$Q$-phonon description of the low lying $1^{-}$ two-phonon states in spherical nuclei

The properties of $1_1^{-}$ two-phonon states and the characteristics of $E1$ transition probabilities between low-lying collective states in spherical nuclei are analyzed within the $Q$-phonon approach to the description of collective states. Several relations between observables are obtained. Microscopic calculations of the $E1$ $0_1^{+}\to 1_1^{-}$ transition matrix elements are performed on the basis of the random phase approximation. A satisfactory description of the experimental data is obtained.

Figure 1

Absolute values of the reduced matrix elements for the $E1$ $0_1^{+}\to 1_1^{-}$ transitions in $\mathrm{Cd}$, $\mathrm{Sn}$, and $\mathrm{Ba}$ isotopes calculated with the inclusion of all contributions (dashed line), without inclusion of the contribution coming from the two-quasiparticle admixture (dotted line), and the experimental data (solid line).

Figure 2

The same as in Fig. 1, but for $\mathrm{Ce}$, $\mathrm{Nd}$, and $\mathrm{Sm}$ isotopes.