A solid, nonconducting sphere of radius \(R\) has a total negative charge \(-Q\) distributed uniformly throughout its volume. A narrow, frictionless radial tunnel extends from the center of the sphere to its surface. A small particle of mass \(m\) and positive charge \(+q\) is initially at the center of the sphere. In terms of \(Q\), \(q\), \(m\), \(R\), and fundamental constants, what is the minimum launch speed \(v_0\) required for the particle to escape to infinity?