POLISHED SURFACE SUPPORT

POST ~ QUARTZ BOAT " R-F COIL CARBON CRUCIBLE BASE OF CHAMBER

Fig. 3.6: The apparatus for the preparation of Hg targets. Before

the evaporation, the boat is raised so that its polished surface is in contact with the microscope slides.

Because the bombarding energy must be known to ~ 0.1% (subsection 3.1.3), allowance must be made for the projectile's loss of energy in passing through the target and the carbon facing on the front of the

target. Since the carbon layer is ~ 1 yg.cm- 2 , the beam loses ~ 0.01%

of its energy in passing through it. The correction for the energy

is made by subtracting half of this energy loss from the incident energy. The stopping powers used in these calculations were obtained from Northcliffe and Schilling [No70].

3.2.5 Detectors and Electronics

Throughout these experiments, silicon surface-barrier detectors supplied by ORTEC Inc. were used. The response of silicon detectors to heavy ions has been extensively studied [e.g. Fi73, Se73, Ka74 and references therein]. It is observed that to obtain the same pulse height from the detector as is produced by an alpha particle, a heavy ion must have a higher energy than the alpha particle. This energy difference is referred to, somewhat confusedly, as the pulse height defect. Two obvious causes of energy loss, the energy loss in the gold layer on the front of the detector and the energy loss due to nuclear stopping, together account for about half of the observed pulse height defect [Wi71a]. The remainder is attributed to the increased recombination and trapping in the highly dense plasma

produced by the heavy ion. Extrapolation from the data of Kassirov et

at. [Ka74] suggests that the pulse height defect for 100 MeV 24Mg ions is ~ 1 MeV.

As well as producing the pulse height defect, all of the

processes mentioned above contribute statistical fluctuations to the pulse height. Thus the resolution of these detectors worsens with increasing charge of the particle being detected. Further, this effect is not symmetric about the mean pulse height, but produces a low energy tail on the pulse height distribution. Nothing can be done about the contributions from the gold layer (except by making it as thin as possible) or nuclear stopping, but it might be hoped that recombination could be reduced by applying the highest possible electric field across the detector. For this reason, we requested that ORTEC supply us with annular detectors capable of withstanding fields of at least lVyirf1. For the 90° detectors, ORTEC "F" series detectors, which were rated at 1.4Vynf 1 to 2.0 V y m " 1, were used. Toward the end of this series of measurements, we requested from ORTEC an "F" series detector with an 8 mm hole drilled in it and received a

detector which could withstand 3.5 V ym 1. The performance of this detector was not substantially better than that of the regular annular detectors. Perhaps this is evidence that the limit of what can be achieved by increasing the field has been reached, as suggested by England [En72]. One deleterious effect of a very high field was identified and this is shown in fig. 3.7. The spectra in fig. 3.7 were obtained by placing an "F" series detector in the focal plane of an ESP 90 magnetic spectrograph which was set to detect projectiles scattered through 15° from a Pb target. A 0.8 mm slit was placed in front of the "F" series detector so that it was irradiated by a beam of essentially monoenergetic particles. The only difference between the two spectra in fig. 3.7 is the bias applied to the "F"

series detector. It has been suggested that the broad peak on the high energy side of the elastic peak is due to charge multiplication

in the detector [En77]. Its behaviour with bias supports this. The pulses from the detectors were amplified by ORTEC model 125 preamplifiers and TENNELEC model 203BLR amplifiers and analysed by CANBERRA model 8060 analogue-to-digital converters.

3.3 19 8Hg DATA

The quadrupole moment of the first excited state of 198Hg was determined by bombarding 198HgS targets with various projectiles. It is usual in experiments of this type to use two projectiles only, e.g. 4He and 160. However, as the energy of the first excited state is only 412 keV, peak-to-valley ratios for the 160 spectra are low (~ 8), so, in order to improve the reliability of the result, 12C projectiles were also used. These give spectra with peak-to-valley ratios of better than 12, but have the disadvantage that the reorientation sensitivity parameter p is 7 x10- 4 e~ 1 fm~ 2 compared with

9 x 10"4 e" 1 fm~2 for 160.

The use of three projectiles also provides a check for systematic errors by testing the linearity of the ratio P/F with p (eq. 2.50).

80 MeV Si

bias = 39v

111 II. Ill II I U I channel

Fig. 3.7: The response of an ORTEC "F" series silicon surface-barrier 2 8

detector to 80-MeV monoenergetic Si ions. The two spectra were collected under identical conditions except for the bias across the detector. The broad peak on the high energy side of the full- energy peak in the top spectrum is attributed to the effect of charge multiplication in the detector.

3.3.1 160 and 12C Data

160 spectra were collected at bombarding energies ranging from 60 MeV to 80 MeV. The best peak-to-valley ratio obtained was a value of 9.6 for the 67 MeV data, arid the worst was 6 for the 64 MeV data. These two spectra are shown in fig. 3.8. The full curves shown in

4

E = 67 MeV

<t>= 174-6°

channel

Fig. 3.8: Spectra of 64 MeV and 67 MeV 160 ions scattered through 1 u o

174.6° from Hg. The peaks are labelled according to the

angular momentum of the final state of Hg, the peak labelled 0 being due to elastic scattering. The full lines show the

results of fits to the spectra. See the text for details. The line underneath the elastic peak shows the area subtracted to allow for the other isotopes of Hg in the target.

2

fig. 3.8 are X fits of a mathematical function to the spectra. The function used was

f (z) H [ e x p (- H [ e x p (- z Z/2G 2 ) + f H z 2/2G 2 ) + f Li A exp(- b s s e x p (-(z-p)2/20^ 2 )] + B e x p (-(z-p)2/2G 2 ) ri z I ) {1 - exp (- z2/2c s öh2)}] + B (z > 0) (z < 0) , (3.7)

where z = x - x , x being the mode of the peak, a n d B is a flat background. The parameters H, G , f , p, o , A , b and c were adjusted to obtain

Li S S S

the lowest x 2 • The features of this lineshape are —

(a) It is a skewed Gaussian, that is G and o may be different.

H L

shoulder is a detector artifact which is present in all heavy ion backscattering spectra, including those taken with a 2O0Pb target. It is fitted with a Gaussian positioned about G above the mode and whose relative height f

H

increases with the charge of the detected ion, varying from ~ 1% for 12C to ~ 8% for 24Mg. The actual value of f varies

from detector to detector and tends to increase with the radiation received by the detector.

(c) It has a low energy tail which is zero at x = x , rises to a maximum at about x = x - 2 and falls exponentially with decreasing x thereafter.

In fitting the 160 data, it was assumed that the elastic and inelastic peaks have the same lineshape parameters apart from position and

height. The structure under the elastic peak is due to the other isotopes of Hg in the target. Their intensities were calculated using the assay shown in table 3.1 (p.127).

The area of the inelastic peak was determined by summing the data and subtracting the elastic tail as predicted by the lineshape. The uncertainty in the fit to the elastic tail was determined by varying the height of the tail (parameters A and B of eq. 3.7) and visually judging the effect on the fit. For example, fig. 3.9 shows the same spectrum as fig. 3.8a, but the height of the tail has been altered by ±20%. From this it is concluded that ±20% is a reasonable estimate of the relative uncertainty in the determination of the area of the

elastic tail under the inelastic peak. As this area is about 4% of the gross area of the peak, it contributes about ±1% to the

uncertainty in the net area — a contribution which is of the same order of magnitude as that due to statistics.

The procedure described above for unfolding the elastic and inelastic peaks makes some assumptions about the shape of the elastic tail where it is hidden underneath the inelastic peak. To verify these assumptions, a spectrum of 65 MeV 160 ions backscattered from a

2 0 fl

Pb target was collected. This allowed that portion of the line- i q o

shape which is under the inelastic peak in the Hg spectra to be seen, as the first excited state of 2O0Pb is at 2.615 MeV. Fig. 3.10a

channel

Fig. 3.9: The effect of varying

the height of the background and the low-energy tail by ±20%.

Fig. 3.10: Spectra of 65 MeV 160

ions backscattered from (a)

2 0 8Pb and (b) 198Hg. The full

lines on these two spectra show the results of fits to

the data. Part c shows the

result of fitting the data of part b using lineshape

parameters derived from the data of part a. O on Pb E = 65 MeV

0

0

\ ]

208

shows the fit to this Pb spectrum. Clearly the lineshape of eq. 3.7 is quite adequate. The dispersion in fig. 3.10a is the same as in figs. 3.10b and 3.10c which show the same spectrum — that of 65 MeV 160 ions backscattered from 198Hg — but with two different fits. The full line in fig. 3.10b was obtained by allowing all parameters to vary while that of fig. 3.10c is the same lineshape as in fig. 3.10a. The difference in the values of the excitation probability P ,

exp defined as

inelastic peak area

exp sum of elastic and inelastic peak areas ' (3.8) given by these two different lineshapes is 0.6%. This can be compared with the statistical uncertainties of ~ 1%.

Spectra of C ions were collected at bombarding energies ranging from 43 MeV to 54 MeV. The spectra with the best and worst peak-to-valley ratios are shown in fig. 3.11, where the fits are also indicated. These spectra differ from those above by requiring an additional "long range" component in the low energy tail. This is provided by adding the term

A exp.(- b

I

I

ö

-L Li l_j

to the terms in square brackets for the case z <0 in eq. 3.7. The quantities A , b and c are three additional adjustable parameters.

Li Lj Li

Again, the relative error in the determination of the area of the elastic tail under the inelastic peak was taken as ±20%, this area being less than 2% of the gross area in all cases.

To check this lineshape, a spectrum of 46 MeV C ions back-

2 0 8

scattered from Pb was collected. Fig. 3.12 shows this spectrum with its fit and fits to the 46 MeV 198Hg data obtained by allowing all lineshape parameters to vary and by using the " Pb" lineshape of fig. 3.12a. The difference in the inferred excitation probability is 0.8%, which is again less than the statistical uncertainties.

E - 45 MeV

<1> = 174-6*

E = 4 3 MeV

<l> = 174-6°