6533b7d6fe1ef96bd12664e3

RESEARCH PRODUCT

Zu notwendigen Resonanzkriterien im station�ren Einkanal-Fall

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First will be exhibited, for the stationary case, a connection between the probability, to find a particle in the region of interaction, and the derivative of the scattering phase shift for the momentum. From the idea, that in stationary scattering a resonance is linked with an appreciable increase of this probability, one obtains new and quantitative criteria for the behavior ofδl(k). For instance, the nonresonant behavior can be characterised by the condition 2kdδl(k)/dk<1. The maximum of probability for the particle to be in the region of interaction, is considered in accordance with the criterium of maximal change of the phase shift, as a function ofk. This characterises the location of the resonance. Wigner's lower limit fordδl(k)/dk allows to formulate a resonance condition directly for the cross section. Furthermore will be discussed some connections with the pole approximations of theS-matrix and the “collision lifetime” of Smith.