Is expiation required for one who swore falsely by Allah, intending a thoughtless oath (laghw) and not a deliberate one (aqd), and what should be done in this situation?

If a person swears falsely by Allah concerning a past matter, that is a 'ghamus' oath, for which there is no expiation. Rather, repentance and seeking forgiveness are obligatory, along with restoring rights to their owners if possible, or seeking their absolution if he has usurped a right or harmed someone. However, if he swore unintentionally, that is a 'laghw' (unintended) oath, which is pardoned, with no sin or expiation, as Allah Almighty says: (Allah will not impose blame upon you for what is unintentional in your oaths).