Coulomb excitation of vibrational-like states in the even-Aactinide nuclei

Coulomb excitation of vibrational-like states in the even-$A$ actinide nuclei ($230\le A\le 248$) was measured using ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ions in order to test nuclear models describing these states. In particular, the one-phonon octupole vibrational interpretation of the low-lying negative parity states provides an interesting theoretical framework with which to compare the experimental information. The excitation probabilities were determined relative to the elastic scattering by the observation of elastically and inelastically scattered ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ions using a split-pole magnetic spectrometer equipped with a position-sensitive proportional detector. The values of $B(E\lambda ,0_g\to J=\lambda )$ range from 0.5 to 4 single-particle units for $\lambda =2\mathrm{}$ and from 10 to 30 single-particle units for $\lambda =3\mathrm{}$. For those cases, where the $K$, $J^{\pi }$ assignments are known, the agreement between the experimental results and the microscopic calculations by Neegard and Vogel of the $B(E3,0\mathrm{}\to 3)$ for the $3^{-}$ members of the one-phonon octupole quadruplet is good when the Coriolis coupling between the states with $K$ and $K\pm 1$ is taken into account. The magnitudes of the reduced $E0\mathrm{}$ nuclear matrix elements, $\rho (E0,2^{\prime }\to 2_g)$, extracted from the $E0\mathrm{}$ transition probabilities, $T(E0,2^{\prime }\to 2_g)$, for decay of the $\beta$-vibrational-like ${2\prime }^{+}$ state are 0.37 ± 0.06 and 0.43 ± 0.06 for ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, respectively. Several $2^{+}$ states observed in this Coulomb excitation reaction survey are presumed to be $2^{+}$ members of rotational bands based on $0^{+}$ excited states which are strongly populated in the ($p,t$) reaction.