Is expiation incumbent upon someone who swore not to repeat ablution due to obsessive doubts, then repeated it because he forgot to wipe his head?

We advise anyone afflicted by obsessive doubts (waswas) to disregard them and strive against their own soul to abandon them without resorting to oaths, lest one put oneself in a difficult position, as Almighty Allah says: "And do not make Allah an excuse in your oaths." As for a sworn oath made to ignore waswas, and then violating it by repeating ablution (wudu'), there are two scenarios:

1. If the violation is due to waswas (such as doubting the wiping of the head and succumbing to the waswas and repeating the wiping): An expiation for breaking an oath is required, unless one was overwhelmed in making the oath or in violating it, in which case nothing is binding. 2. If the violation is due to certainty that the head was not wiped (and not just doubt): Then nothing is binding, because one has not violated what was sworn upon, which was not to repeat ablution due to waswas.