TY - JOUR

T1 - Cross section versus time delay and trapping probability

AU - Luna-Acosta, G. A.

AU - Fernandez-Marin, A. A.

AU - Mendez-Bermudez, J. A.

AU - Poli, Charles Joseph

PY - 2016/7/29

Y1 - 2016/7/29

N2 - We study the behavior of the s -wave partial cross section σ(k)σ(k), the Wigner–Smith time delay τ(k)τ(k), and the trapping probability P(k)P(k) as function of the wave number k. The s-wave central square well is used for concreteness, simplicity, and to elucidate the controversy whether it shows true resonances. It is shown that, except for very sharp structures, the resonance part of the cross section, the trapping probability, and the time delay, reach their local maxima at different values of k . We show numerically that τ(k)>0τ(k)>0 at its local maxima, occurring just before the resonant part of the cross section reaches its local maxima. These results are discussed in the light of the standard definition of resonance.

AB - We study the behavior of the s -wave partial cross section σ(k)σ(k), the Wigner–Smith time delay τ(k)τ(k), and the trapping probability P(k)P(k) as function of the wave number k. The s-wave central square well is used for concreteness, simplicity, and to elucidate the controversy whether it shows true resonances. It is shown that, except for very sharp structures, the resonance part of the cross section, the trapping probability, and the time delay, reach their local maxima at different values of k . We show numerically that τ(k)>0τ(k)>0 at its local maxima, occurring just before the resonant part of the cross section reaches its local maxima. These results are discussed in the light of the standard definition of resonance.

KW - Scattering

KW - Resonances

KW - Square well

U2 - 10.1016/j.physleta.2016.06.001

DO - 10.1016/j.physleta.2016.06.001

M3 - Journal article

VL - 380

SP - 2494

EP - 2500

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

IS - 33

ER -