Heart-shaped nuclei: Condensation of rotational-aligned octupole phonons

The strong octupole correlations in the mass region $A\approx 226$ are interpreted as rotation-induced condensation of octupole phonons having their angular momentum aligned with the rotational axis. Discrete phonon energy and parity conservation generate oscillations of the energy difference between the lowest rotational bands with positive and negative parity. Anharmonicities tend to synchronize the rotation of the condensate and the quadrupole shape of the nucleus forming a rotating heart shape.

Figure 1

Symmetry of a heart-shaped nucleus and the spin-parity sequence of the rotational ground band (even-even, $\sigma =0$).

Figure 2

(a) Energy diff- erence $\Delta E(I)=E_{-}(I)-(E_{+}(I+1)+E_{+}(I-1))/2$ between the positive and negative parity yrast sequences in ${}^{220}\mathrm{Ra}$. (b) Angular momentum $I(\omega )$ as a function of the angular frequency $\hslash \omega (I)=(E(I)-E(I-2))/2$ of the two sequences. Data are from the ENSDF base.

Figure 3

(a) Energies of aligned octupole multiphonon bands. Full lines show $\pi =+$ states and dashed lines show $\pi =-$ states. The straight line is the common tangent of the curves with the slope ${\omega }_c$. (b) Energy in the rotating frame (Routhian), relative to the zero-phonon state. (c) Same as Panel (a), assuming an interaction between the phonons and anharmonicities such that $E_3>3/2E_2>2E_1$. The slope of the tangent, ω, increases slowly during condensation.

Figure 4

An octupole wave traveling over the surface of a quadrupole-deformed nucleus. In Panel (c), the octupole wave has turned by ${90}^{°}$ as compared to that in Panel (b).

Figure 5

Same as Fig. 2 except for the Th isotopes. Data are from the ENSDF base and Ref. [9]. For more expanded versions of Panel (b) see Fig. 15 of Ref. [10].