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Description
The merger of a He white dwarf (WD) and a CO WD is the favored formation channel for R Coronae Borealis (RCB) stars. These stars exhibit $^{16}$O/$^{18}$O ratios that are orders of magnitude lower than the solar value. However, it is not fully understood whether such low $^{16}$O/$^{18}$O ratios can be achieved in WD merger remnants for the predicted lifetime of RCB stars of around 1$0^4$ years. In this work, we perform detailed nucleosynthesis calculations of a 3D magnetohydrodynamical simulation of a merger of a 0.3 M$_\odot$ He WD and a 0.6 M$_\odot$ CO WD for 4000 s at which point a steady state in temperature and density is reached. From this point, we follow several radial zones to study the long-term production of $^{18}$O and its variability throughout the burning region. We find that the asymmetric merger process leaves an imprint on the distribution of the abundances at the end of our hydrodynamic simulation. During the long-term evolution up to 100 years, we observe $^{16}$O/$^{18}$O ratios of order of unity, although the timescale on which $^{18}$O is destroyed again is highly location dependent. Importantly, our calculations suggest that in the outer layers of the burning shell, the dominant production channel is $^{14}$C($\alpha$, $\gamma$)$^{18}$O instead of the commonly considered $^{14}$N($\alpha$, $\gamma$)$^{18}$F($\beta^+$)$^{18}$O reaction, whereby the former can be sustained for longer periods of time. Furthermore, these outer regions do not reach the conditions necessary for fast $\alpha$-captures in $^{18}$O to $^{22}$Ne, thus being favorable to maintaining a low $^{16}$O/$^{18}$O ratio.