Evolution of Octupole Deformation in Radium Nuclei from Coulomb Excitation of Radioactive ${}^{222}\mathrm{Ra}$ and ${}^{228}\mathrm{Ra}$ Beams

There is sparse direct experimental evidence that atomic nuclei can exhibit stable “pear” shapes arising from strong octupole correlations. In order to investigate the nature of octupole collectivity in radium isotopes, electric octupole ($E3$) matrix elements have been determined for transitions in ${}^{222,228}\mathrm{Ra}$ nuclei using the method of sub-barrier, multistep Coulomb excitation. Beams of the radioactive radium isotopes were provided by the HIE-ISOLDE facility at CERN. The observed pattern of $E3$ matrix elements for different nuclear transitions is explained by describing ${}^{222}\mathrm{Ra}$ as pear shaped with stable octupole deformation, while ${}^{228}\mathrm{Ra}$ behaves like an octupole vibrator.

Figure 1

Spectra of $\gamma$ rays emitted following the Coulomb excitation of ${}^{222}\mathrm{Ra}$ (left) and ${}^{228}\mathrm{Ra}$ (right) using a ${}^{120}\mathrm{Sn}$ target (blue, upper), and ${}^{60}\mathrm{Ni}$ (red, lower). The $\gamma$ rays were corrected for Doppler shift assuming that they are emitted from the scattered projectile. Random coincidences between Miniball and the silicon detector have been subtracted. The transitions that give rise to the observed full-energy peaks are labeled by the spin and parity of the initial and final states.

Figure 2

Absolute values of the intrinsic dipole moments ${\mathcal{Q}}_1$ as a function of spin. The values are deduced from the measured matrix elements [14], and correspond to transitions between states with spin $I$ and $I-1$.

Figure 3

Values of the intrinsic quadrupole moments ${\mathcal{Q}}_2$ plotted as a function of spin. The values are deduced from the measured matrix elements given in Table 1. The values correspond to transitions between states with spin $I$ and $I-2$; in some cases they are also derived from diagonal matrix elements. The solid horizontal lines correspond to the values of ${\mathcal{Q}}_2$ obtained assuming that the matrix elements are related by the rotational model.

Figure 4

Values of the intrinsic octupole moments ${\mathcal{Q}}_3$ plotted as a function of spin. The values are deduced from the measured matrix elements given in Table 1. Here the values of ${\mathcal{Q}}_3$ are shown separately for transitions connecting $I^{+}\to (I+1{)}^{-}$, $I^{+}\to (I+3{)}^{-}$, $I^{-}\to (I+1{)}^{+}$, and $I^{-}\to (I+3{)}^{+}$. The upper dashed line is the average value of ${\mathcal{Q}}_3(0^{+},3^{-})$ for the radium isotopes. To aid comparison, the values of ${\mathcal{Q}}_3$ for ${}^{148}\mathrm{Nd}$ have been multiplied by 1.78.

Figure 5

The difference in aligned angular momentum, $\mathrm{\Delta }{i}_x=i_x^{-}-i_x^{+}$, plotted as a function of rotational frequency $\omega$. The upper dashed line corresponds to the vibrational limit, $\mathrm{\Delta }{i}_x=3\hslash$