A small circular wire loop of radius \(r\) is coplanar and concentric with a much larger circular wire loop of radius \(R\), where \(r \ll R\). The mutual inductance of this two-loop system is \(M_0\). If the radius of the inner loop is changed to \(2r\) and the radius of the outer loop is changed to \(2R\), while maintaining \(2r \ll 2R\), what is the new mutual inductance of the system in terms of \(M_0\)?