Particle identification from track-etch rates in minerals

NUCLEAR I N S T R U M E N T S AND METHODS 157 ( 1 9 7 8 )

185-193 ; Q

N O R T H - H O L L A N D PUBLISHING CO.

PARTICLE IDENTIFICATION FROM TRACK-ETCH RATES IN MINERALS P. F. GREEN, R. K. BULL and S. A. DURRANI

Department of Physics, University of Birmingham, Birmingham B15 2TT, England Received 8 May 1978 A method of charge identification from etched tracks in minerals is presented which utilizes etch-rate measurements as a function of particle range, as is commonly done in plastic track detectors. Such a method could have considerable application in cosmic ray studies in meteoritic minerals, and also possibly in nuclear reaction studies. Calibration of the track-etch rate to primary ionization is effected externally by accelerator irradiations, the information on track-etch velocity as a function of residual range [Vt (R)] being obtained in a number of ways. Fitting of a response curve for various values of the constant K allows an optimum value of this parameter to be found; and by using this value, fitted Vt (R) profiles can be built up, which lead to charge identification. It is found that Ca and qi track-etch rates are not compatible with data from heavier nuclei. This fact may throw some light on the nature of the track-formation process.

1. I n t r o d u c t i o n The detailed chemical composition and energy spectrum of the galactic cosmic rays contain a great deal of information on their origin, source conditions and subsequent history, as well as on the physical processes involved in these phenomenal-3). This information has, in recent years, often been obtained from studies of etched tracks in plastic stacks exposed to contemporary cosmic rays in balloon or satellite experiments. Particle identification is made by measurement of track-etch rate as a function of range along individual tracks4). Calibration of the charge scale is effected internally by means of the known predominance of Si and Fe nuclei in the cosmic ray fluxS), and extrapolation to heavier nuclei is made on theoretical grounds. The record of heavy cosmic rays stored in extraterrestrial mineral crystals 6) in the form of latent etchable tracks provides an additional source of information on these particles, the potential of which has yet to be fully realized. In addition to providing a wealth of irradiated material, the meteoritic crystals also offer the means for investigating the time-dependence of the phenomena described above, as discussed by Bhandari and Padia7). In a number of papersS-11), the use of total etchable TINT (Track-in-Track) length as a measure of charge has enabled workers to place some constraints on the relative abundance of elements in the VH ( 2 0 < Z < 2 8 ) group of ancient cosmic rays. A number of attempts to use this method to measure the abundance of ultra heavy ( U H ; Z > 3 0 ) cosmic rays have also been described~2,~3). The major limitation of this technique

has been the lack of calibration data, which must be taken f r o m external accelerator irradiations. Measuring total etchable lengths creates a need for calibration with exceedingly high energy nuclei of charge up to ~92, which are not yet generally available. Also, in the work on UH cosmic rays, theoretical extrapolations are necessary, which must be regarded as tentative at present. An alternative method is the track-etch rate versus range (V~ versus R) technique, as used in plastics. Kr~itschmer 14) has developed a two-stage etching technique for tracks in the VH group, to elucidate Vt versus R information, although in this method, also, calibration data are not extensive. We present here a method of particle identification in minerals which is a more direct extension of the technique used in plastics. To relate Vt versus R data to the charge of track-forming particles, a response curve of Vt versus J (primary ionization) is constructed via irradiating with calibration nuclei from accelerators. Since J is peaked at or below the energies at which calibration nuclei are available, interpolation on this response curve allows complete Vt versus R profiles for all nuclei of interest to be constructed, up to Z = 92, from which particle identification may be made. Thus this method is inherently more accurate in charge determination than those based on the total track length, since extrapolation of calibration data is unnecessary. Price et al.~5), who have reported response curves of V~ versus J based on a limited number of nuclei in a number of different minerals, have suggested that such a method should be possible. It is shown below that a resolution of _ 1 unit is possible in the charge region 2 6 < Z < 4 0

186

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and perhaps beyond, with every chance of improvement as further calibration data become available, and as techniques are improved. It should also be noted that this technique may find additional application in nuclear physics experiments, in measuring charges of particles produced in heavy-particle nuclear reactions, especially where high backgrounds of light particles render the use of plastics unsuitable. 2. Experimental details

Two mineral samples were employed in the work described in this paper, both being members of the orthopyroxene family. One sample was of terrestrial origin, namely bronzite from Jackson County, North Carolina (British Museum sample No. BM 65303). The other sample, of extraterrestrial origin, was hypersthene from the Shalka meteorite (British Museum sample No. BM 33761). Large, clear mineral fragments were mounted in epoxy resin on glass mounts, ground and polished, the final treatment being with 1/,tin diamond paste. These polished samples were then irradiated at known dip angles with heavy nuclei for calibration purposes. Beams of 4°Ca and 48Ti at - 5 MeV/nucleon and ~32Xe at 1.1 MeV/nucleon were obtained from the cyclotron of the Joint Institute for Nuclear Research, Dubna, U.S.S.R.; 238U ions at 7 MeV/nucleon were obtained from the heavy-ion accelerator of GSI, Darmstadt, Fed. Rep. Germany; while S6Fe, SSNi, 63CL1 and 84Kr nuclei at 9.6, 4.14 and 1.04 MeV/nucleon were obtained from the LINAC of the University of Manchester, England. After any subsequent treatment (see below), samples were etched in boiling 60% (by weight) NaOH for, typically, one hour. Track lengths were measured with a filar micrometer fitted to a Leitz Ortholux Pol-Bk II optical microscope, using an air objective, with a total magnification of - 1 0 0 0 × . 3. Etch-rate versus range data for minerals from calibration nuclei

The necessary calibration data for this work take the form of etch rate (V,) measurements at various points along the trajectory of various track-forming particles in minerals. Three methods of obtaining these data were employed. a) SurJiwe-etchable tracks For particles which are sufficiently ionizing at

the energy with which they enter the sample, etchable tracks will be produced at the sample surface. Thus a short etch (for a time t) to give a measurable track length L (less than the total etchable range R), followed by a longer etch to enable R to be measured, will give the etch rate, which we will take to be v, = L / t .

(1)

This etch rate, following the convention proposed by Price and Fleischer4), is taken to refer to a point on the trajectory half-way down the etched cone. This '~residual range", RR, is therefore given by

RR

(2)

= R-L~2.

This simple approach was preferred to the integrating method (see, e.g., ref. 1), in which t may be expressed by the relation =

fR L - dv, l

"

(3)

In practice, these two approaches were found to give nearly identical results, differences in the resulting etch-rate versus range profiles only being important where Vt reaches its maximum value for a given ion. The magnitude of these differences depends, to some extent, on the etch time employed (owing to the length of the etched track portion), the difference amounting to -10%, after 1 h. Shorter etch times were often used in our experiments for samples where the etch rate was near the maximum, in order to reduce this discrepancy. A limitation on the applicability of this technique is set by the time taken by a track to etch out radially (at the etch rate of the bulk material, VB) to such a width as to render the track visible by optical microscopy (-0.2/zm). If, for tracks having very high etch rates V~, this time is larger than the time taken by the etchant to reach the end of the track, then this method cannot be used. To overcome this limitation where necessary, a new "etch-anneal-etch" method was used. In this method, following a short etch, after which the track was still not visible, the sample was annealed sufficiently to remove the remaining unetched track portion. Annealing conditions usually employed were 700°C for 2 h, on the basis of extensive annealing experiments on Kr tracks in bronzitel6). A further etching for 30-60 rain was then carried out in order to enlarge the originally etched track to

PARTICLE

IDENTIFICATION

visible width, thus allowing a measurement of L to be made. The initial etch time was used to calculate Ft. The original etchable range in these samples was measured in an unannealed control sample which was simply etched for, typically, 60 min. b) Non-surface-etchable tracks For particles which enter the sample with such high energies that the etchable portion of the trajectory lies below the sample surface, it is possible to remove the non-etchable part of the trajectory before applying procedure (a) above. This was done in our experiments either by placing a layer of absorber material (e.g., AI foil) above the sample during irradiation, so as to degrade the particle energy, or by removing the sample surface itself, by repolishing, possibly after grinding. Using methods (a) and (b), it is possible to prepare a series of samples, either by irradiating through different thicknesses of absorber, by polishing away different thicknesses of surface, and/or using different incident particle energies, in order to obtain etch-rate data at various values of range. c) L-R plots The third method is a slight adaptation of the L-R plot procedure of Price et al.~5). In this technique, a sample containing collimated tracks at a known dip angle is ground and repolished at a small angle to the original surface, preserving a little of the latter. In this way, all values of range from zero to R, the total etchable range of the particle at the sample surface, are available in a single sample. The tracks with the lowest ranges will be fully etched. If the etched range of these tracks is plotted against horizontal position across the sample from some (arbitrary) origin, extrapolation of this relationship into the region of the sample where tracks are not fully etched yields the range of tracks, and thus V~ versus R data may be obtained. Fig. 1 shows the method used in measuring L and R on tracks at a known dip angle 5. Measurements of the projected lengths $1 and S 2 were made from the centre of the track opening to the furthest projection of the track tip in the track direction. L and R were then evaluated from the approximations S~ --L cos 6 and $2 -~R cos 6. These measurements do not take into account the effect of removal of the sample surface at the bulk etch rate VB, which, as indicated in fig. 1, means that

FROM T R A C K - E T C H

RATES

187

the values of V~ and R derived from the methods described above will be slightly lower than the true values. These effects can be described theoretically by a simple model~7), which is not presented here. Since the bulk etch rate will, in general, depend on crystallographic orientationlS), there should be a small dependence of measured V~and R values on the orientation of tracks. In practice, track parameters measured in the above way were found not to vary with track orientation in any significant, systematic way for tracks of Fe and heavier nuclei. We take this to indicate that the effect of bulk etching on the determination of these parameters may be neglected. Work is currently in progress on a more detailed study of such effects, and allowance may be made for these in further developments of this technique. Crystallographic orientation was found, however, to influence measurements on tracks due to Ca and Ti nuclei, a point which will be further discussed below. The full set of data in terms of V, versus RR obtained by the above methods is shown in fig. 2, for tracks due to Ca, Ti, Fe, Ni, Cu, Kr, Xe and U nuclei. The curves drawn in fig. 2 are discussed below. Data for U and Xe tracks were obtained by the etch-anneal-etch method described above. For Kr and Cu tracks, methods (a) and (b) were used, while for the remaining nuclei L-R plots were used. In the latter case the individual L-R plots for each ion [which show considerable spread, and contain many points~S)] were converted to a few mean values, as shown in fig. 2. Values of bulk-etch rate ~ were found to vary with crystallographic orientation in the samples, in the range 0.2--0.5~m/h for bronzite and from 0.6-1.2/~m/h in hypersthene. It is clear from fig. /

,B'2

.q

~-

(

j

, /I

Fig. l. The approximations S l = L c o s & and S 2 = R c o s 6 (where 6 is the dip angle) are used in measurement of etched length L and range R which yield etch-rate versus residualrange data (see text). The effect of the amounts of surface removal VB t I and VB t 2 (shown exaggerated in the figure) after the respective etch times q and t 2, on L and R are ignored.

188

P.F.

GREEN

et al.

BRONZITE

HYPERSTHENE

/

200

0

Vt (}Jm/hr) 100

5Lxe

o

~×e

50

+-->t

20

\ \

1 0

I 10

J 20

?

3~

2 F e 28Ni

2

36Kr

I

30

I

4.0

I

1

1

t

.--

50 60 70 80 Residua[ Range(pro)

I 26F(~ 20 10

29 1

I

30

l+0

I

I

I

I

50 60 70 80 Residual Range (/urn)

Fig. 2. Final calibration data of etch-rate Vt versus residual-range from m e a s u r e m e n t s on eight nuclei (symbols as in fig. 4) in two minerals, bronzite and hypersthene. M e a s u r e m e n t s by various m e t h o d s (see text) have been averaged to yield these data. T h e curves are those predicted for the nuclei specified from the fitted response curve of fig. 4, and suggest a possible charge resolution of _+1 unit in the region 26_
2 that our measured values of V~ for tracks of all nuclei heavier than Ti are much in excess of these figure, and this supports our foregoing discussion of the influence of VB on the measurement of track parameters.

aZ,2 Ii n J fl2-

L-

f12 (1- - - - ~ ) + K--fl21'

(4)

where Z* is the "effective charge" of the particle2°), and is given by

Z2/~]j,

4. Response curve of Vt versus J: optimization of K

Z* = Z 1 - e x p

(5)

To achieve our desired aim of identifying trackforming particles form etch-rate versus range measurements on individual tracks, we must be able to predict the response of all nuclei in the charge range of interest, using the calibration data derived from tracks of a few nuclei. In this analysis, we shall assume that the track-etch rate Vt at a particular point on the trajectory of a given particle, is a unique function of the primary ionization j~9) appropriate to that point. Knowledge of the dependence of J on the range of individual nuclei then allows construction, from the data in fig. 2, of a response curve of V~versus J, which can then be used to predict I/it versus range profiles of any nuclei .of interest. The primary ionization may be expressed, for a particle of relative velocity i3(=v/c) and charge Z, as

and a and K are constants for a given detector material. Theoretical range-energy relations may be used to convert eq. (4) into J versus range-profiles for any nuclei. However, these profiles are not directly comparable with the data of fig. 2, because of the existence of the "range deficit" as defined by Fleischer et al.~), i.e., the lowest-energy portion of the particle trajectory, where ionization falls to such a low level that the track-etch rate approaches that of the bulk material. For this reason the etched ranges of particles that are etchable from a sample surface will be less than their theoretical range. Price et al. 21) found that, using lowenergy I, Br and Fe nuclei (<2MeV/nucleon), consistent values of range deficit for those nuclei

PARTICLE

IDENTIFICATION

could be derived by comparing etched ranges and theoretical ranges. They used these measurements to derive a value of the constant K in eq. (4). However, in comparing such measurements over a wider range of particle energies, we have found that no consistent value of range deficit can be calculated for each ion. Table 1 shows these measurements in bronzite, with theoretical range derived from two sourcesn,23). As indicated in the table, range deficits increase with particle energy in all cases where we can make such a comparison. Of the two range-energy tabulations used, that due to Henke and Benton n) (H.B.) is found to give much better agreement with experimentally measured (etched) ranges, especially at higher energies, than that due to Northcliffe and Schilling 23) (N.S.). Consequently, H.B. data were used in the following work. The data of table 1 tend to suggest that measured values of range deficit may be significantly influenced by inaccuracies in rangeenergy relations. In the absence of any solution to this problem, a general method of allowing for range deficits was adopted. A "threshold" was assumed in J, such that this value was equal to the maximum value of J for the lightest nucleus of which tracks could be observed in the minerals of interest. On the basis of L-R plot studies, Ca was adopted for both bronzite and hypersthene. The ranges corresponding to this value of J for each ion are then the range deficits, which must be added to the measured residual ranges of fig. 2 to render them equivalent to theoretical ranges. Having made these corrections to the data of

FROM T R A C K - E T C H

189

RATES

fig. 2, values of J corresponding to each etch rate for the varying calibration nuclei may be calculated from eq. (4) and H.B. In this way, the response curve can be built up. However, although in eq. (4) the constant a is merely a scaling factor, the value of K influences the form of the J(E) curves, and also, therefore, of the J(R) curves for each ion. Thus it is necessary to adopt an optimum value of K such that different nuclei, producing the same primary ionization at certain points along their trajectory, form tracks having the same etch rate at these residual ranges. To find this optimum value, a response curve was constructed for a range of values of K (from 8.5 upwards); and for each value of K a curve was fitted to the data points in the form of a third-order polynomial. The goodness of the fit was evaluated for each value of K on a least-squares basis. The optimum value of K is taken to be that which gives the least deviation of points from the fitted line. An optimum value of 8.9 was found for bronzite and hypersthene, in contrast to the value of 9.7 given by Price et al.2'). Variation of _+0.1 about our value did not significantly affect the fitted curve. The present value is considered to represent a more reliable estimate, because the measurements of Price et al. were confined to low-energy nuclei (<2MeV/nucleon), whereas the measurements presented here cover a wide span of energies up to N 10 MeV/nucleon. Fitting the curves on a Z 2 criterion did not change the values of K obtained. The analysis was also found to be insensitive to the value of range deficit selected for each nucleus. Variation of _+3 units in the "threshold" of

TABLE I Measured etched ranges for various particles, as shown, together with theoretical ranges derived from two sources, Henke and Benton 22) (H.B.) and Northcliffe and Schilling 23) (N.S.). Also shown are the range deficits, defined as the difference between etched and theoretical ranges. No consistent value can be defined for each particle. Particle

Kr Kr Kr Cu Cu Ni Ni Nb Xe

9.6MeV/nucl 4.14MeV/nucl 1.04 MeV/nucl 4.14MeV/nucl 1.04 MeV/nucl 4.14MeV/nucl 1.04 MeV/nucl 4.14MeV/nucl 1.1 MeV/nucl

Measured etched range (um)

Theoretical range (~ m)

Range deficit (/1m)

H.B.

N.S.

H.B.

N.S.

56.5 _+0.4 24.4 _+0.7 7.75___0.08 20.5 _+0.9 5.88___0.05 21.0 -+0.8 5.59_+0.07 23.2 --0.2 9.13-+0.06

63.7 27.3 9.31 25.7 8.31 24.13 7.73 26.8 11.39

78.8 31.8 11.0 29.5 9.75 28.0 9.20 32.0 14.0

7.2 _+0.4 2.9 +_0.7 1.56_+0.08 5.2 _+0.9 2.43+_0.05 3.13_+0.08 2.14+_0.07 3.6 -+0.2 2.26~0.06

22.3 +_0.4 7.4 _+0.7 3.25+_0.08 9.0 _+0.9 3.87+_0.05 7.0 _+0.8 3.61 +_0.07 8.8 -+0.2 4.87+_0.06

190

P.F. GREEN et al.

J in these calculations did not affect the final K value in either mineral. Part of the V~versus J response curve for bronzite is shown in fig. 3 for values of K = 8.5, 8.9 and 9.7. The effect of varying K is best seen in the group of points with etch rates between 9 t t m / h and 14/~m/h. With K = 9.7, Kr data fall above Cu data, which in turn fall above Ni data. At K = 8.5 the trend is reversed, while for K = 8.9, the data for all nuclei fall along a single curve, and the spread is greatly diminished. The complete response curves for both minerals, with data for all nuclei currently investigated, are shown in fig. 4, where values of range deficits are also shown. In the fitting of the solid curves, the U, Ca and Ti data were left out. Omission of Ca and Ti data did not affect the optimum K value, but although at first sight these points would seem to define an acceptable asymptotic approach to V~, these nuclei give etch rates which do not correlate at all well with data from heavier nuclei, being too high for their J values. This point is further discussed below. The U data and the extension of the response curve to high J (dashed line) must, at present, be regarded as tentative; but with further experiments, we expect that the response curve will be extended with confidence into this region. It does seem, however, from measurements in both minerals, that the etch rate tends towards saturation at high J. From the curves of

fig. 4, V~versus residual-range profiles may be calculated in the reverse way to the procedure discussed in this section. These curves are those shown in fig. 2, for a number of nuclei in the charge region where reliable calibration data are available. An interesting point emerges if we attempt to represent the response curve of V~ versus J as a power law, a relationship which has been assumed in the past. In bronzite it is found that (excluding U data) such a relationship can only be represented by two separate indices, viz. 8.1 below J = 22, and 3.3 for J above this value (up to JN40). The assumption of general power-law behaviour is therefore invalid. 5. E n h a n c e m e n t of Ca and Ti t r a c k - e t c h rates

Although we have shown above that etch-rate data for Fe and heavier nuclei are mutually consistent for the optimum K value (= 8.9), we have found (see section 4) that tracks of Ca and Ti nuclei do not fit into this scheme. Fig. 2 shows an etch rate for Ca tracks in bronzite of 1.6 # m / h at a residual range of - 4 # m . If we extend the V, versus J response curve for bronzite, as shown by the dotted line in fig. 4, through the Ca and Ti data points, then this predicts the above etch rate (1.6/zm/h) at ranges of 35/.zm, 53 # m and 64 Fzm in Fe, Ni and Cu tracks, respectively. This is in great contrast to our experimental results, which

oCa Z~T i x Fe

ONi uCu + Kr

Vt

{~Jm/hr) 20

15 D

10

C +/DO

J

5

0

[]

I 15

I 20

15 J

I 20

I 20 J

I 25

I 30 J

Fig. 3. Response curves of Pi versus J in bronzite, derived by using three values of the constant K in eq. (4). A value of 8.9 is found to give the m i n i m u m variation o f points from different nuclei about the fitted curve in both bronzite and hypersthene, and is adopted as our optimum value of this constant.

PARTICLE

IDENTIFICATION

FROM

TRACK-ETCH

BRONZIT E

Vf [}Jm/hr)

191

RATES

HTPERSTHENE

-9-

200

0

100 50

20

Range defictfs~ bron hyp. Ca 5 1 66 Ti k 1 t~6 Fe 3 3 I 36

,~ x

10

i

Ni Cu Kr

2 9 31 30 3.1 31 3.1 3 2 3.3 3.9 60

Xe

5

U

2

I

0

I

I

I

1

I

10

20

30

60

50

I

I

60 70 JlK=89)

I

I

80

0

[

10

1

I

I

I

20

30

60

S0

I

I

60 70 J (K=89)

I

80

Fig. 4. Full Vt versus J response curves, using K = 8.9 for both bronzite and hypersthene. The solid curves are fitted by excluding the U, Ca and Ti data. Measurements on U tracks are as yet tentative, but both curves show a saturation o f etch rate at high J. Ca and Ti data are incompatible with data from heavier nuclei, as discussed in the text,

suggest that Vt should fall to this value at ranges of 20 #m, 28/2m and 32/~m, respectively, for the above nuclei. The observation that Cu nuclei at 9.6 MeV/nucleon (having a range of N56 gm) are not etchable in bronzite also illustrates this contrast, since extrapolation of the Ca etch rate predicts an etch rate of - 2 / 2 m / h for such Cu nuclei. Therefore it seems that the etch rates of the lightest nuclei, Ca and Ti, are enhanced above the val•aes expected on the basis of data from heavier nuclei. Values of K in excess of 10.5 are necessary for Ca and Fe data to be mutually consistent, a value which cannot hold for the main body of the response curve. Some evidence for enhanced etch.ability of light nuclei was also reported by Price et al.15). It is possible that this may be due to inelastic nuclear collisions in the lowest energy portion nf the track, as suggested by these authors, although the energies at which such processes become important would seem to be too low ~) to explain the extent of the total etchable region of Ca tracks (N 5/~m). It is of interest that the nature of Ca and Ti tracks in bronzite varied markedly with crystallographic orientation in the sample. Because Vt for Ca and Ti tracks is not very much greater than bulk

etching rates, we would expect some variation in track shape with orientation. However, the observed differences were much larger than could be understood as being purely due to this influence. These differences were present, moreover, in Ca and Ti TINTs (Tracks-in-Track)8), which should not be affected as greatly by bulk etching as are surface tracks. Thus the observed effects may be due to actual differences in track-formation processes in different orientations. 6. Discussion In the light of the foregoing results, it is not possible at present to extend the above techniques of particle identification to tracks of the lighter portion of the VH group of nuclei. Such work must wait until more understanding of the problems discussed above has been gained. However, we have shown that it is possible to use track-etch rate in minerals to provide charge identification for nuclei of Z > 2 6 . Application of the technique to the study of the UH cosmic rays in meteoritic minerals has only recently begun, using sequential etching of mapped tracks to provide V~ versus range data on these fossil tracks. On the basis of the data in fig.

192

e . F . GREEN et al.

2, plus the extensive L - R plot studies which provided these s m o o t h e d data, it should be possible to obtain a resolution in these m e a s u r e m e n t of ± 1 charge unit in the charge region 26_
be extended to other minerals (e.g., olivine, feldspar) before far-reaching conclusions may be drawn. However, on the basis of our results it is tempting to postulate that the e n h a n c e m e n t of the etch rates for Ca and Ti tracks over that expected from primary ionization may be due to a contribution to etchable damage from secondary ionization in the low-energy region of the trajectory of these nuclei. At low values of fl, a larger proportion of low energy & r a y s will deposit energy within a few tens of ~ of the particle trajectory than in the high-fl regions of the trajectory25). Therefore the damage produced by primary ionization may be s u p p l e m e n t e d by this process. Channelling of these low energy a rays may produce crystallographic effects as found above. This must remain a tentative suggestion until more detailed investigations of these lightest observable (i.e., etchable) nuclei are m a d e ; but such investigations may offer new insight into our understanding of the trackformation process. We would like to thank Dr. R. Hutchison of the British M u s e u m (Natural History) for the supply of samples. T h a n k s are also due to Dr. V. Perelygin and Professor G. Flerov of the Joint Institute for Research, Dubna, Dr. R. Spohr of the G.S.I., Darmstadt, and Dr. R~ B. Clark of the LINAC, Manchester, for providing irradiation facilities. The financial support of the Science Research Council is also gratefully acknowledged.

References t) R. U Fleischer, P. B. Price and R. M. Walker, Nuclear tracks in solids (University of California Press, Berkeley, 1975). 2) M. H. Israel, P. B. Price and J. Waddington, Physics Today (May 1975) 23. 3) j. p. Wefel, D. N. Schramm and J. B. Blake, Astrophys. Space Sci. 49 (1977) 47. 4) p. B. Price and R. L. Fleischer, Ann. Rev. Nucl. Sci. 21 (1971) 295. 5) G. Siegmon, H. J. K~hnen, K.-P. Bartholom~i and W. Enge, Solid stale nuclear track detectors, Proc. 9th Int. Conf., Munich, 1976,Editors: F. Granzer, H. Paretzke and E. Schopper (Pergamon Press, Oxford, 1978) 137. 6) R. k Fleischer, P. B. Price, R. IVl. Walker and M. Maurette, J. Geophys Res. 72 (1967) 331. 7) N. Bhandari and J. T. Padia, Proc. 5th Lunar Sci Conf. (1974) 2577. 8) D. Lal, R. S. Rajah and A. S. Tamhane, Nature 221 (1969) 33. 9) T. Plieninger, W. Kr~itschmer and W. Gentner, Proc. 3rd Lunar Sci. Conf. (1972) 2933. 10) T. Plieninger, W. Kr~itschmer and W. Genmer, Proc, 4th Lunar Sci. Conf. (1973) 2337.

PARTICLE

IDENTIFICATION

11) R. K. Bull and S. A. Durrani, Earth and Planet Sci. Lett. 32 (1976) 35. 12) O. Otgonsuren, V. P. Perelygin, S. G. Stetsenko, N. N. Gavrilova, C. Fieni and P. Pellas, Astrophys. J. 210 (1976) 258. 13) V. P. Perelygin, S. G. Stetsenko, P. Pellas, D. Lhagvasuren, O. Otgonsuren and B. Jakupi, Nucl. Track Detection 1 (1977) 199. 14) W. Kr~itschmer and W. Gentner, Proc. 7th Lunar Sci. Conf. (1976) 501. 15) p. B. Price, D. Lal, A. S. Tamhane and V. P. Perelygin, Earth and Planet Sci. Lett. 19 (1973) 377. 16) p. F. Green, PhD Thesis, Birmingham University (1978). 17) R. K. Bull, PhD Thesis, Birmingham University (1975). 18) G. W. Dorling, R. K. Bull, S. A. Durrani, J. H. Fremlin and H. A. Khan, Rad. Effects 23 (1974) 141.

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RATES

193

19) R. L. Fleischer, P. B. Price and R. M. Walker, J. Appl. Phys. 36 (1965) 3645. 2o) H. H. Heckman, B. L. Perkins, W. G. Simon, M. F. Smith and W. H. Barkas, Phys. Rev. 117 (1960) 544. 21) p. B. Price, R. L. Fleischer and C. B. Moak, Phys. Rev. 167 (1968) 277. 22) R. P. Henke and E. V. Benton, U.S. Naval Rad. Defense Lab. TR-67-122 (1967). 23) L. C. Northcliffe and R. F. Schilling, Nuclear Data Tables A7 (1970) 233. 24) p. B. Price, I. D. Hutcheon, V. P. Perelygin and D. Lal, in Lunar science III (ed. C. Watkins; Lunar Science Institute, Houston) 619. 25) R. Katz and E. J. Kobetich, Phys. Rev. 170 (1968) 401. 26) j. Tripier and M. Debauvais, Nucl. Instr. and Meth. 147 (1977) 221.