Origin of Low-Lying Enhanced $E1$ Strength in Rare-Earth Nuclei

The experimental $E1$ strength distribution below 4 MeV in rare-earth nuclei suggests a local breaking of isospin symmetry. In addition to the octupole states, additional $J^{\pi }=1^{-}$ states with enhanced $E1$ strength have been observed in rare-earth nuclei by means of ($\gamma$,$\gamma$′) experiments. By reproducing the experimental results, the $spdf$ interacting boson model calculations provide further evidence for the formation of an $\alpha$ cluster in medium-mass nuclei and might provide a new understanding of the origin of low-lying $E1$ strength.

Figure 1

Macroscopic interpretations of the different low-lying dipole modes. (a) $\alpha$-clustering mode, (b) octupole mode, and (c) neutron-skin oscillation [pygmy dipole resonance (PDR)].

Figure 2

$E1$ distribution in ${}^{144-150}\mathrm{Nd}$. Top panel: Experimentally firmly assigned $J^{\pi }=1^{-}$ states or assigned $\mathrm{\Delta }K=0$ ground-state transitions are marked in black [36, 37, 38, 67]. States with $J=1$ assignment but no parity and no $\mathrm{\Delta }K=0$ assignment are marked in red [36]. Dipole states measured in Ref. [66] by means of $(p,p^{\prime })$ and $(d,d^{\prime })$ reactions are presented in gray. Midpanel: $B(E1)\uparrow$ strengths and bottom panel: $n_p/n_f$ ratios predicted by the $spdf$ IBM calculations, respectively.

Figure 3

$E1$ matrix element (a) $⟨1_1^{-}\parallel \widehat{T}(E1)\parallel 0_1^{+}{⟩}^2$ and (b) $⟨3_1^{-}\parallel \widehat{T}(E1)\parallel 2_1^{+}{⟩}^2$ for ${}^{142-150}\mathrm{Nd}$. Shown are the bare contributions to the $spdf$ IBM $E1$ operator of Eq. (2). No fit parameters have been adjusted. (c) Evolution of the fit parameters ${\chi }_{sp}$ and ${\chi }_{df}$ in Eq. (2) used to describe the experimental $E1$ strength.

Figure 4

Same as Fig. 2 but for ${}^{148,150}\mathrm{Sm}$, ${}^{156,160}\mathrm{Gd}$, and ${}^{162,164}\mathrm{Dy}$. In addition, states with an experimentally ambiguous $\gamma$-decay branching are marked in yellow.