Alpha emission paradox says that an alpha particle with energy ~4 MeV is able to "come out" of the nucleus of U-238 but an alpha particle of energy ~9 MeV is unable to penetrate the Coulomb barrier of the nucleus. My question is, if the charge on the nucleus is positive then the barrier which the 4 MeV alpha particle has to overcome is the nuclear force and not the Coulomb repulsion barrier of the nucleus as the nucleus anyways would repel the alpha particle making it more possible to come out. So why in Gamow's theory we take the barrier as the Coulomb barrier for the 4 MeV alpha particle?
Edit: The potential barrier used to solve the problem is that of Coulomb potential and not of nuclear potential. Coulomb potential barrier makes sense if we are considering the outer alpha particle but when we consider the inner one, Coulomb repulsive potential just makes it easier for the inner one to come out. So why we are considering Coulomb potential barrier for the inner alpha particle?