(Abriged) In the framework of the Herschel GTKP The earliest phases of star formation, we have imaged B68 between 100 and 500 um. Ancillary (sub)mm data, spectral line maps of the 12/13CO(2-1) transitions as well as a NIR extinction map were added to the analysis. We employed a ray-tracing algorithm to derive the 2D mid-plane dust temperature and volume density distribution without suffering from LoS averaging effects of simple SED fitting procedures. Additional 3D radiative transfer calculations were employed to investigate the connection between the external irradiation and the peculiar crescent shaped morphology found in the FIR maps. For the first time, we spatially resolve the dust temperature and density distribution of B68. We find T_dust dropping from 16.7 K at the edge to 8.2 K in the centre, which is about 4 K lower than the result of the simple SED fitting approach. N_H peaks at 4.3x10^22 cm^-2 and n_H at 3.4x10^5 cm^-3 in the centre. B68 has a mass of 3.1 M_sun of material with A_K > 0.2 mag for an assumed distance of 150 pc. We detect a compact source in the southeastern trunk, which is also seen in extinction and CO. We find the radial density distribution from the edge of the inner plateau outward to be n_H ~ r^-3.5. Such a steep profile can arise from either or both of the following: external irradiation with a significant UV contribution or the fragmentation of filamentary structures. Our 3D radiative transfer model of an externally irradiated core by an anisotropic ISRF reproduces the crescent morphology. Our CO observations show that B68 is part of a chain of globules in both space and velocity, which may indicate that it was once part of a filament which dispersed. We also resolve a new compact source in the SE trunk and find that it is slightly shifted in centroid velocity from B68, lending qualitative support to core collision scenarios.
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