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We study dynamical interactions of star--planet binaries with other singlestars. We derive analytical cross sections for all possible outcomes, andconfirm them with numerical scattering experiments. We find that a wide massratio in the binary introduces a region in parameter space that is inaccessibleto comparable-mass systems, in which the nature of the dynamical interaction isfundamentally different from what has traditionally been considered in theliterature on binary scattering. We study the properties of the planetarysystems that result from the scattering interactions for all regions ofparameter space, paying particular attention to the location of the"hard--soft" boundary. The structure of the parameter space turns out to besignificantly richer than a simple statement of the location of the"hard--soft" boundary would imply. We consider the implications of ourfindings, calculating characteristic lifetimes for planetary systems in densestellar environments, and applying the results to previous analytical studies,as well as past and future observations. Recognizing that the system PSRB1620-26 in the globular cluster M4 lies in the "new" region of parameterspace, we perform a detailed analysis quantifying the likelihood of differentscenarios in forming the system we see today.Comment: Accepted for publication in ApJ. Minor changes to reflect accepted  version. 14 pages, 14 figure

Dynamical Interactions of Planetary Systems in Dense Stellar Environments