The Galactic Center H II region, G0.18-0.04, also known as the ``Sickle'', is located where the nonthermal ``Arc'' crosses the Galactic plane. The Sickle appears to be the ionized edge of a dense molecular cloud. The source of ionization has been ascribed to both the interaction of the cloud with the magnetic field of the Arc and to the hot stars in the adjacent cluster, AFGL 2004, also known as the ``Quintuplet Cluster''. This paper addresses the relative locations of the stars, the ionized and molecular gas, and the sources of gas excitation and dust heating. The far-infrared forbidden lines of [S III] 18.7 and 33.5 micron, [Si II] 34.8 micron, [Ne III] 36.0 micron, [O III] 51.8 and 88.4 micron, [N III] 57.3 micron, [O I] 63.2 and 146 micron, [C II] 158 micron, and [N II] 205 micron and the adjacent continua were observed with NASA's Kuiper Airborne Observatory at 11 positions around G0.18-0.04, including G0.15-0.05, also known as the ``Pistol''. The beam size was 40'' - 60''. The electron density, the ionic abundances, and the ionization structure of the H II region were estimated from the doubly ionized line fluxes. The density and radiation field found in the photodissociation region (PDR) between the H II region and the molecular cloud were estimated from the [C II] and [O I] line fluxes and the far-infrared continuum. The ionization structure and the PDR properties were compared to shell models of H II regions with varying distances from their exciting stars. The agreement of observations and models indicates that the hot stars of AFGL 2004 are the likely source of ionization of the Sickle. Additional hot stars are necessary to ionize the more outlying positions. However, the low ionization and high PDR radiation field of the Pistol imply that it cannot be as close to AFGL 2004 as is indicated by its proximity on the sky. Instead, the Pistol is probably ionized by the luminous blue variable candidate, Pistol Source A. The extinction to the region was estimated from the IRAS low resolution spectrum of AFGL 2004 and from the distribution of the J, H, and K' magnitudes of previously observed stars in the field. The extinction is fairly uniform, with no apparent enhancement due to the molecular clouds. The strength of Brackett gamma, the 19 micron lines and continuum, and the IRAS 25 micron continuum are all consistent with the absence of a dense, foreground molecular cloud. We conclude that the H II region is on the near side of the dense cloud.
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