Is a husband's taking back of his wife valid merely by holding and touching her without intercourse, or is intercourse required to take her back after the second divorce?

Reconciliation (raj'ah) is achieved either verbally or by action. Verbal reconciliation occurs through an explicit statement, such as "I have reconciled with my wife," or through writing or a gesture. As for action, it is through sexual intercourse, provided there is the intention to reconcile. Mere touching with desire does not constitute reconciliation unless the husband intends reconciliation by it, which is the view of the majority of jurists. The waiting period ('iddah) for a woman who has been revocably divorced (talaq raj'i) is three menstrual cycles. If the husband does not reconcile with his wife during the 'iddah, she becomes irrevocably separated from him, and she is not permissible for him again except through a new contract and dowry, with her consent and that of her guardian.