The presence of H2D+ in dense cloud cores underlies ion-molecule reactions that strongly enhance the deuterium fractionation of many molecular species. We determine the H2D+ abundance in one starless core, Barnard 68, that has a particularly well established physical, chemical, and dynamical structure. We observed the ortho-H2D+ ground-state line 1_10-1_11, the N2H+ J=4-3 line, and the H13CO+ 4-3 line with the APEX telescope. We report the probable detection of the o-H2D+ line at an intensity Tmb=0.22 +- 0.08 K and exclusively thermal line width, and find only upper limits to the N2H+ 4-3 and H13CO+ 4-3 intensities. Within the uncertainties in the chemical reaction rates and the collisional excitation rates, chemical model calculations and excitation simulations reproduce the observed intensities and that of o-H2D+ in particular.
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