Mapped $spdf$ interacting boson model for quadrupole-octupole collective states in nuclei

Dipole bosons are introduced in the interacting boson model (IBM) by means of the self-consistent mean-field method. The constrained mean-field calculations employing a given nuclear energy density functional yield the potential energy surfaces in terms of the axially-symmetric quadrupole-octupole, dipole-quadrupole, and dipole-octupole deformations. By mapping these energy surfaces onto the expectation values of the IBM Hamiltonian in the coherent state of the interacting $s$, $p$, $d$, and $f$ bosons, strength parameters of the $spdf$-IBM Hamiltonian are determined. In an illustrative application to octupole-deformed actinides $^{218-230}$Ra and $^{220-232}$Th, it is shown that effects of including $p$ bosons in the IBM mapping are to lower significantly negative-parity yrast levels, and to improve descriptions of observed energy-level systematic in nearly spherical and transitional nuclei, and of the behaviors of the reduced electric dipole transitions and intrinsic dipole moments with neutron number.