other extreme, if ␣ is allowed to approach infinity, the factor D ␣ (J 2 ;J , ) in the integrand of Eq. 3,12,13,[17][18][19] At the other extreme, if ␣ is allowed to approach infinity, the factor D ␣ (J 2 ;J , ) in the integrand of Eq.…”
Section: ͑79͒mentioning
confidence: 99%
“…At a somewhat higher level, the primitive semiclassical formula ͑PSC͒ for the S-matrix, derived independently by Miller 2-10 and Marcus, [11][12][13][14][15][16][17][18][19] expresses the S-matrix elements as a sum over root trajectories in which each term is the product of two factors: the square root of the corresponding classical-semiclassical probability term, and a phase factor. The introduction of this phase factor makes it possible for the PSC expression to describe interference among the root trajectories, so that classically allowed transitions can be treated more accurately.…”
Section: Introductionmentioning
confidence: 99%
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