Regular Article

Siegert state approach to quantum defect theory

¹ Institute of Atomic Physics, P.O. Box MG-6, Bucharest, Romania
² Fakultät für Physik, Universität München, Am Coulombwall 1, 85748 Garching, Germany

^a e-mail: amilcar@tandem.nipne.ro

Received: 8 November 2019
Received in final form: 6 February 2020
Published online: 9 April 2020

Abstract

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 − R_nnL_n = 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 − R_nnL_n)⁻¹, of multichannel collision matrix. The Siegert equation 1 − R_nnL_n = 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.