Is intercourse permissible between the Adhan and the Iqama, with evidence from the Qur'an and Sunnah?

It is permissible for a man to have sexual intercourse with his wife between the Adhan and the Iqamah, provided he catches the congregational prayer. The default rule is permissibility unless there is evidence to prohibit it, and congregational prayer is obligatory for men in the mosque. An exception to this is if time is short and the man's mind is preoccupied with intercourse, which would affect his devotion in prayer. In such a case, it is permissible for him to engage in intercourse and prioritize it over prayer, even if it leads to missing the congregation, by analogy with someone who has food present or is restraining the two most noxious excretions, as stated in the Hadith: "No prayer when food is present, nor when one is restraining the two most noxious excretions."