Factorization relations and consistency conditions in the sudden approximation
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Ames National Laboratory is a government-owned, contractor-operated national laboratory of the U.S. Department of Energy (DOE), operated by and located on the campus of Iowa State University in Ames, Iowa.
For more than 70 years, the Ames National Laboratory has successfully partnered with Iowa State University, and is unique among the 17 DOE laboratories in that it is physically located on the campus of a major research university. Many of the scientists and administrators at the Laboratory also hold faculty positions at the University and the Laboratory has access to both undergraduate and graduate student talent.
The Department of Chemistry seeks to provide students with a foundation in the fundamentals and application of chemical theories and processes of the lab. Thus prepared they me pursue careers as teachers, industry supervisors, or research chemists in a variety of domains (governmental, academic, etc).
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The Department of Chemistry was founded in 1880.
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1880-present
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- College of Liberal Arts and Sciences (parent college)
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Abstract
Linear factorization relations are derived for the matrix elements of quantum mechanical operators defined on some space H = H1⊕⋅2 which are diagonalizable on H1. The coefficients in these relationships do not depend on the operators per se but do depend on the representations in which the operators are diagonal. The formulation is very general with regard to the nature of the ’’input’’ information in the factorization. With each choice of input information there are associated consistency conditions. The consistency conditions, in turn, give rise to a flexibility in the form of the factorization relations. These relations are examined in detail for the operators of scattering theory which are local in the internal molecular coordinates. In particular, this includes S and T matrices in the energy sudden (ES) approximation. A similar development is given for the square of the magnitude of operator matrix elements appropriately averaged over ’’symmetry classes.’’ In the ES these relations apply to transition cross sections between symmetry classes. In particular, they apply to degeneracy averaged cross sections in situations where the symmetry classes correspond to energy levels.
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This article is published as Chan, C., J. W. Evans, and D. K. Hoffman. "Factorization relations and consistency conditions in the sudden approximation." The Journal of Chemical Physics 75, no. 2 (1981): 722-737, doi:10.1063/1.442113. Posted with permission.