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Mass resolution in investigations of the isotopic composition of heavy elements in cosmic radiation
N U C L E A R I N S T R U M E N T S A N D M E T H O D S 84 (I97O) 2 8 9 - 2 9 2 ; © N O R T H - H O L L A N D
PUBLISHING
CO.
MASS R E S O L U T I O N IN I N V E S T I G A T I O N S OF T H E I S O T O P I C C O M P O S I T I O N OF HEAVY E L E M E N T S I N C O S M I C R A D I A T I O N L. MALMQVIST
Department of Physics, University of Lund, Lund, Sweden Received 14 April 1970 This paper discusses the mass resolution which can be expected in mass measurements of cosmic ray particles stopping in a stack of nuclear emulsions. The mass determinations are based on accurate measurements of the relation between track width and
residual range. The results show that it is possible to perform a mass measurement with a standard error less than 0.5 atomic mass units for nuclei in the charge interval 4 < Z < 12 if a track length of a b o u t 10 m m is available for measurement.
1. Introduction
The M T W - R relations for particles of equal charge but different masses thus constitutes a manifoldness of curves, each curve being characterized by the particle mass M. For two particles of the masses M1 and M2 eq. (3) gives the relation R,/R2 = M,/M2, (4)
In a paper by J/Snsson et al. 1) an experimental method was presented which was used for a study of the isotopic composition of cosmic ray carbon. The identification technique was based on photometric mean track width measurements in tracks of stopping particles in nuclear emulsions. The mass resolution of the method amounted to 0.35 atomic mass units. It is of great interest to learn whether the same method can also be used for other elements than carbon in the radiation. This paper discusses the mass resolution to be expected in a study in the charge interval 4 _< Z _< 12. 2,, Calculation of the expected mass resolution
The energy loss relation of a charged particle passing through an absorber can be written
dE/dR =f~(v,Z),
(1)
where E, Z and v are the kinetic energy, the atomic number and the velocity of the particle, and R is the residual range in the absorber. A relation also including tile mass M of the particle can be obtained if (1) is integrated.
R = M'f2(v,Z).
(2)
When a charged particle passes through a nuclear emulsion it loses energy and a track of silver grains is obtained after the processing. The grain density in the track is a function of the energy loss of the particle. hi a track of a heavy nucleus the grain density is so hJigh that it is not possible to count the number of grains in the track. In this study the mean track width of the track has been measured with a nuclear track plhotometer. The mean track width is a function of the grain density in the track. For particles of the same nuclear charge the relation between R, M and M T W can be written 2) R = M - f 3 ( M T W ).
(3) 289
if R1 and R 2 a r e the ranges from positions having the same MTW. We now want to know which curve, denoted by (M+AM), corresponds to a measurement (R, M T W + A MTW). For two particles of the masses M + A M and M the relation (4) can be written
(R + AR)/R = (M + A M)/M
(5)
for the new MTW-level ( M T W + A M T W ) . This gives
AR/R =AM/M.
(6)
In eq. (6) AR can be substituted by means of the relation A MTW/AR ~- dMTW(R)/dR, (7) giving A M -~ M" A MTW/R(dMTW/dR). (8) By means of this relation a deviation AMTW in the photometrically measured quantity M T W can be transformed into a deviation in the mass A M. The relation (8) has been the basis of the estimate of the error to be expected in a mass measurement. The standard deviation of the M T W measurements at the residual range R i has been determined. This standard deviation has substituted A M T W in formula (8) and the standard deviation in the mass a(Mi) has been calculated. The error in the mass a(M) can finally be calculated from the relation
[i/a(M)] 2= ~ [I/a(Mi)] 2. i=l
(9)
290
L. MALMQVIST
600M T W
TABLE 1
Charge (Z) Number of particles
4, 3
6 10
8 10
10 5
12 10
The procedure only regards statistical errors in the photometric measurements. The results are significant for a real experiment only if all systematic errors are reduced to such a level that they are negligible.
400t
i
I
600 MTw
400~
1
o
i
n
I
50x5~a Z 12 108
200
o
6
;
I
Residualrange(ram)
2o
Fig. 1. The experimental relation between residual range and mean track width obtained with the 5 #m wide slit.
Slitdimension50~10lJ2
200
-
I
3. Experimental details The estimates of the mass resolution are based on photometric measurements of the M T W - R relations for particles in the charge interval 4 _< Z -< 12. The tracks were found in an emulsion stack which consisted of 24 Ilford G5 emulsion sheets, each one being 10 x 10 x 0.06 cm 3 in size. The stack was exposed during a 10-h balloon flight at Fort Churchill in 1963. The degree of development was found to be somewhat below normal, relativistic singly charged particles having a blob density of 13 blobs/100 pm. Table 1 shows the number of particles selected for the study. The nuclei have been identified with certainty in previous studies of the cosmic ray charge spectrum3'4). The particles in the charge group 6 were chosen among the 12C particles found by J6nsson et al.~). The very few beryllium particles were included only because of the great astrophysical interest in the isotopic composition of cosmic ray beryllium. The photometric measurements have been performed with the nuclear track photometer described by J6nsson et al.l). All tracks were measured with a slit arrangement 50 x 5 pm 2 in size. The charge groups 6, 8, 10 and 12 were also measured with a slit arrangement 50 x 10 p m z in size. The photometric measurements started at the end of
!
5
I
I
10 15 Residualrange(mm)
-
121o 8 6_
20
Fig. 2. The experimental relation between residual range and mean track width obtained with the 10 #m wide slit. the tracks and continued to a residual range of 20 mm, if possible. The measurements have been corrected according to the methods described in ref. 1. From the corrected mean track width measurements the M T W - R relations have been calculated. They are shown in fig. 1 and fig. 2 for the slit widths 5/~m and 10 pm, respectively. The MTW-scale is expressed in arbitrary units, but the same in both figures. A comparison shows that the M T W - R relations depend both on the slit width and the charge of the particle. The two different slits cut the largest g-rays at different distances from the track centre. This effect gives rise to different shapes of the M T W - R relations of the same charge. This is best seen for small R-values. From the M T W - R relations the derivatives dMTW/dR have been calculated numerically as a function of residual range for the charge groups shown in figs. 1 and 2. The slopes of the curves for large R-values are slightly uncertain. The standard deviations of the MTW-measurements were calculated from the corrected mean track width measurements for the charge groups 6, 8 and 12. They were nearly constant along the tracks. The variation of the standard deviation along the tracks was found to be about 10%. A small charge dependence was found. This charge dependence is shown in table 2. The figures are expressed in the same MTW-scale as used in figs. 1 and 2.
4. Results The standard deviation of mass determinations has been calculated as a function of measured track length by means of formulae (8) and (9). The results are shown for the 5 pm and 10/tin slit arrangements, respectively, in figs. 3 and 4. The figures show that there exists a large reduction in the standard error of a mass determination when the
ISOTOPIC
12.0
COMPOSITION
1
i
i
Slit dimension 50x5 ~z
Z e,o
4
,~ 4J o
6
I
o
291
OF H E A V Y E L E M E N T S IN C O S M I C R A D I A T I O N
to
20
Residualrange(mm)
Fig. 3. T h e calculated s t a n d a r d deviation o f m a s s d e t e r m i n a t i o n as a function of m e a s u r e d track length with a 5 / ~ m wide slit. T h e circles s h o w the s t a n d a r d deviations obtained in real m a s s
measurements on z~C. measured track length increases up to about 10 mm. Further increase of measured track length improves the mass resolution only slightly. It is obvious that most information about the mass of a particle is found in the range interval 1 < R < 10 mm. It is also clear that there is an increase in the mass resolution for all
as used in the present study. The measurements were carried out in the range interval 1 < R < 12 mm. The experimental masses and the standard deviations of the identified 12C particles were determined for track intervals 1-R mm where 5 < R-< 11 mm. The results are shown in fig. 3. The circles represent the real mass measurements on 12C, and the carbon curve the result of the statistical estimation. The agreement is good. It indicates that the systematical errors are small making the statistical estimation of the mass resolution usable. The calculated standard deviation of mass measurements is expressed in atomic mass units in fig. 5. The curves are valid for 9Be, 12C, 16C, 2°Ne and 24Mg. The figure shows that a standard deviation less than 0.5 units of mass can be obtained with a 5/~m slit for all elements in the charge interval 4 _ Z < 12. It is again
0.8if(M)
•~i N,
I
I
E 0.6 TABLE 2 Charge group tr, (50 × 5) p m ~ slit or, (50 × 10)/~m 2 slit
6 6
8
12
16.9 16.4
17.6 17.1
20.4 19.0
52:5 ?-/~.~o
~ O.g
"~ o
~
s0=s i~snt
......
SO,lO J~st~t
0.2
residual ranges and for the whole charge interval of this study when the 10 #m slit is changed to a 5/~m slit. A comparison between the result of this study and that obtained in the carbon experiment by JiSnsson et al. 1) has been made. The mass measurements in the carbon experiment were performed with the same track photometer and the same 5/~m slit arrangement 12.0
•
I
i
I 5
1 10
Residualrange(rnm)
I 15
20
Fig. 5. T h e calculated s t a n d a r d deviation of m a s s determinations, expressed in atomic m a s s units, as a function o f m e a s u r e d track length. T h e curves are valid for 9Be, z2C, 160, ZONe a n d 24Mg respectively.
clear that the 5/~m slit gives a higher mass resolution than the 10 ktm slit. Some aspects on the slit choice are given in the next section.
I
5. Discussion
~ ~SJ)
~
1
0
n
50x10~2 z
°/4.0 o 12_
li0
Residualrange(mm)
Ii5
20
Fig. 4. T h e calculated s t a n d a r d deviation o f m a s s determinations as a function o f m e a s u r e d track length with a 10 F m wide slit.
Fig. 5 shows that the slit dimensions are very important for the result. The structure of the track varies a great deal in the range interval used for mass measurements. The size of the slit is fixed in this type of photometer. The optimal slit choice for a certain particle charge must therefore be the best compromise between those which are the ideal ones of different ranges. It has not been possible to carry out a systematical investigation of the slit choice problem from the measurements available in this study. Some aspects on the slit size will, however, be discussed.
292
L. MALMQVIST
5.1. THE SLIT WIDTH The factors which influence the mass resolution are evident from formula (3). The standard deviation of the MTW-values was found to be approximately constant along a track and independent o f the slit width. If the slit is made narrower, the track fills the slit to a higher degree and the MTW-value increases according to the changed relation between the track area and the slit area. This means that the derivative d M T W / d R increases when the slit width decreases. Consequently, the slit width should be chosen as narrow as possible. When the slit width is reduced, the &rays o f the track are successively cut. This effect reduces in the mean the derivative d M T W / d R . A smaller derivative means a reduction of the mass information from the track. When the slit width is reduced there is thus one effect which increases and one which decreases the mass information from the track. Obviously there is a best choice of the slit width which is different for different charges. I believe that the 5/am wide slit is a good choice for the charge interval 6 < Z < 10. In a beryllium mass measurement a somewhat narrower slit would be preferable. 5.2. THE SLIT LENGTH
The carbon experiment by JGnsson et al. ~) was at first carried out with a slit corresponding to 100x 6 l~m 2 in the object plane and with a Leitz 22 x objective. The standard deviation of the measured masses of the 12C particles was 0.84 atomic mass units. This result has to be compared to 0.35 atomic mass units obtained with a 50 x 5/~m 2 slit and with a Leitz KS 53 x objective. The difference between the results is most probably chiefly influenced by the large difference in slit length. The main reason for this influence is the following. To get a reliable MTW-value of a measured track section the whole emulsion area in which the
track measurement and the background measurements are made must be uniform. If this is not fulfilled the measurements will not be completely representative for the track section. It is obvious that the probability to find uniform emulsion areas along the track will increase if the slit length is decreased. To what degree the mass resolution could be further increased by choosing a still shorter slit length could not be decided from these measurements. I believe, however, that the mass resolution will increase to some extent for slit length shorter than 50/~m until a constant level is reached when the error from the small scale irregularities in the emulsion is smaller than the statistical error in the grain density of the track. I wish to express my sincere gratitude to Dr. K. Kristiansson and ill. lic. G. JGnsson for much advice and many valuable discussions. I am grateful to Miss B. Lindkvist for an excellent processing of the stack and for the microscopic examination of the plates. I thank ill. lic. U. Dellien, ill. kand. K. SGderstrGm and Dr. K. Kristiansson for leaving the charges of the primaries at my disposal, and Mrs. K. Malmqvist for the dataprocessing. The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research, O A R , through the European Office of Aerospace Research, United States Air Force, under Grant No A F - E O A R 66-35. This is gratefully acknowledged. 1 am also grateful to the Swedish Atomic Research Council and to the Swedish Space Research Committee for their support. References I) G. JGnsson, K. Kristiansson and L. Malmqvist, Report KS 7005 (Lund, 1970). e) G. JGnsson, K. Kristiansson and L. Malmqvist, Astrophys. Space Sci. (1970) in print. a) k. Malmqvist, Arkiv Fysik 34 (1967) 33. 4) U. Dellien, K. SGderstrGm and K. Kristiansson, Report KS 6902 (Lund, 1969).
PUBLISHING
CO.
MASS R E S O L U T I O N IN I N V E S T I G A T I O N S OF T H E I S O T O P I C C O M P O S I T I O N OF HEAVY E L E M E N T S I N C O S M I C R A D I A T I O N L. MALMQVIST
Department of Physics, University of Lund, Lund, Sweden Received 14 April 1970 This paper discusses the mass resolution which can be expected in mass measurements of cosmic ray particles stopping in a stack of nuclear emulsions. The mass determinations are based on accurate measurements of the relation between track width and
residual range. The results show that it is possible to perform a mass measurement with a standard error less than 0.5 atomic mass units for nuclei in the charge interval 4 < Z < 12 if a track length of a b o u t 10 m m is available for measurement.
1. Introduction
The M T W - R relations for particles of equal charge but different masses thus constitutes a manifoldness of curves, each curve being characterized by the particle mass M. For two particles of the masses M1 and M2 eq. (3) gives the relation R,/R2 = M,/M2, (4)
In a paper by J/Snsson et al. 1) an experimental method was presented which was used for a study of the isotopic composition of cosmic ray carbon. The identification technique was based on photometric mean track width measurements in tracks of stopping particles in nuclear emulsions. The mass resolution of the method amounted to 0.35 atomic mass units. It is of great interest to learn whether the same method can also be used for other elements than carbon in the radiation. This paper discusses the mass resolution to be expected in a study in the charge interval 4 _< Z _< 12. 2,, Calculation of the expected mass resolution
The energy loss relation of a charged particle passing through an absorber can be written
dE/dR =f~(v,Z),
(1)
where E, Z and v are the kinetic energy, the atomic number and the velocity of the particle, and R is the residual range in the absorber. A relation also including tile mass M of the particle can be obtained if (1) is integrated.
R = M'f2(v,Z).
(2)
When a charged particle passes through a nuclear emulsion it loses energy and a track of silver grains is obtained after the processing. The grain density in the track is a function of the energy loss of the particle. hi a track of a heavy nucleus the grain density is so hJigh that it is not possible to count the number of grains in the track. In this study the mean track width of the track has been measured with a nuclear track plhotometer. The mean track width is a function of the grain density in the track. For particles of the same nuclear charge the relation between R, M and M T W can be written 2) R = M - f 3 ( M T W ).
(3) 289
if R1 and R 2 a r e the ranges from positions having the same MTW. We now want to know which curve, denoted by (M+AM), corresponds to a measurement (R, M T W + A MTW). For two particles of the masses M + A M and M the relation (4) can be written
(R + AR)/R = (M + A M)/M
(5)
for the new MTW-level ( M T W + A M T W ) . This gives
AR/R =AM/M.
(6)
In eq. (6) AR can be substituted by means of the relation A MTW/AR ~- dMTW(R)/dR, (7) giving A M -~ M" A MTW/R(dMTW/dR). (8) By means of this relation a deviation AMTW in the photometrically measured quantity M T W can be transformed into a deviation in the mass A M. The relation (8) has been the basis of the estimate of the error to be expected in a mass measurement. The standard deviation of the M T W measurements at the residual range R i has been determined. This standard deviation has substituted A M T W in formula (8) and the standard deviation in the mass a(Mi) has been calculated. The error in the mass a(M) can finally be calculated from the relation
[i/a(M)] 2= ~ [I/a(Mi)] 2. i=l
(9)
290
L. MALMQVIST
600M T W
TABLE 1
Charge (Z) Number of particles
4, 3
6 10
8 10
10 5
12 10
The procedure only regards statistical errors in the photometric measurements. The results are significant for a real experiment only if all systematic errors are reduced to such a level that they are negligible.
400t
i
I
600 MTw
400~
1
o
i
n
I
50x5~a Z 12 108
200
o
6
;
I
Residualrange(ram)
2o
Fig. 1. The experimental relation between residual range and mean track width obtained with the 5 #m wide slit.
Slitdimension50~10lJ2
200
-
I
3. Experimental details The estimates of the mass resolution are based on photometric measurements of the M T W - R relations for particles in the charge interval 4 _< Z -< 12. The tracks were found in an emulsion stack which consisted of 24 Ilford G5 emulsion sheets, each one being 10 x 10 x 0.06 cm 3 in size. The stack was exposed during a 10-h balloon flight at Fort Churchill in 1963. The degree of development was found to be somewhat below normal, relativistic singly charged particles having a blob density of 13 blobs/100 pm. Table 1 shows the number of particles selected for the study. The nuclei have been identified with certainty in previous studies of the cosmic ray charge spectrum3'4). The particles in the charge group 6 were chosen among the 12C particles found by J6nsson et al.~). The very few beryllium particles were included only because of the great astrophysical interest in the isotopic composition of cosmic ray beryllium. The photometric measurements have been performed with the nuclear track photometer described by J6nsson et al.l). All tracks were measured with a slit arrangement 50 x 5 pm 2 in size. The charge groups 6, 8, 10 and 12 were also measured with a slit arrangement 50 x 10 p m z in size. The photometric measurements started at the end of
!
5
I
I
10 15 Residualrange(mm)
-
121o 8 6_
20
Fig. 2. The experimental relation between residual range and mean track width obtained with the 10 #m wide slit. the tracks and continued to a residual range of 20 mm, if possible. The measurements have been corrected according to the methods described in ref. 1. From the corrected mean track width measurements the M T W - R relations have been calculated. They are shown in fig. 1 and fig. 2 for the slit widths 5/~m and 10 pm, respectively. The MTW-scale is expressed in arbitrary units, but the same in both figures. A comparison shows that the M T W - R relations depend both on the slit width and the charge of the particle. The two different slits cut the largest g-rays at different distances from the track centre. This effect gives rise to different shapes of the M T W - R relations of the same charge. This is best seen for small R-values. From the M T W - R relations the derivatives dMTW/dR have been calculated numerically as a function of residual range for the charge groups shown in figs. 1 and 2. The slopes of the curves for large R-values are slightly uncertain. The standard deviations of the MTW-measurements were calculated from the corrected mean track width measurements for the charge groups 6, 8 and 12. They were nearly constant along the tracks. The variation of the standard deviation along the tracks was found to be about 10%. A small charge dependence was found. This charge dependence is shown in table 2. The figures are expressed in the same MTW-scale as used in figs. 1 and 2.
4. Results The standard deviation of mass determinations has been calculated as a function of measured track length by means of formulae (8) and (9). The results are shown for the 5 pm and 10/tin slit arrangements, respectively, in figs. 3 and 4. The figures show that there exists a large reduction in the standard error of a mass determination when the
ISOTOPIC
12.0
COMPOSITION
1
i
i
Slit dimension 50x5 ~z
Z e,o
4
,~ 4J o
6
I
o
291
OF H E A V Y E L E M E N T S IN C O S M I C R A D I A T I O N
to
20
Residualrange(mm)
Fig. 3. T h e calculated s t a n d a r d deviation o f m a s s d e t e r m i n a t i o n as a function of m e a s u r e d track length with a 5 / ~ m wide slit. T h e circles s h o w the s t a n d a r d deviations obtained in real m a s s
measurements on z~C. measured track length increases up to about 10 mm. Further increase of measured track length improves the mass resolution only slightly. It is obvious that most information about the mass of a particle is found in the range interval 1 < R < 10 mm. It is also clear that there is an increase in the mass resolution for all
as used in the present study. The measurements were carried out in the range interval 1 < R < 12 mm. The experimental masses and the standard deviations of the identified 12C particles were determined for track intervals 1-R mm where 5 < R-< 11 mm. The results are shown in fig. 3. The circles represent the real mass measurements on 12C, and the carbon curve the result of the statistical estimation. The agreement is good. It indicates that the systematical errors are small making the statistical estimation of the mass resolution usable. The calculated standard deviation of mass measurements is expressed in atomic mass units in fig. 5. The curves are valid for 9Be, 12C, 16C, 2°Ne and 24Mg. The figure shows that a standard deviation less than 0.5 units of mass can be obtained with a 5/~m slit for all elements in the charge interval 4 _ Z < 12. It is again
0.8if(M)
•~i N,
I
I
E 0.6 TABLE 2 Charge group tr, (50 × 5) p m ~ slit or, (50 × 10)/~m 2 slit
6 6
8
12
16.9 16.4
17.6 17.1
20.4 19.0
52:5 ?-/~.~o
~ O.g
"~ o
~
s0=s i~snt
......
SO,lO J~st~t
0.2
residual ranges and for the whole charge interval of this study when the 10 #m slit is changed to a 5/~m slit. A comparison between the result of this study and that obtained in the carbon experiment by JiSnsson et al. 1) has been made. The mass measurements in the carbon experiment were performed with the same track photometer and the same 5/~m slit arrangement 12.0
•
I
i
I 5
1 10
Residualrange(rnm)
I 15
20
Fig. 5. T h e calculated s t a n d a r d deviation of m a s s determinations, expressed in atomic m a s s units, as a function o f m e a s u r e d track length. T h e curves are valid for 9Be, z2C, 160, ZONe a n d 24Mg respectively.
clear that the 5/~m slit gives a higher mass resolution than the 10 ktm slit. Some aspects on the slit choice are given in the next section.
I
5. Discussion
~ ~SJ)
~
1
0
n
50x10~2 z
°/4.0 o 12_
li0
Residualrange(mm)
Ii5
20
Fig. 4. T h e calculated s t a n d a r d deviation o f m a s s determinations as a function o f m e a s u r e d track length with a 10 F m wide slit.
Fig. 5 shows that the slit dimensions are very important for the result. The structure of the track varies a great deal in the range interval used for mass measurements. The size of the slit is fixed in this type of photometer. The optimal slit choice for a certain particle charge must therefore be the best compromise between those which are the ideal ones of different ranges. It has not been possible to carry out a systematical investigation of the slit choice problem from the measurements available in this study. Some aspects on the slit size will, however, be discussed.
292
L. MALMQVIST
5.1. THE SLIT WIDTH The factors which influence the mass resolution are evident from formula (3). The standard deviation of the MTW-values was found to be approximately constant along a track and independent o f the slit width. If the slit is made narrower, the track fills the slit to a higher degree and the MTW-value increases according to the changed relation between the track area and the slit area. This means that the derivative d M T W / d R increases when the slit width decreases. Consequently, the slit width should be chosen as narrow as possible. When the slit width is reduced, the &rays o f the track are successively cut. This effect reduces in the mean the derivative d M T W / d R . A smaller derivative means a reduction of the mass information from the track. When the slit width is reduced there is thus one effect which increases and one which decreases the mass information from the track. Obviously there is a best choice of the slit width which is different for different charges. I believe that the 5/am wide slit is a good choice for the charge interval 6 < Z < 10. In a beryllium mass measurement a somewhat narrower slit would be preferable. 5.2. THE SLIT LENGTH
The carbon experiment by JGnsson et al. ~) was at first carried out with a slit corresponding to 100x 6 l~m 2 in the object plane and with a Leitz 22 x objective. The standard deviation of the measured masses of the 12C particles was 0.84 atomic mass units. This result has to be compared to 0.35 atomic mass units obtained with a 50 x 5/~m 2 slit and with a Leitz KS 53 x objective. The difference between the results is most probably chiefly influenced by the large difference in slit length. The main reason for this influence is the following. To get a reliable MTW-value of a measured track section the whole emulsion area in which the
track measurement and the background measurements are made must be uniform. If this is not fulfilled the measurements will not be completely representative for the track section. It is obvious that the probability to find uniform emulsion areas along the track will increase if the slit length is decreased. To what degree the mass resolution could be further increased by choosing a still shorter slit length could not be decided from these measurements. I believe, however, that the mass resolution will increase to some extent for slit length shorter than 50/~m until a constant level is reached when the error from the small scale irregularities in the emulsion is smaller than the statistical error in the grain density of the track. I wish to express my sincere gratitude to Dr. K. Kristiansson and ill. lic. G. JGnsson for much advice and many valuable discussions. I am grateful to Miss B. Lindkvist for an excellent processing of the stack and for the microscopic examination of the plates. I thank ill. lic. U. Dellien, ill. kand. K. SGderstrGm and Dr. K. Kristiansson for leaving the charges of the primaries at my disposal, and Mrs. K. Malmqvist for the dataprocessing. The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research, O A R , through the European Office of Aerospace Research, United States Air Force, under Grant No A F - E O A R 66-35. This is gratefully acknowledged. 1 am also grateful to the Swedish Atomic Research Council and to the Swedish Space Research Committee for their support. References I) G. JGnsson, K. Kristiansson and L. Malmqvist, Report KS 7005 (Lund, 1970). e) G. JGnsson, K. Kristiansson and L. Malmqvist, Astrophys. Space Sci. (1970) in print. a) k. Malmqvist, Arkiv Fysik 34 (1967) 33. 4) U. Dellien, K. SGderstrGm and K. Kristiansson, Report KS 6902 (Lund, 1969).