Analytical calculation of the Smith lifetime Q matrix using a Magnus propagator: applications to the study of resonances occurring in ultracold inelastic collisions with and without an applied magnetic field.
We take advantage of the simple expression of the sector adiabatic wave functions of the Magnus propagator to obtain accurate values of the energy derivative of the S matrix which, in turn, is used to get the Smith lifetime Q matrix. The procedure involves the simultaneous generation of both the R matrix and its energy derivative dR/dE which are propagated along the scattering coordinate. We present a few examples of application to the field free He-N(2)(+) inelastic collisions which we previously studied. This method is then applied to the calculation of the lifetime of tuned zero energy Feshbach resonances using a magnetic field. We give and discuss the law of variation as a function of the magnetic field of the Q matrix eigenvalues across such resonance. Some examples of application are given for the He-N(2)(+) collisions in a magnetic field.
Institut des Sciences Moléculaires, CNRS-UMR 5255, Université de Bordeaux, 351 cours de la Libération, 33405 Talence, France.
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Guillon
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Stoecklin