Siegert State Approach to Quantum Defect Theory

• Main Authors: Hategan, C, Ionescu, R. A, Wolter, H. H
• Format: Journal Article
• Language: English
• Published: 26-07-2016
• Subjects: Physics - Atomic Physics; Physics - Nuclear Theory
• DOI: 10.48550/arxiv.1607.07649

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 $1- R_{nn}L_n = 0$, relating R- matrix
element $R_{nn}$ to decay channel logarithmic derivative $L_n$. Extension of
Siegert state equation to multichannel system results into replacement of
channel R- matrix element $R_{nn}$ by its reduced counterpart ${\cal R}_{nn}$.
One proves the Siegert state is a pole, $(1 - {\cal R}_{nn} L_{n})^{-1}$, of
multichannel collision matrix. The Siegert equation $1 - {\cal R}_{nn} L_{n} =
0$, ($n$ - 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.