Identification of the BeutlerFano formula in eigenphase shifts and eigentime delays near a resonance
Abstract
Eigenphase shifts and eigentime delays near a resonance for a system of one discrete state and two continua are shown to be functionals of the BeutlerFano formula using appropriate dimensionless energy units and line profile indices. Parameters responsible for the avoided crossing of eigenphase shifts and eigentime delays are identified. Similarly, parameters responsible for the eigentime delays due to a frame change are identified. With the help of new parameters, an analogy with the spin model is pursued for the S matrix and time delay matrix Q. The S matrix is found to be put into exp[i(a+bσ>.n̂)]. The time delay matrix Q is shown to be given as Q=12τ_{r}(1+P>_{a}.σ>+P>_{f}.σ>), where the first term is the time delay due to resonance, the second term is the one due to avoided crossing interaction, and the last term is the one due to a frame change. It is found that P^{2}_{a}+P^{2}_{f}=1.
 Publication:

Physical Review A
 Pub Date:
 December 1998
 DOI:
 10.1103/PhysRevA.58.4581
 arXiv:
 arXiv:physics/9811026
 Bibcode:
 1998PhRvA..58.4581L
 Keywords:

 03.80.+r;
 03.65.Ge;
 33.80.Gj;
 34.10.+x;
 Solutions of wave equations: bound states;
 Diffuse spectra;
 predissociation photodissociation;
 General theories and models of atomic and molecular collisions and interactions;
 Physics  Atomic Physics
 EPrint:
 17 pages, 3 figures, RevTeX