  We present a new method by which wavefunctions with simple structure are
renormalized so as to contain more complicated structure. This method, called
$H^n$-cooling method, is applied to the study of the quadrupole collective
motion of $^{56}$Fe, $^{54}$Cr, $^{58}$Fe and $^{56}$Cr. The shell-model
wavefunctions of lowest-lying states of these nuclei are well treated by this
method. By using the wavefunctions obtained via the $H^n$-cooling method, IBM-2
parameters are derived from a realistic shell-model hamiltonian and transition
operators. The Majorana interaction becomes sizably repulsive, primarily as an
effect of the renormalization. The bosonic E2 effective-charges are enhanced
due to the renormalization, while a quenching occurs in the M1 and M3
parameters for proton bosons. It is shown that the $\chi$ parameters take
similar values in the hamiltonian and in the E2 operator.
