Coulomb Excitation and Reorientation of the Octupole State inPb208

The static quadrupole moment ($Q$) of the 2.614-MeV $3^{-}$ level in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been measured by observing the angular distribution of inelastically scattered ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ions following $E3\mathrm{}$ Coulomb excitation. The reduced matrix element for the $E3\mathrm{}$ transition from the ground state to the $3^{-}$ state, $B\left(E3\mathrm{}\right)\mathrm{}\uparrow$, was also obtained. Distributions were taken over the range 80°-170°, using a multiple solid-state-detector array, at $\alpha$-particle energies of 19, 18, and 17.5 MeV, and at an oxygen energy of 69.1 MeV. Differential inelastic cross sections were in the range 10-40 μb/sr for $\alpha \text{'}\mathrm{s}$ and 200-300 μb/sr for oxygen. The 19-MeV data showed strong interference between the Coulomb-excitation amplitude and an amplitude resulting from direct nuclear excitation. The remaining three sets of data showed no such intereference and were analyzed simultaneously using the symmetrized semiclassical Coulomb-excitation theory of Alder et al.: The fitted parameters $B\left(E3\mathrm{}\right)\mathrm{}\uparrow$ and $Q$ are correlated, with best-fit values of $B\left(E3\mathrm{}\right)\mathrm{}\uparrow =0.58\mathrm{}\pm 0.04e^2$ ${\mathrm{b}}^3$ and $Q=-1.3\mathrm{}\pm 0.6$ b. The $\alpha$ data are not very sensitive to $Q$ and yet are essential to the result, for the analysis of the $\alpha$ and oxygen data together limits the acceptable parameter range much more than if the oxygen data alone are used.