Energy resolution

The spectroscopic study of nuclei via transfer reactions with radioactive beams offers unrivalled prospects for pinning down their structure, but also poses important experimental problems that need to be addressed carefully. Based on our experience in this type of experiment, the TIARA array has been designed to take proper account of the specific problems of using weak radioactive beams. In the first instance we address the question of transfer reactions induced by light targets such as ¹H and ²H contained in solid foil targets of polyethylene. Reactions induced by `heavy ion' targets such as ¹³C or ⁹Be represent interesting possibilities for the future but pose additional experimental problems in terms of cross section and difficult kinematics. Kinematic studies, and our experimental experience, indicate that transfer reactions such as (p,d), (d,p), (d,³He) or (d,t) can be studied by recording the beam-like particle near zero degrees in a high resolution magnetic spectrometer, provided that the beam energy is either defined or measured accurately in some fashion. This works best for light nuclei (A<40) for which the kinematic focussing of reaction products towards zero degrees assists the yield but does not place unreasonable demands upon the angular resolution of the spectrometer. However, it is still necessary to detect the light target-like particle in coincidence in order to be sure of measuring a proper transfer reaction and to remove contaminants from other target elements (notably carbon). Especially for reactions in which the charge of the beam-like particle is changed (e.g. (d,³He)), the target thickness is limited severely in order to maintain good resolution for separating excited states. Typical maximum target thicknesses are $\sim 1$mg/cm² and the achievable energy resolution is >200 keV. For heavier beams, the demands are even harsher, and for excited states the resolution is further damaged by the gamma-decay (and associated recoil) of the excited nucleus as it enters the spectrometer. As an alternative to a spectrometer-based measurement, the light target-like particle can be used to deduce the excitation energy of the nucleus under study. This is kinematically favoured for heavier beams as discussed above, but is also preferable for light nuclei when gamma-broadening of the spectrometer peaks is appreciable. In these cases, the target thickness becomes even more of a limitation on the experiment since the difference in energy loss between the beam and the light ejectile determines the excited state energy resolution. In favourable cases, the combination indicated above, of $\sim 1$mg/cm² and 200 keV resolution could be achieved. Combining all of these considerations, the potential advantages of detecting gamma-rays in coincidence with the charged reaction products are clear. Calculations indicate that the target thickness can be increased by up to an order of magnitude if the energy resolution of the outgoing light particle is no longer the limiting criterion. The new limit is imposed by the need for the light particle to escape and be detected with an acceptably low amount of angular scattering. Together with the detection of the correct element near zero degrees in a $\Delta$E.E telescope, the energy-angle systematics will identify the reaction of interest and allow the angular distributions of light particles to be measured. The gamma-ray detection then allows the selection of individual excited states in the final nucleus. To achieve good efficiency and yet be able to avoid Doppler broadening of the gamma-rays from the fast-moving (0.10-0.20c) beam-like nuclei, large and segmented gamma-ray detectors are required. With the Exogam detectors in a close-packed cube configuration the calculated photopeak efficiency at 662 keV is 28% and a resolution of order 20 keV could be recovered for these gamma-rays. Thus, the thicker target and the gamma-ray efficiency combine to give up to a factor of 3 increase in yield for the same beam exposure, and the gamma-ray energy results in a factor of 10 improvement in the excited state energy resolution. This provides a strong case for combining gamma-ray methods with transfer studies. Not every experiment will reap this full benefit in yield, but the improved energy resolution will always be significant. In addition, information about the gamma-decays between levels could be extracted.