What is the expiation for a man's oath by God not to touch his wife for six months, and is expiation obligatory for that oath?

There is a difference of opinion regarding the phrase "I call Allah to witness" (أشهد الله) as to whether it constitutes an oath or not. Some hold that it is an oath if the swearer intended it as such, and this is the view of Al-Shafi'i, Abu Thawr, and the Malikis. Others maintain that it is not an oath due to the absence of common usage, such as the Hanafis.

If one swears not to touch his wife for a specific period, he is a muli (one who makes an oath of abstention), and the rulings of ila' (oath of abstention) apply to him if he intended sexual intercourse by "touching." Ila' is when a man swears not to approach his wife. If the period (four months) passes and he has not had intercourse with her, he is given the choice between resuming marital relations or divorce.

If you touch your wife before the period ends, you are liable for an expiation for breaking an oath (kaffarat yamin). It is advisable to reconcile with your wife and treat her kindly. Even if the period has not ended, have intercourse with your wife and expiate for your oath, based on the saying of the Prophet, peace and blessings be upon him: "Whoever swears an oath and then sees something better than it, let him do that which is better and expiate for his oath." The expiation for an oath is feeding ten needy persons, or clothing them, or freeing a slave. Whoever cannot find these, then fasting three days.

If you did not break your oath and did not touch your wife, and she remained silent about her right until the period expired, then there is nothing upon you. You must seek forgiveness for the ila' and not return to it.