From a mathematical point of view, the presented solution appears to be correct. Therefore, the cause of the problem is probably an oversimplification of the system. Since the charge at the center of the nucleus does not move, it produces only a static electric charge. In reality, electrons enter and leave the nucleus. Furthermore, this charge should be most of the time outside the nucleus. Therefore, the net contribution might not be negative. On the other hand, since electrons are moving charges, other effects due to the electron’s magnetic field may also be considered.