does the nucleus contain electrons?

Based on the some study of our scientist and persons who deal with physics, they can say that electrons can trace inside of the nucleus and it is explain by decay process; the alpha decay, beta decay, and electron capture. But, it also shows that it is impossible to find the electrons inside of the nucleus. Because nucleus has energy level of Mev,while electrons has Kv only. Therefore, the electrons needs more energy in able to penetrate the nucleus. So what do you think? Does the nucleus contains electrons?