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The scattering diameters of Sgr A* and several nearby OH masers (~ 1" at 1GHz) indicate that a region of enhanced scattering is along the line of sightto the Galactic center. We combine radio-wave scattering data and free-freeemission and absorption measurements in a likelihood analysis that constrainsthe following parameters of the GC scattering region: The GC-scattering regionseparation, d; the angular extent of the region, \psi_l; the outer scale onwhich density fluctuations occur, l_0; and the gas temperature, T. The maximumlikelihood estimates of these parameters are d = 133_{-80}^{+200} pc, 0.5degrees <= \psi_l <~ 1 degrees, and (l_0/1 pc)^{2/3}T^{-1/2} = 10^{-7 +/- 0.8}.As host media for the scattering, we consider the photoionized surface layersof molecular clouds and the interfaces between molecular clouds and the 10^7 Kambient gas. We are unable to make an unambiguous determination, but we favoran interface model in which the scattering medium is hot (T ~ 10^6 K) and dense(n_e ~ 10 cm^{-3}). The GC scattering region produces a 1 GHz scatteringdiameter for an extragalactic source of 90", if the region is a single screen,or 180", if the region wraps around the GC, as appears probable. We modify theTaylor-Cordes model for the Galactic distribution of free electrons in order toinclude an explicit GC component. Pulsars seen through this region will have adispersion measure of approximately 2000 pc cm^{-3}, of which 75% arises fromthe GC component. We stress the uniqueness of the GC scattering region,probably resulting from the high-pressure environment in the GC.Comment: 39 pages with 9 PostScript figures; LaTeX2e with AASTeX macro aaspp4,  to be published in Ap

Hyperstrong Radio‐Wave Scattering in the Galactic Center. II. A Likelihood Analysis of Free Electrons in the Galactic Center