Summary of experimental constraints

The experimental factors affecting the energy resolution that can be obtained in practice have been discussed by Winfield et al [10] and previous authors [11,12]. The factors taken into account included the energy and angular resolution of the beam, as well as those of the detectors. To summarise, the best resolution attainable for excitation energy is of order 200 keV, and this requires targets as thin as 0.5 mg/cm². (If plastic polymer targets are used, rather than say solid hydrogen, then the partial thickness of hydrogen is even less). In the case of light beams (A<20) good results can be obtained by recording the angle and energy of just the beam-like particle precisely (though the coincident detection of the light particle from the target can remove background reactions on target contaminants very effectively). More generally, the light particle needs to be recorded. The various options have been enumerated previously [13,14] and are discussed in more detail below:

1.

Rely on detecting the beam-like ejectile in a spectrometer: This has the advantage that the particles are kinematically focussed into a small angular range that can be spanned by a high resolution magnetic spectrometer. If the beam mass is too high, however, the focussing is so great that the required angular resolution becomes prohibitive. A disadvantage is that any spread in the beam energy is translated directly into excitation energy resolution. This must be overcome either by using a dispersion-matched spectrometer (which implies a spatially dispersed beam spot at the target), or else by tagging the energies of individual beam particles somehow. Even then, the resolution is intrinsically limited by the gamma-decay of the detected particles in flight, which spreads the image at the focal plane.

2.

Rely on detecting the target-like ejectile in a Si detector: In this case, the particles are spread over a significantly larger angular range, but it is possible to envisage covering this range with suitable high resolution detectors such as Si strips. Any spread in the beam energy has little effect on the resolution, so no energy tagging is needed and a focussed beam spot can be employed. However, the target thickness becomes an important constraint, due to the differential energy loss suffered by ejectiles produced at different depths, and gives the limit cited above. This method is of course the only possible choice to study the production of unbound states. It can be combined with the detection of recoils or breakup particles near zero degrees, to give improved channel selection.

3.

Detect decay gamma-rays in addition to particles: The limitations on resolution that are imposed by the target thickness can be avoided when gamma-ray energy information is used to give precise excitation energies. This method is clearly limited to bound excited states, but that includes many cases of interest. Taking into account the low intensities of radioactive beams, an exceptionally high gamma-ray efficiency is demanded, say of order 25% or better. This is achievable with modern arrays, but a closely packed geometry is implied, and the Doppler broadening introduced by the angular acceptance of the gamma-ray detectors is a potential problem. This also can be solved, using a segmented germanium detector to measure the point of gamma-ray interaction. For example, with the EXOGAM array [15] in its closest geometry, a typical Doppler-limited resolution of 20 keV is attainable. Then, the target thickness requirements can be relaxed, and the new limitation becomes the multiple angular scattering of the ejectiles. This must not obscure the angular distribution from the nuclear reaction, which is required to identify the transferred angular momentum. Typically, this allows almost an order of magnitude increase in the target thickness, so overall there is an increase in counting rate of a factor of $\sim 2$ compared to option 2 above.

Whilst the third option is very attractive, the experimental challenges should not be overlooked. Of course, gamma-decays will in general occur in cascades and with branching ratios. It will be necessary to measure this information in order to extract angular distributions for individual excited states. Some (usually small) corrections will need to be applied for gamma-ray angular distribution effects. The efficiency of the gamma-ray detectors will also need to be known accurately, especially in order to extract the results for the ground state. The ground state distribution must be obtained from a particle singles measurement, by subtracting suitably scaled numbers of gamma-ray coincident counts. The feasibility of such techniques has been demonstrated in the knockout studies mentioned earlier, e.g. ref. [3], which followed just such a procedure.