The alpha-element abundances in the most oxygen-poor planetary nebula PN G 135.9+55.9

We present extensive new spectroscopy and imaging of PN G 135.9+55.9. We use these data as constraints to photoionization models to derive limits on the oxygen abundance. We find that PN G 135.9+55.9 has an oxygen abundance less than 1/50 of the solar value. Our models favour a value of 12 + \log O/H between 5.8 and 6.5 dex, confirming that PN G 135.9+55.9 is the most oxygen-poor planetary nebula known (Tovmassian et al. 2001). We also derive Ne/O = 0.5 +/- 0.3, S/O < 0.094, and Ar/O < 0.23. Although the value of Ne/O is nominally high, it need not imply that the progenitor of PN G 135.9+55.9 converted any of its initial oxygen abundance to neon. The helium abundance appears to be very low, He/H ~ 0.08, but a precise determination will require a much more detailed study. We find that Ha/Hb is lower than expected and perhaps variable, a finding for which we have no clear explanation.