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Because of the level of precision required in these measurements, there are many effects, subtle and otherwise, which the experimenter must investigate and, if necessary, allow for. These are listed below. Neglect of any of them would cast doubt on the reliability of the inferred value of the quadrupole moment.

(i) The beam energy

From the plots of the various excitation functions in the

previous chapter, it can be seen that they are all strong functions of energy through the adiabaticity In addition, from eq. 2.22

EA

X

a E

Thus it is found that for £ = 1, the fractional change with energy of the parameter F, which is defined in eq. 2.50 and is given by

RE 2 (0'5o£)/ B(E2;O + £) ' (3.3) is about five times the fractional change in the energy. In order then to determine the excitation probability to ±1%, the beam energy must be known to better than ±0.2%.

(ii) Scattering angle

For backscattering there is no problem, since, for example, the fractional change with angle of R ^ (©»£)/ and hence F, is about 0.1%

per degree near 0 = 180°. So an uncertainty of a degree or so in the scattering angle is quite small enough.

However, away from 180°, things are different. For 0 = 90°, the fractional change of F with angle is 2% per degree, requiring the determination of the scattering angle to ~ 0.5%. At smaller

scattering angles, the variation with angle increases — it is 5% per degree at 0 = 6 0 ° .

It should be noted that 0 is the centre of mass angle. The variation of 0 with the lab angle $ is given by

d0 dO 1 + Y* [1 - Y' 2 s i n 2 -k $] cos $ (3.4) where

—k

For the case of largest Y' considered (24Mg on 200Pb), d0/d$ differs from unity by 10% at most.

(iii) The extraction of the peak area

In these experiments the peak in the spectrum due to elastically scattered particles may be as much as 1500 times larger than any inelastic peaks. Because of various effects (see section 3.2.5), the elastic peak has a low energy "tail" which extends down into the region of the inelastic peaks of interest. Thus, to determine the ratio of the areas of the elastic and inelastic peaks, the area of the "elastic tail" under the inelastic peak must be determined in a

reliable and consistent manner.

A useful guide to the quality of the spectrum is the ratio of the height of the inelastic peak to the height of the valley between the elastic and inelastic peaks. In heavy ion scattering, this ratio is ~ 10, which corresponds to an elastic tail which accounts for 5% - 1 0 % of the area of the inelastic peak. Thus the area of the tail must be determined to ±(10% -20%) in order to provide sufficient accuracy in the net area of the inelastic peak. This is done by fitting a

functional form to the spectrum, and using it to estimate the magnitude of the elastic tail under the inelastic peak.

To increase one's confidence in the fitted lineshape, an attempt should be made to determine the lineshape experimentally by collecting spectra under conditions where the excitation probability is

negligible thus revealing that part of the lineshape of the elastic peak which is underneath the inelastic peak. The ability of the functional form to fit these spectra gives confidence in its

appropriateness and the application of such experimental lineshapes to the data will indicate the degree to which the inferred excitation probability depends on the details of the lineshape used.

(iv) The avoidance of nuclear effects

The necessity of taking data under conditions where nuclear

effects are negligible has been pointed out in subsection 2.5.1. This will be considered in more detail in subsection 3.6.1, but the general conclusion is that reorientation-effect measurements should include experimental evidence that the data used for the determination of the quadrupole moment are negligibly influenced by the nuclear force.

(v) Absence of contaminant peaks

In addition to the elastic and inelastic peaks, the spectrum may also contain peaks due to elastic and inelastic scattering from target contaminants, nuclear reactions between the projectile and the target or reactions between the scattered particles and the silicon nuclei in the detector. The last case refers to events where part of the energy of the particle incident on the detector is converted by a nuclear

interaction to gamma radiation which then escapes from the detector — it is the problem of determining the lineshape of the detector.

Clearly, if any of the above processes should contribute counts to the spectrum in the region of the inelastic peak of interest, then errors will occur. A reorientation experiment should, therefore, contain evidence that

(a) there are negligible levels of target impurities which could produce elastically or inelastically scattered particles of an energy similar to the inelastically scattered particles of interest.

(b) the cross section of any nuclear reaction which may produce products in the energy range of interest is negligibly small. (c) the lineshape of the detector does not contain any

significant peaks which may be hidden under the inelastic peak of interest.

3.2 GENERAL