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By using the supersymmetry method we derive an explicit expression for theparametric correlation function of densities of eigenphases $\theta_a$ of theS-matrix in a chaotic quantum system with broken time-reversal symmetry coupledto continua via M equivalent open channels;$\,\,a=1,..,M$ .We use it to findthe distribution of derivatives of these eigenphases over the energy("phaseshift times") as well as over an arbitrary external parameter.We alsofind the parametric correlations of Wigner-Smith delay timesComment: The text is essentially restructured and new expressions are added 4  pages, RevTE

Parametric Correlations of Scattering Phase Shifts and Fluctuations of Delay Times in Few-Channel Chaotic Scattering