The effect of the quadrupole moment is strongest in scattering through 180° because at other scattering angles substates other than that with M = 0 can be populated and because for a given bombarding energy, the two nuclei approach most closely in 180° scattering.
It is clear that, as well as affecting the total excitation probability, the transient hyperfine splitting also affects the
relative population of the projection substates and hence the angular distribution of the de-excitation gamma rays. A number of distinct experimental techniques have been developed to exploit these effects. These are considered in detail below.
(i) Reorientation precession
If attention is restricted to one particular scattering angle, then the excited nuclei are, in general, partially polarized causing a perturbation of the angular distribution of the de-excitation gamma rays. This perturbation takes the form of a precession plus an attenuation [Gr73]. Because the collision time is short, the amount of precession is small, typically < 1° [Gr73]. One way of detecting this is to place particle detectors at ±90° and to compare the
coincidence rates between each of these detectors and a gamma ray detector. Alternatively, two gamma ray detectors and one particle detector can be used [Bo68]. A problem with this sort of measurement is the attenuation of the gamma ray angular distribution, known as "deorientation", which may occur if the excited nucleus recoils into vacuum. This attenuation is due to the strong magnetic field produced by unpaired atomic electrons. In order to correct for this effect, one must know both the fraction of recoil nuclei which are accompanied by, in particular, a single Is or 2s electron and the magnetic field
at the nucleus due to these electrons. These difficulties combined with the smallness of the effect sought usually result in experimental results with relatively large uncertainties.
(ii) Gamma-ray angular distribution
This method determines the quadrupole moment by its effect on the angular distribution of the de-excitation gamma ray. Scattered
particles are not detected. The same problems that affect
reorientation precession measurements also arise here. Olsen et at.
[0174] present details on the analysis of this type of experiment. It has the advantage that the value of Q^+ obtained is insensitive to the value assumed for the reduced transition probability. However, the effect sought is again very small.
(iii) Gamma-ray lineshapes
This method uses the Doppler shift of the de-excitation gamma rays. To date, its use has been restricted to light nuclei, targets of which are bombarded with projectiles of greater mass, the
de-excitation gamma rays being detected at 0°. The reorientation effect is such that the ratio of the cross section for backward projectile scattering (in the centre of mass frame) to the cross
section for scattering with 0 < 90° is enhanced if > 0 and reduced if Qj<0. This variation is reflected in the angular distribution of the excited target recoils and hence in the details of the Doppler-
broadened gamma-ray lineshape which is seen at 0°. This technique has been discussed by Schwalm et at. [Sc72a]. It also has the advantage that it is insensitive to the value of the reduced excitation
probability. However, deorientation must again be taken into account and the effects sought are almost as small as those in the
reorientation-precession and gamma-ray-angular-distribution techniques, so that the results still have relatively large uncertainties.
(iv) Gamma-ray yields
In principle, the quadrupole moment of a state could be measured simply by measuring the yield of gamma rays from a thick target. Such methods have been used [e.g. Pe69] but they require that, among other things, the gamma ray detector be calibrated absolutely to sufficient
accuracy and the beam-current integration system be sufficiently reliable. These problems can be avoided if one is prepared to
restrict oneself to relative measurements of quadrupole moments. In this case, beam current integration is not required and only the relative efficiency of the gamma-ray detector is needed. The big advantage of this technique is that, by using a thick target of natural composition, information on many nuclei can be obtained with relatively small amounts of accelerator time. However, this must be weighed against the problem of unfolding relatively complex gamma-ray
spectra. These difficulties are discussed by Maynard et al. [Ma77b] in a report of some recent work on isotopes of Ru, Pd and Cd using this method.
(v) Particle-gamma coincidence yields
This, perhaps the most popular of the techniques, aims to infer the value of the quadrupole moment from its effect on the inelastic scattering cross section. No attempt is made to resolve the
elastically and inelastically scattered particles with the particle detector but rather the detection of a coincident gamma ray of the right energy is used to identify an event as inelastic. Being a coincidence experiment, this method is less affected by gamma-ray backgrounds, or target contaminants. However, deorientation may again be a problem, particularly in experiments to measure the excitation of the projectile.
(vi) Particle singles
The most direct method of measuring quadrupole moments using Coulomb excitation is to use particle detectors with sufficient resolution to resolve the elastically and inelastically scattered particles thus dispensing with the need to detect gamma rays and
greatly simplifying the experimental arrangement. This simplification is the main advantage of this method and was the reason why we chose it to make the measurements described in later chapters. The main disadvantage of this method is that, being a singles experiment, it is
E = 60 MeV
<J> =172°
scattering
channel
17 208
Fig. 1.7: A spectrum of 60 MeV O ions backscattered from Pb.
The positions of peaks due to elastic and inelastic scattering and to the reactions 208P b (170 , 160)209Pb and 2 0 8Pb (1 70, 1 80) 2 07Pb are shown.
sensitive to background effects such as target contaminants and
nuclear reactions. For example, fig. 1.7 shows a spectrum of 60 MeV
1 7 » 2 0 8
O ions backscattered from a Pb target. The presence of single
nucleon transfer peaks makes this spectrum useless for the
17
determination of the quadrupole moment of the ground state of O.
Doth magnetic spectrometers and silicon surface-barrier detectors
have been used to detect the scattered particles. So far as solid
angle is concerned, surface-barrier detectors are better for
scattering angles near 180° where annular detectors may be used. For
other scattering angles, magnets will have larger solid angles if
considerable advantage, as is shown in subsection 3.2.3, in having two detectors, one on each side of the target. As there are very few laboratories with two magnetic spectrometers attached to the one scattering chamber, it may be desirable to sacrifice the solid angle and use surface-barrier detectors for $ = 90°.
The other consideration in making a choice between magnets and surface-barrier detectors is the one of lineshape and resolution. Fig. 1.8 shows a spectrum of 120 MeV S ions backscattered from a 208Pb target and detected by an annular surface-barrier detector. The elastic peak has a low-energy exponential tail which is substantial even in the region of the inelastic peak due to the excitation of the projectile. Also, the projectile-excitation and target-excitation peaks are not resolved. This spectrum is probably not good enough to be used to determine Q of 32S. For 32S and heavier projectiles
2+
then, magnets appear to be required. The main problem with a magnet is that all of the particles of a given scattered energy do not appear in one peak, but are split according to their atomic charge states. One must therefore, either determine the relative charge state
distributions of the elastically and inelastically scattered particles or know the variation of effective solid angle along the focal plane to sufficient accuracy to enable one to sum the yields of the
different charge states.
(vii) Other methods
The six techniques used above are not the only possible ways of exploiting the reorientation effect in Coulomb excitation, but they are the most commonly used ones. Two others which have come to my notice are described below.
Andreyev
et al.
[An70] measured the value of Q in 114Cd with a 2+cyclotron using basically the particle-gamma coincidence yield method. Cyclotrons have the difficulty of poorer energy stability than
electrostatic accelerators and also of a pulsed beam which increases the proportion of random coincidences. These problems were overcome by simultaneously bombarding il4Cd targets with 4He + and 12C 3+ ions.