Electromagnetic properties of theK=1band in the rotational limit of the neutron-proton interacting boson model

Abstract

Within the framework of the SU(3) limit of the neutron-proton interacting boson model the matrix elements of the angular momentum and the quadrupole operator between states belonging to the $K=1$ band are given in closed forms. To obtain the matrix elements analytically, we first derive the extended $\mathrm{U}(6)\ensuremath{\supset}\mathrm{SU}(3)$ isoscalar factors associated with low-lying bands by using the intrinsic SU(3) states. The extended $\mathrm{U}(6)\ensuremath{\supset}\mathrm{SU}(3)$ isoscalar factor is defined as the product of the ordinary $\mathrm{U}(6)\ensuremath{\supset}\mathrm{SU}(3)$ isoscalar factor and the U(6)-reduced matrix element of the one-body boson operator. Using these results, $M1$ and $E2$ intraband transition probabilities and the electromagnetic moments in the $K=1$ band are derived in closed forms.