The work by U. Fano (1961) provides a descriptive picture of the interaction between discrete and continuum states. In between the steps, there occurs the discussion on the Transition operator (T-cap) (the screenshot from that paper is attached for reference [https://journals.aps.org/pr/pdf/10.1103/PhysRev.124.1866]). The author has not talked much about the form of this operator rather than leaving it by saying "some suitable transition operator".

Please share your suggestions and comments on the form and properties of this transition operator or any relevant article(s) where its description could be expected.

Thank you.