We present a new method by which wave functions 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 wave functions of lowest-lying states of these nuclei are well treated by this method. By using the wave functions obtained via the $H^n$-cooling method, interacting boson model-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 $E2\mathrm{}$ effective charges are enhanced due to the renormalization, while a quenching occurs in the $M1\mathrm{}$ and $M3\mathrm{}$ parameters for proton bosons. It is shown that the $\chi$ parameters take similar values in the Hamiltonian and in the $E2\mathrm{}$ operator.

• Received 30 September 1996

DOI:https://doi.org/10.1103/PhysRevC.55.748