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Hategan, Cornel; Ionescu, Remus Amilcar; Wolter, Hermann H. (2020): Siegert state approach to quantum defect theory. In: European Physical Journal D, Vol. 74, No. 4
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The Siegert states are approached in framework of Bloch-Lane-Robson formalism for quantum collisions. The Siegert state is not described by a pole of Wigner R-matrix but rather by the equation 1 - RnnLn = 0, relating R-matrix element R-nn to decay channel logarithmic derivative L-n. Extension of Siegert state equation to multichannel system results in the replacement of channel R- matrix element R-nn by its reduced counterpart R-nn. One proves the Siegert state is a pole, (1 - RnnLn)(-1), of multichannel collision matrix. The Siegert equation 1 - RnnLn = 0, (n - Rydberg channel), implies basic results of Quantum Defect Theory as Seaton's theorem, complex quantum defect, channel resonances and threshold continuity of averaged multichannel collision matrix elements.