I am learning about BCS theory and how Cooper pairs are formed. They have opposite k$k$ and opposite spin. But what I do not understand is why cooperCooper pairs don't break up on their own. I have pictures like this to get an idea.:
But if one electron has $k$$k,$ and the other electron has a momentum $-k$,$-k,$ does this mean they move in different directiondirections in real space? How can the interaction be attractive if so?
It seems like I am missing something here. Maybe you can explain how cooperCooper pairs can move in the same direction but have opposite momentum $k$?