Analysis of correlations between dipole transitions $1^-_1\rightarrow 0^+_1$ and $3^-_1\rightarrow 2^+_1$ based on the collective model
R. V. Jolos, E. A. Kolganova
TL;DR
The paper addresses how isovector dipole coupling to low-lying quadrupole–octupole collective modes affects the E1-transition ratio $R$ in near-magic nuclei. It develops a phenomenological collective model with $H=H_{quad}+H_{oct}+H_{dip}$, where a giant dipole resonance phonon couples to $2^+$ and $3^-$ phonons, producing mixed wave functions for the low-lying states and yielding an analytic expression for $R$ in terms of GDR parameters and mixing strengths. The main finding is that GDR admixture lowers $R$ below the pure $7/3$ value predicted by the quadrupole–octupole model, with the reduction increasing for larger $\omega_2$ and $\omega_3$; two parameter choices for $C'/C$ are examined to fit data, using a GDR energy formula $\omega_{GDR}=94.68\,(A^{-1/3}-A^{-2/3})$ MeV. Limitations include treating high-lying $1^-$ strength as a single collective state, and the authors note that realistic calculations require distributing high-lying $1^-$ strength over a range of energies.
Abstract
The purpose of the work is to evaluate effect of the isovector dipole and quadrupole-octupole modes coupling on the $B(E1;1^-_1\rightarrow 0^+_1)/B(E1;3^-_1\rightarrow 2^+_1)$ ratio. The Hamiltonian of the phenomenological collective model is used to calculate mixing of the isovector dipole and quadrupole and octupole modes. The effect of the admixture of the giant dipole resonance to the low-lying collective quadrupole and octupole modes is estimated. It is shown that the coupling of the quadrupole and octupole collective modes to giant dipole resonance leads to decrease of the ratio $B(E1;1^-_1\rightarrow 0^+_1)/B(E1;3^-_1\rightarrow 2^+_1)$ relative to the value 7/3 predicted by the pure collective quadrupole-octupole model.