Dimensionality control of coupled scattering equations using partitioning techniques

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 Qψ scat. 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.