Coulomb excitation near the barrier

For Coulomb excitation near the barrier, the excitation probability typically falls with scattering angle. However, the number of scattered particles is a strongly forward peaked function and this means that forward angles also make an important contribution to the yield. In addition, the angles near 90 degrees are favoured in solid angle terms in the conversion from the usual $d\sigma /d\Omega$ to $d\sigma /d\theta$. The net results, according to calculations using the de Boer-Winther code is that the maximum overall yield for excitation is achieved using the barrel part of the detector array. If quantitative electromagnetic transition densities are to be extracted, then the beam energy should be chosen to be low enough to be ``safe''. In this context, this means that for all scattering at all angles the nuclei avoid approaching so close that a nuclear interaction can occur. In these circumstances, the interaction probability is greatest at backward angles where the approach of the colliding nuclei is the closest. However, the combination of the increasing elastic yield at more forward angles and the increased $\Delta \Omega (\theta )$ at angles near $\theta =90$ degrees compensate for the falling interaction probability at forward angles, and the net result is that the greater fraction of the recorded counts for Coulomb excited projectiles will come from the barrel. The angles backward of 90 degrees correspond to the the most rapid acceleration of the particle and hence the highest multiple excitations of rotational bands will occur for events recorded in the barrel and the rear annular detector. For spectroscopic studies concentrating on the measurement of excitation energies and gamma-decay branching ratios, the yield for inelastic scattering to excited states can be enhanced by using higher bombarding energies. By straying above the safe energy limits, the interaction mechanism is made less certain, and it is no longer possible to extract electromagnetic matrix elements with confidence. At these slightly higher energies, the counts from the barrel detectors will still dominate the counting rate. Intermediate situations may prove to be advantageous, for example choosing a bombarding energy that is ``safe'' for scattering into the angles spanned by the forward detector and the barrel, but which is too high for the rear annular detector. In this case, the data from the forward annulus and the barrel could be analysed to measure electromagnetic transition strengths, whilst the data from the rear annulus could be included when analysing the excitation energy spectrum of the highest-lying excited states. Particle identification is not provided by the TIARA array, but in the energy range close to the barrier, which is best for Coulex studies, other reaction channels will be weak. Further, the energy angle systematics allow some degree of particle determination and of course the gamma-ray energy as an extra coincidence requirement acts to remove contaminant particle counts from the analysis. In Coulomb excitation it is necessary to measure the angle of the scattered beam both to interpret the data using the de Boer-Winther code (and hence extract electromagnetic B(E2) and other transition strengths), and also to enable Doppler correction of the gamma-ray energy. The angular resolution of the barrel and annular detectors, at better than a degree in the laboratory frame, are sufficient for these purposes.