Interrelation between the isoscalar octupole phonon and the proton–neutron mixed-symmetry quadrupole phonon in near-spherical nuclei

Abstract

The interrelation between the octupole phonon and the low-lying proton–neutron mixed-symmetry quadrupole phonon in near-spherical nuclei is investigated. The one-phonon states decay by collective E3 and E2 transitions to the ground state and by relatively strong E1 and M1 transitions to the isoscalar 2 + 1 state. We apply the proton–neutron version of the interacting boson model including quadrupole and octupole bosons ( sdf -IBM-2). Two F -spin symmetric dynamical symmetry limits of the model, namely the vibrational and the γ -unstable ones, are considered. We derive analytical formulae for excitation energies as well as B( E1) , B( M1) , B( E2) and B( E3) values for a number of transitions between low-lying states.