Dimensionality control of coupled scattering equations using partitioning techniques |
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Authors: | Georgia Englot Herschel Rabitz |
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Institution: | Department of Chemistry, Princeton University, Princeton, New Jersey 08540, USA |
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Abstract: | A method of variable reduction of the dimensionality of the coupled equations for inelastic scattering is presented, based upon a projection operator P with a restricted range of orbital angular momentum states. For rotational states in the range O?j ?j* and total angular momentum large, the coupled equations have dimensionality (j* + 1) ? N ?(j* + 1)2, where the value of N is controlled by the choice of P. This is in contrast to conventional partitioning techniques which utilize further restrictions on the important molecular rotational states. The equations for the P subspace and its complementary Q subspace are decoupled by an approximation on the equation of motion of Qψscat. Information about scattering into the Q subspace is retained, within this degree of approximation, and is reintroduced at the end of the computation with little additional labor. The theory is developed in terms of atom-rigid-rotor scattering, although addition of vibrational modes would not in any way interfere with the basic techniques used. |
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