Perturbation by a broad intruder level

The formal K matrix theory for a Rydberg manifold perturbed by a broad intruder state was setup by Lane [393]. The results have been related in detail to the (/-reversal problem by Connerade et al. [380], whose 

When an extra level B is added to a series of levels labelled by n, then the K-matrix has the form 

For a general set of levels n which are arbitrarily spaced, as occur in 

We now discuss a problem involving two open channels a strongly coupled particle channel a and a weakly coupled radiative channel 7, so that Kai and Kyy are of first and second order of smallness respectively. It turns out that the exact result can be specialised to yield the S-matrix  

If the radiative widths Tg and Hy are very small and the background constant Kay is neglected, then the formula simplifies to the following useful expression  

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