Transition probability matrix between surfaces

A computer program was developed to accomplish this and to carry out the iteration procedure described above. Computational facilities at our disposal (Harris 500) allowed the consideration of matrices of order not exceeding 60. Considering that the order of the transition probability matrix is 4 times the width (M) of the interfacial region, the computational limitation restricts the present investigation to the systems in which the distance between the confining the surfaces is less than 15 units (1 unit = d). 

The main difference between (2S-D1ABAT1C) and (IS-GP) results is the appearance of broad Fano profiles on the (2S-D1ABAT1C) transition probabilities, which suggests that the upper adiabatic PES can support resonances which do not exist in the single ground adiabatic surface calculation. This can be investigated further with the lifetime matrix formalism described in Sect. 3.4. Smith lifetime matrices for the (2S-DIABATIC) case differ from the (IS-GP) ones only by the appearance of Lorentzian-shape eigenvalues near and above 4 eV. 

Interaction matrix elements between states of different symmetry involving the spin-orbit operator have also been evaluated in various instances. A typical example is the predissociation of the b Z state in Oj by the Z and f Ilg states. The interaction is very much dependent on the internuclear separation and varies from zero around 2.4 a.u. to approximately 60cm at 3.5 a.u., where the potential surface crossing occurs in the neighborhood of 3 a.u. Hence in a detailed treatment of the probability y for non-radiationless transition, the explicit form of this matrix element has to be taken into account as... 

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