2.2.2. Reorientation Effect and Spectroscopic Quadrupole Moments

The reorientation effect [10] is another second-order effect in Coulomb excitation, which provides experimental sensitivity to spectroscopic quadrupole moments (*Qs*) of excited nuclear states. This effect essentially consists in a double-step excitation, in which the intermediate state is identical to the final state, but the magnetic substate is different (see Figure 1). For a given state *Iπ*, reorientation produces a second-order correction to its Coulomb-excitation cross section, which is proportional to the diagonal matrix element *Iπ*||*E*2||*Iπ*, i.e., to *Qs*(*Iπ*). Since this matrix element, and not its square, appears in the expression for cross section, its sign is also an observable. In favourable conditions, the reorientation effect may have a considerable influence on the measured *γ*-ray intensities. For example, in a recent study of 74Kr Coulomb-excited on 208Pb [11], a change of sign of the *Qs*(2<sup>+</sup> <sup>1</sup> ) from negative to positive resulted in a 1.8-fold increase of the 4<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>2</sup><sup>+</sup> <sup>1</sup> /2<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>0</sup><sup>+</sup> 1 intensity ratio measured in coincidence with Kr nuclei scattered at 130◦ in the centre-ofmass frame.

The influence of the reorientation effect on Coulomb-excitation cross sections is often comparable to that of multi-step excitations. Consequently, the impact of the spectroscopic quadrupole moment can compete with, for instance, that of the sign of an interference term. This is why in early low-energy Coulomb-excitation measurements two values of the spectroscopic quadrupole moment were often reported: one corresponding to a positive sign of the 0<sup>+</sup> <sup>1</sup> ||*E*2||2<sup>+</sup> <sup>1</sup> 2<sup>+</sup> <sup>1</sup> ||*E*2||2<sup>+</sup> <sup>2</sup> 2<sup>+</sup> <sup>2</sup> ||*E*2||0<sup>+</sup> <sup>1</sup> interference term, and the other one for a negative sign. This ambiguity can be solved by measuring *γ*-ray yields as a function of the scattering angle, thus exploiting the different angular dependence of the two effects [5,12]. This approach, typically referred to as a differential Coulomb-excitation measurement, is often employed in modern Coulomb-excitation studies. Alternatively, the use of different beam-target combinations in the same experiment can also help to disentangle competing contributions to the cross sections, and more constraints can be provided by including known spectroscopic data (lifetimes, branching ratios, and *E*2/*M*1 branching ratios) in the Coulomb-excitation data analysis.
