- Email: [email protected]
Coincidence spectroscopy of fission fragments via mica track detectors
NUCLEAR
INSTRUMENTS
AND
METHODS
IO9 (1973) 355-363; ©
NORTH-HOLLAND
PUBLISHING
CO.
COINCIDENCE S P E C T R O S C O P Y OF FISSION FRAGMENTS VIA MICA TRACK D E T E C T O R S F. M I C H A E L
K I E L Y and B R I A N D. P A T E
Department of Chemistry, Simon Fraser University, Burnaby 2, British Columbia, Canada Received 28 December 1972 T h e utility o f mica track detectors in a sandwich configuration has been investigated in m e a s u r e m e n t s o f m a s s and a n g u l a r distributions o f fission f r a g m e n t s from za5U + t h e r m a l neutrons, 238U + 14-MeV neutrons, and 1 9 7 A u + 8 0 - M e V alpha particles.
It is concluded that, while a n g u l a r distributions are poorly reproduced (due to problems with tracks at small angles to the mica surface and to the observation direction), fragment mass distributions m a y be inferred with useful accuracy.
1. Introduction
studied must be measured. This will be more or less serious depending on the fissioning nucleus mass, the fission energy and the cross-section. For the scattering array, the disadvantages include the impossibility of identifying all tracks from a given fission event, and the small detection solid angle. The advantages include registration of all fragments incident on the detector and ease of scanning, arising from their identical angle of incidence and direction on an individual detector segment. Remy et al. a) studied ternary fission using makrofol (polycarbonate) detectors in a sandwich configuration, via the interaction of 3- to 23-GeV protons with uranium, lead and gold targets. They converted the track length data for ternary events to fragment mass distributions in a manner somewhat analogous to that to be described here. However, their track length data was less precise than that obtained in the present study, and they used theoretical relationships relating track lengths to mass and energy, rather than the empirical data presently employed. Ait-Salem et al. 9) also used the sandwich technique to investigate low energy neutron induced fission of 23aU by means of "acetylcelluloid" detectors. They extracted a mass distribution from their data in a manner comparable to that described here. The mass distribution they obtained is similar to that obtained in the present work, with slightly better separation of the two mass peaks although, as in the work of Remy et al.8), theoretical mass-energy relationships were used. In contrast, in the work reported in the present paper, information on the relationship between projectile mass (charge) and range was derived entirely from independent calibration experimentst°). In the present work, muscovite mica detectors in a sandwich configuration were employed, together with previous calibration data for muscovite mica1°), in an attempt to obtain spectroscopic information on
Solid state nuclear track detectors, of mica') or glass 2) or of an organic polymer such as polycarbonate or polyimide3), can usefully be applied to measurements of fission fragments in a nuclear or cosmological context4). The existence of a lower limit of projectile charge or mass, below which a track is not recorded~), leads to excellent discrimination between fission fragments and particles of lower mass which may also be emitted (generally in very much higher intensity for medium mass targets). The relationship between the mass, charge and energy of the projectile on one hand and the length of track it produces (for example in mica) on the other offers the possibility of a spectroscopic application of nuclear track detectorsS). Such measurements on the fragments from a binary or ternary fission event may be conducted in two ways: the sandwich configuration6), in which the target is mounted between two mica detectors in close proximity, and the scattering array configurationT), in which a target is mounted at the centre of a circular array of detectors, each receiving the fragments at the same angle to the mica surface (i.e. 30 or 45°). For the sandwhich configuration, which is investigated in the present study, the potential advantages include the ability to recognize and measure all of the (2 or 3) fragments from a given fission event (and hence to make use of mass and energy conservation), and also the ability to work with small fission cross-sections following from the detection geometry of nearly 4~ sr. Potential disadvantages include the need for 3-dimensional measurement of the track lengths, and the loss of information on particles which would form tracks at angles near 0 ° or 90 ° to the detector surface (see below). Further, since the detectors must be exposed to the beam together with the target, the effects of the beam on the detectors constitute a background (of small tracks) against which the fragments to be 355
356
F. M I C H A E L
K I E L Y A N D B R I A N D. P A T E
several fissioning systems. These experiments required that the micas be scanned in three dimensions in order to obtain true track lengths rather than two dimensional projections, since the projection angle was variable and unknown. Fissioning systems were chosen whose characteristics were reasonably well established by previous studies: 235U "b thermal neutrons I 1),238U --[-14-MeV neutrons 11), and 197Au + 80-MeV alpha particles~2). The ability of the present technique to reproduce the known mass and angular distributions of the fragments from these systems provided a check on the validity of the technique, in the face of the complication that the track length in mica is a function not only of incident fragment mass, but also of fragment energy.
2. Eximrimental Targets and detectors were prepared as follows: squares of mica of 2.5cm x 2.5cm in size were cleaned by several acetone washes, and were then cleaved to about 0.1 mm thickness. The appropriate target material was then vacuum deposited on one of the freshly cleaved surfaces over a 1 cm z area. The two cleaved sheets of mica were finally clamped together at one edge by two pieces of lucite glued together with ethylene dichloride, at which time good adhesion of the clean mica surfaces was also obtained, providing they had not suffered too long an atmospheric exposure. The vacuum evaporations were carried out at a pressure of < 10 - s torr using a resistance-heated tungsten filament. Gold was deposited in the elemental state, while uranium was deposited as the tetrafluoride. The amount of material deposited was determined by weighing. The target thickness was such that a negligible effect was expected on the energies of the escaping fission fragments, and was typically of the order of 100/~g/cm 2. Calculations based on the data due to Northcliffe ~4) indicated that, for a particle of most probable mass (i.e. at the peak of the mass distribution) emitted at 10° to the target surface and traversing the entire thickness of the target, the energy loss in the target was less than 10% of the total kinetic energy in the worst case. Consequently, there should be a negligible effect on detection efficiency and on the mass distribution from this source. After irradiation with the appropriate projectiles, the sandwiches were wedged open with teflon plugs in order to expose the interior surfaces to the etchant. The target material was dissolved with aqua regia at room temperature. After an aqueous wash, the micas were then etched in 4 8 0 H F for 20 min at 20°C, conditions
previously found 1°) to be optimum for track formation. After several subsequent washes, the sandwiches were allowed to dry and the teflon plugs removed. Both detectors of the sandwich were then dry-mounted, together and in register, on standard glass microscope slides and under cover glasses. The micas were scanned using the system described previously~°). A 100 x oil immersion objective and an overall magnification of 1600x were used. The magnification factor was calibrated (with the other components of the system) using the stage micrometer as described previously1°). The stage of the microscope was fitted with three mechanical gauges, two of which measured displacements in two coordinates in the plane of the stage, and a third measured travel along the focussing axis. The gauges were calibrated using the stage micrometer and found to be accurate within +0.3 ~m. The projected track length along the viewing axis was obtained as the difference in gauge readings for sharp focus on each end of the track. (These were the most difficult measurements to make and are believed to be subject to the largest uncertainty, as will be discussed in a later section.) The three projected lengths were then, by a simple geometrical calculation, converted into a true track length and incident track angle. There were several criteria used for judging two tracks to be members of a coincident pair (i.e. arising from the same fissioning nucleus). First, it could readily be determined by inspection if they were in opposite hemispheres with respect to the stage plane, and if their projections in that plane had a common point of origin. Second, the two tracks had to be in the field of view simultaneously (area ~ 4000 pm2). This criterion may have caused elimination of events whose angle of incidence to the mica surface was small, because of the non-zero separation of the mica surfaces during irradiation. Third, the two track projections were required to be roughly colinear (i.e. within +__15 °) in the plane of the microscope stage. Since the scanning axis was identical to the incident beam axis, it was not expected that this criterion would cause rejection of a significant proportion of the events due to centre of mass motion effects; one could anticipate the direction of motion of the center of mass to be close to the beam axis, for the systems and energies employed here. In addition to these selection criteria, it was essential that the track density be sufficiently low to avoid significant numbers of accidental coincidences. A density of ~ 2000 events/mm 2 (or g 8 pairs simultaneously in view) seemed to be the maximum in terms of scanning convenience.
COINCIDENCE SPECTROSCOPY OF FISSION FRAGMENTS 3. Results and discussion
3.1. SINGLE TRACKS In order to determine the precision with which the measurements could be made, a mica detector containing tracks of known orientation formed by projectiles of known mass and energy was first scanned. This detector was one of those used in the calibration study detailed previously 1°) and was selected because it contained tracks of approximately the same lengths as those encountered in the case of fission fragments. Design of the calibration experiment geometry ensured that the angle of incidence of fragments on the particular mica segment examined was 30 ° to the surface, and two dimensional measurement of the track projections in the plane of the microscope stage plus knowledge of the angle of incidence yielded a true track length of ( 7 . 5 + 0 . 3 ) # m . The uncertainties expressed here and subsequently are generally the fwhm of the measured distribution, unless otherwise noted. Measurement of the track length projections in three dimensions led to an average true track length of (7.7+0.4)/~m and an angle of incidence of (32+6) °. It should be emphasized that the uncertainties quoted in this case should not be considered typical of those to be expected in the general case. Here the relative ease or scanning tracks at 30 °, as opposed to tracks at either very steep or very shallow angles, led to results of above average quality. 3.2. THERMALNEUTRON INDUCED FISSIONOF 2351.] This system was chosen, not only because it has been thoroughly investigated using other techniques, but
also because there was no center of mass motion which might complicate the analysis of the track length data. The track length distributions in the forward and backward hemispheres (relative to the direction of the incident neutrons) are shown in fig. I. It can be seen that they are considerably broader than those for the monoenergetic fragments of unique mass referred to above. This is to be expected, however, because of the asymmetry of the fission mass distribution and the width of the fragment energy distribution. It will be noticed that the distribution in the forward hemisphere is slightly wider than that for the backward. This is believed to result from a problem in the scanning, namely the fact that forward tracks are viewed through both sheets of mica. As a result, the image is not quite as sharp, and therefore the depth measurements are subject to a slightly greater uncertainty, than for tracks in the backward hemisphere. The track angular distribution is displayed in fig. 2. One would expect that the distribution with respect to the direction of view (since there was no preferred incident neutron direction in this case) would be isotropic in the laboratory for this fissioning system. There are however, several experimental problems which, it is believed, contribute to the shape observed in fig. 2: 1) Tracks which deviate from the beam axis < 20 ~ are quite difficult to measure accurately. These are tracks which enter the mica nearly normal to the surface, and, viewed end-on, are the most difficult to recognise as coincident track pairs. 2) The critical angle for mica (i.e. the minimum angle to the surface at which a particle may enter and still leave a recognizable track) has been determined 13) to be ~ 5 °. Therefore, most fission
90 ....
FORWARD BACKWARO
125
f
FORWARD
.....
8/ICKWARD
~__.I O 0 - -r
r ....
60 (/1 IZ hi > bJ
357
-,
l
.....
, t ....
i
+ 30 . . . .
" ..... l ..... :
J
.....
o
%
aJ
+
; TRACK
,i LENGTH
15
lS~-'~
'-21
. . . .
io
20 310 4B /o LABORATORY ANGLE (DEGREES) i
8'o
,
90
(/J.)
Fig. I. Track length distributions in mica from the fission of 2asU induced by thermal neutrons.
Fig. 2. Angular distributions of the tracks from '~35U+ thermal neutrons. The angle is measured with respect to the beam axis in each hemisphere.
358
E. M I C H A E L
KIELY
Jl
~Oi- I
z t~ 40
°I O
0
5
I~)
15 20 25 D~VERGENCE(DEGREES)
~
r~5
40
Fig. 3. D i s t r i b u t i o n o f t h e d e v i a t i o n s f r o m c o l i n e a r i t y f o r t h e
tracks from 2asU+ thermal neutrons. fragments emitted at 85-95 ~ to the beam will not leave recognisable tracks, while tracks at nearby angles will be difficult to recognise. 3) A third problem is that of the irreducible spacing between the mica sheets during irradiation. Such spacing will cause the members of a track pair to be separated by a distance related to this spacing and to the angle made with the mica surface (becoming rapidly larger for angles approaching 0 ° to the surface). Thus track pairs at such angles would be rejected by one of the scanning criteria mentioned earlier. The conclusion from the foregoing is that overall angular distribution data obtained from this kind of measurement may be so distorted as to be of doubtful utility. However the distribution in direction of one track of a pair with respect to the direction of the other could still be measured. Such a distribution is shown in fig. 3. The fwhm of this distribution is seen to be about +_2 °, which is well within the value expected from the calibration data on single tracks. This colinearity, incidentally, is not related to the colinearity criterion used in scanning the tracks. The latter was concerned with orientation of the track projections in a plane perpendicular to the beam axis, whereas the quantity
AND
BRIAN
D. P A T E
measured to produce the data of fig. 3 is the departure from colinearity in three dimensions. The track lengths of coincident pairs measured for the system 235U+ thermal neutrons were converted into data on fragment masses by the following procedure: Previous experimental studie¢ °) of the track lengths in mica of ions of known characteristics have indicated a rather systematic variation of track length with mass as well as with kinetic energy. Because of the small amount of experimental data available, however, and the present need for track length data for a complete range of masses and energies, the functional form of the variation of track length with such parameters was determined from the range-energy data of Northcliffe et al) 4) which were fitted to fourth degree polynomials. These equations were then normalized in such a way as to reproduce the existing experimental data for track lengths in mica ~°) as closely as possible. In the analysis of the present fission data, a trial mass was selected for one member of the track pair. The energy corresponding to this mass and track length was obtained from a table generated from the equations just described. A trial mass for the other track was then selected and the corresponding energy obtained from the table. An error function was then calculated according to =
+W~ Af
/
+ WI,(P'-P2"~ 2, \ Pl /
+
Ef
(1)
where subscript 1 refers to one track, subscript 2 refers to the other track, subscript f refers to the fissioning nucleus, A is the mass number, E is the kinetic energy in the laboratory, P is the corresponding linear momentum, and W is an arbitrary weighting factor. El, the fission energy, was calculated via the formulation due to Nix ~5) and was corrected for fission asymmetry. The masses selected for the second track were confined to within 50 units of the value corresponding to mass conservation based on the selected trial value for the first track. This latter was restricted to between 25 (the approximate detection threshold for mica) and (A i,,g~,-25). After trying all mass combinations within the limits just stated, the pair with the smallest error factor was then accepted as "correct".
COINCIDENCE
SPECTROSCOPY
The results of this calculation for the data from z3sU + thermal neutrons are shown as the histogram in fig. 4. The solid curve in the figure is derived from the radiochemical datatl). These data are expected, however, to correspond to an infinitely small mass resolution, whereas mass data from the present experiment (histogram) are known to contain effects from a poorer mass resolution derived from the track length uncertainties. Therefore each point on the radiochemical mass yield curve was replaced by a gaussian curve of width corresponding in mass to the width (in track length) of the track length distribution measured in the calibration studies 1°) for ions of unique mass and energy, and assuming a constant fission fragment velocity (in MeV/amu). These gaussians were then summed to yield the dashed curve shown in fig. 4. In view of the approximations and averaging techniques used, the agreement between the mass distribution obtained from the measured track length data and that derived from the known mass distributions is reasonably good. it should be noted that the weighting factors Win eq. (I) were initially assumed to be equal at a value of unity. It was found that this yielded results very similar
OF F I S S I O N
359
FRAGMENTS
to those presented here with the exception that the sum of the fission fragment masses was about 10 amu less than the mass of the fissioning nucleus. This was true, not only for the system 23SLr+thermal neutrons, but also the systems presented later. It was discovered that an increase in W A to a value of 5.0 removed this discrepancy, while very little else was affected (including the average kinetic energies of the fission fragments). Consequently, a value of WA = 5.0 was arbitrarily adopted for all subsequent calculations. 3.3. 14-MeV NEUTRON INDUCED FISSION OF URANIUM The track length distributions in the forward and backward hemisphere for this system are shown in fig. 5. As can be seen, the forward distribution again appears to be slightly the broader. The angular distribution, displayed in fig. 6 and expected to be nearly isotropic,
IOC - -
FORWARO
.....
EIACKWAR0
80
,,n6C
'9O
I-Z hi
4C
120
70
'I'°°
,
2C
3
6
8o ~
9 12 15 TRACK LENGTH (/.L)
18
-21
Fig. 5. Track length distributions for the fission o f 2asU with 14-MeV neutrons.
125
I
,; j ol
,
~/
f'
- -
FORWARD
....
BACKWARD
IOO 2O
Z
7s
---i
tJ,J
,
. l. . . . . . .
17'5
FRAGMENT
MASS
Fig. 4. Mass yield distribution for the fission o f 235U with thermal neutrons. T h e histogram was calculated from the mica track data. T h e solid curve was obtained from radiochemical experiments (ref. 11). T h e dashed curve represents modification o f the radiochemical data (see text). Both curves were normalized to the area u n d e r the histogram.
2
0
F ......
Io
1
20
3~3 4'0 5'o 6'0 7'0 LABORATORY ANGLE (DEGREES)
do
9o
Fig. 6. A n g u l a r distribution o f the tracks from '~3su+ 14-MeV neutrons.
360
F. MICHAEL
KIELY
AND
BRIAN
D. PATE
60-
30
i’l n
1
Ll\
01
I
I
0
5
IO
-mm x)
35
4
DI”kGENC%GR&
Fig. 7. Distribution
about colinearity for sssU + 14-MeV neutrons.
the
tracks
from
suffers from the same problems at angles near 0” and 90” as discussed earlier, (but perhaps to a lesser extent following a smaller separation between the mica detectors during this bombardment). The distribution about colinearity in fig. 7 again indicates a fwhm of +2”. The data of fig. 5 were subjected to the analysis detailed above in order to extract a mass distribution for this fissioning system; the result is displayed as the histogram in fig. 8. Again, the solid curve represents the result of radiochemical studies”) while the dashed curve displays the radiochemical data modified by the expected mass resolution of the present experiment. Again, the agreement may be considered fairly satisfactory, although the modified radiochemical mass distribution is somewhat broader than that derived from the track length data. The low mass peak of the latter distribution appears to be shifted somewhat towards higher masses relative to that in the radiochemical data. In a manner to be discussed below, the small center of mass motion of the fissioning nucleus was included in the calculation of the mass distribution in this case, and the results are depicted in fig. 9. As might have been anticipated, the effects of this correction are so
Fig. 8. Mass yield distribution for the fragments from sssU+ 14-MeV neutrons. The histogram represents the results of the present experiment, while the solid curve shows radiochemical data (ref. ll), and the dashed curve represents modification of these data (see text).
1
120
J 100
zb
5
I. 60
& 2 ;
%
I 602
?
2
40
0
I
25
50
I
75
I
loo 125 FRAGMENT
!
150 MASS
:\ 1-s
1
200
0 225
Fig. 9. Mass yield distribution from sssU + 14.MeV neutrons assuming compound nucleus formation prior to fission. The curves have the same significance as in fig. 8.
COINCIDENCE
SPECTROSCOPY
small as to be within the statistical uncertainties of the data. The solid and dashed curves are identical to those in fig. 8. 3.4. 80-MeV
ALPHA-PARTICLE INDUCED FISSION OF
GOLD
The track length distributions for this system are displayed in fig. 10. One can notice in these distribu-
FORWARD
60
.......
BACKWARD
45
i'
I---
r.J
OF F I S S I O N
361
FRAGMENTS
tions that the average track length at laboratory angles forward of 90 ° with respect to the beam direction is considerably larger than that in the backward direction (a difference of almost 3/~m). This evidently arises from substantial centre-of-mass motion of the fissioning nucleus in this case. The colinearity plot, in fig. 11, indicates a fwhm of +__15°, considerably wider than observed in the other systems studied. This lack of colinearity may also be partly responsible, in fig. 12, for the angular distributions having maximum intensities at different angles in the two hemispheres. Consequently, it became necessary to include a correction for center of mass motion in the calculation of the mass distribution. This was accomplished under the assumption that the kinetic energy and direction of motion of the fissioning nucleus were those corre-
~-~
-
-
FORWARO
......
15
OACKWARID
I00 0
Fig.
0
,r--,--r
,
3
6
,
~--'--'--,
,
9 12 15 TRACK LENGTH (/,t.)
18
8O
21 IZ
10. Track length distribution for f r a g m e n t s from the 80 MeV alpha-induced fission o f gold.
,>. , 6 0 LI.J
"
40
I!..... .....
-I .....=L
20 .....
0 25
i L ....
0
,b
I I .....
[
q ......
~o ~o 40 50 60 70 80 LABORATORY ANGLE (OEGREES)
90
Fig. 12. A n g u l a r distribution o f the tracks from 197Au-F 80-MeV
20 60 FORWARD ........ >
BACKWARD
15
~J
40 ;;'-
L
20
0
o o
,~
,£
~
2s
~
FI,FI 3~
40
0
"I ~
$
~-q-
J 6
; 9
f2
";
__r-1 ,
15
~-r--~, f8
2t
TRACK LENGTH (/1.)
DIVERGENCE (DEGREES)
Fig. I I. Distribution o f the deviations from colinearity for the tracks from 1 9 7 A u + 80-MeV ~'s.
Fig. 13. Track length distribution o f the tracks from 197Au+ + 8 0 - M e V ~ ' s corrected for centre-of-mass m o t i o n a s s u m i n g c o m p o u n d nucleus formation.
362
F.
MICHAEL
KIELY
AND
s p o n d i n g to c o m p o u n d nucleus f o r m a t i o n between the projectile and target. W h e n each mass pair was selected, the c o r r e s p o n d i n g kinetic energies were corrected for the centre-of-mass motion. The corrected energies were then used to calculate the error function o f eq. (1) and the calculation c o n t i n u e d as before. W h e n the " b e s t " mass pair was found, the corrected energies were used to determine w h a t the t r a c k lengths and angles w o u l d have been in the centre-of-mass system.
/00
- -
FORWARD
......
BACKWARD
BRIAN
D.
(~ I-
4
60 F ..........
60
I
48 °2/-
z > tLi
t
i
i
30[-
24i-
_1
80
PATE
4,8
i
w
F
z 60 > hi
-'112
40
ot6.....
2O
25
0 0
,0
20
.~0 ANGLE
4b
5'0
.....
60
.- . . . . . .
i
70
80
4C
0 0
I 5
I
/ I0
Lf--
15 20 25 DIVERGENCE (DEGREES)
n,-30
35
/ 75
I00 125 150 FRAGMENT MASS
17'5
200
225
90
(DEGREES)
Fig. 14, Angular distribution in the centre-of-mass system for the tracks from 197Au+ 80-MeV :~'s.
1
50
40
Fig. 15. Distribution about colinearity in the centre-of-mass system for the tracks from 197Au+ 80-MeV ~t's.
Fig. 16. Mass yield curve for fragments from the 80-MeV alpha-induced fission of Au. The histogram was calculated from the data of the present experiment assuming compound nucleus formation (see text). The solid curve was obtained from existing radiochemical data (ref. 12), and the dashed curve represents adjustment of those data (see text). The resulting track length and a n g u l a r distributions are displayed in figs. 13 and 14. The track length distributions now peak at a p p r o x i m a t e l y the same value in each hemisphere, while the a n g u l a r distribution now a p p e a r s to be symmetric a b o u t 90 ° . M o r e o v e r the colinearity distribution in fig. 15 has been n a r r o w e d to _+6 °. It is c o n c l u d e d that centre-of-mass m o t i o n has been satisfactorily taken into account. The mass distribution o b t a i n e d from this analysis a p p e a r s as the h i s t o g r a m in fig. 16 and is seen to be in excellent agreement with the unmodified and modified radiochemical d a t a 12) (shown as a solid and dashed curve, respectively). It might be a d d e d t h a t the mass distribution calculated with no correction for centreof-mass m o t i o n exhibited a very b r o a d m a x i m u m (almost two humped), with nearly all the a p p a r e n t l y heavy mass fragments coming from tracks in the forward hemisphere and the a p p a r e n t l y light mass fragments from tracks in the b a c k w a r d direction. Several other centre-of-mass m o t i o n s were tried, from 50% to 125% o f c o m p o u n d nucleus. The results did not seem very sensitive to this p a r a m e t e r within this range, although the colinearity distribution was the
COINCIDENCE SPECTROSCOPY OF FISSION FRAGMENTS narrowest (by a slight a m o u n t ) at 100% o f c o m p o u n d nucleus m o m e n t u m .
363
tion o f the two fragments may, in other words, tend to reduce the uncertainty which would exist for consideration o f a single fragment.
4. Conclusions F r o m the foregoing, two general conclusions m a y perhaps be drawn: 1) F o r the m e a s u r e m e n t o f f r a g m e n t a n g u l a r distributions in detail, the mica sandwich configuration is unsuitable; the technique o f d o u b l e measurement, one with the b e a m at 0 ° to the mica surface and a second with the beam, say, at 45 ° to the surface, may p e r h a p s suffice in some cases, and m a y generally p r o d u c e d a t a c o m p l e t e enough for a useful total crosssection m e a s u r e m e n t to be possible. 2) F o r f r a g m e n t - m a s s distributions the technique is m o r e useful, and should perhaps be c a p a b l e o f detecting an increasing mass distribution width as the fissility o f the target system is reduced t o w a r d s the BusinaroG a l l o n e point I s). It would be preferable, were it possible, to extract the mass-distribution directly from the track length distribution, rather than the present necessity o f c o m p a r i n g the measured track length d i s t r i b u t i o n with that expected for a series o f '~trial" mass distributions. W o r k is presently u n d e r w a y on this possibility. It is interesting that the experimental mass distributions seemed in slightly better agreement with the radiochemical d a t a before the separately d e t e r m i n e d mass-resolution was folded in. It is not c o m p l e t e l y clear why this could be. One possibility which suggests itself is that the t r a n s f o r m a t i o n o f track length uncertainty to mass n u m b e r uncertainty is c o m p l i c a t e d by the use o f the conservation laws in o b t a i n i n g the " c o r r e c t " masses for a p a r t i c u l a r t r a c k pair. C o n s i d e r a -
The a u t h o r s are indebted to Dr T. T. S u g i h a r a and Texas A & M University for their hospitality in providing cyclotron time, to M r H. Blok for carrying out the a l p h a irradiations and to M r T. Bennett for 14-MeV neutron b o m b a r d m e n t s . They also wish to t h a n k D r L. B a b b and the staff o f the University o f W a s h i n g t o n R e a c t o r for their kind assistance with the reactor b o m b a r d m e n t s , and the o p e r a t i n g staff o f the S F U C o m p u t e r Centre for c o m p u t a t i o n a l services. W o r k was p e r f o r m e d under N a t i o n a l Research Council o f C a n a d a , G r a n t N u m b e r A2510.
References 1) R. L. Fleischer et al., Phys. Rev. 133 (1964) A1443. ':) J. P~ter and M. Lecerf, Nucl. Instr. and Meth. 104 (1972) 189. ~) M. Monnin, Th/~se (Facult6 des Sciences, Universit6 de Clermont, France, 1969). 4) R. L. Fleischer, P. B. Price and R. M. Walker, Ann. Rev. Nucl. Sci. 15 0965) I. 3) H. Blok and B. D. Pate, to be published (1973). ~) S. Katcoff and J. Hudis, Phys. Rev. 180 0969) 1122. 7) B. D. Pate and J. P/~tcr, Nucl. Phys. A173 (1971) 520. 8) G. Remy et al., J. Phys. 31 (1970) 27. ~) M. Ait-Salem et al., Nucl. Instr. and Meth. 60 (1968) 45. 10) H. Blok, F. M. Kiely and B. D. Pate, Nucl. Instr. and Meth. 100 0972) 403. tt) H. R. Von Gunte, Actinides Rev. 1 (1969) 275. le) F. Plasil et aI., Phys. Rev. 142 (1966) 696. la) H. A. Khan and S. A. Durrani, Nucl. Instr. and Meth. 98 0972) 229. 14) L. C. Northcliffe and R. F. Schilling, Nucl. Data Tables A7 (1970) 233. 15) j. R. Nix, Nucl. Phys. A130 0969) 241.
INSTRUMENTS
AND
METHODS
IO9 (1973) 355-363; ©
NORTH-HOLLAND
PUBLISHING
CO.
COINCIDENCE S P E C T R O S C O P Y OF FISSION FRAGMENTS VIA MICA TRACK D E T E C T O R S F. M I C H A E L
K I E L Y and B R I A N D. P A T E
Department of Chemistry, Simon Fraser University, Burnaby 2, British Columbia, Canada Received 28 December 1972 T h e utility o f mica track detectors in a sandwich configuration has been investigated in m e a s u r e m e n t s o f m a s s and a n g u l a r distributions o f fission f r a g m e n t s from za5U + t h e r m a l neutrons, 238U + 14-MeV neutrons, and 1 9 7 A u + 8 0 - M e V alpha particles.
It is concluded that, while a n g u l a r distributions are poorly reproduced (due to problems with tracks at small angles to the mica surface and to the observation direction), fragment mass distributions m a y be inferred with useful accuracy.
1. Introduction
studied must be measured. This will be more or less serious depending on the fissioning nucleus mass, the fission energy and the cross-section. For the scattering array, the disadvantages include the impossibility of identifying all tracks from a given fission event, and the small detection solid angle. The advantages include registration of all fragments incident on the detector and ease of scanning, arising from their identical angle of incidence and direction on an individual detector segment. Remy et al. a) studied ternary fission using makrofol (polycarbonate) detectors in a sandwich configuration, via the interaction of 3- to 23-GeV protons with uranium, lead and gold targets. They converted the track length data for ternary events to fragment mass distributions in a manner somewhat analogous to that to be described here. However, their track length data was less precise than that obtained in the present study, and they used theoretical relationships relating track lengths to mass and energy, rather than the empirical data presently employed. Ait-Salem et al. 9) also used the sandwich technique to investigate low energy neutron induced fission of 23aU by means of "acetylcelluloid" detectors. They extracted a mass distribution from their data in a manner comparable to that described here. The mass distribution they obtained is similar to that obtained in the present work, with slightly better separation of the two mass peaks although, as in the work of Remy et al.8), theoretical mass-energy relationships were used. In contrast, in the work reported in the present paper, information on the relationship between projectile mass (charge) and range was derived entirely from independent calibration experimentst°). In the present work, muscovite mica detectors in a sandwich configuration were employed, together with previous calibration data for muscovite mica1°), in an attempt to obtain spectroscopic information on
Solid state nuclear track detectors, of mica') or glass 2) or of an organic polymer such as polycarbonate or polyimide3), can usefully be applied to measurements of fission fragments in a nuclear or cosmological context4). The existence of a lower limit of projectile charge or mass, below which a track is not recorded~), leads to excellent discrimination between fission fragments and particles of lower mass which may also be emitted (generally in very much higher intensity for medium mass targets). The relationship between the mass, charge and energy of the projectile on one hand and the length of track it produces (for example in mica) on the other offers the possibility of a spectroscopic application of nuclear track detectorsS). Such measurements on the fragments from a binary or ternary fission event may be conducted in two ways: the sandwich configuration6), in which the target is mounted between two mica detectors in close proximity, and the scattering array configurationT), in which a target is mounted at the centre of a circular array of detectors, each receiving the fragments at the same angle to the mica surface (i.e. 30 or 45°). For the sandwhich configuration, which is investigated in the present study, the potential advantages include the ability to recognize and measure all of the (2 or 3) fragments from a given fission event (and hence to make use of mass and energy conservation), and also the ability to work with small fission cross-sections following from the detection geometry of nearly 4~ sr. Potential disadvantages include the need for 3-dimensional measurement of the track lengths, and the loss of information on particles which would form tracks at angles near 0 ° or 90 ° to the detector surface (see below). Further, since the detectors must be exposed to the beam together with the target, the effects of the beam on the detectors constitute a background (of small tracks) against which the fragments to be 355
356
F. M I C H A E L
K I E L Y A N D B R I A N D. P A T E
several fissioning systems. These experiments required that the micas be scanned in three dimensions in order to obtain true track lengths rather than two dimensional projections, since the projection angle was variable and unknown. Fissioning systems were chosen whose characteristics were reasonably well established by previous studies: 235U "b thermal neutrons I 1),238U --[-14-MeV neutrons 11), and 197Au + 80-MeV alpha particles~2). The ability of the present technique to reproduce the known mass and angular distributions of the fragments from these systems provided a check on the validity of the technique, in the face of the complication that the track length in mica is a function not only of incident fragment mass, but also of fragment energy.
2. Eximrimental Targets and detectors were prepared as follows: squares of mica of 2.5cm x 2.5cm in size were cleaned by several acetone washes, and were then cleaved to about 0.1 mm thickness. The appropriate target material was then vacuum deposited on one of the freshly cleaved surfaces over a 1 cm z area. The two cleaved sheets of mica were finally clamped together at one edge by two pieces of lucite glued together with ethylene dichloride, at which time good adhesion of the clean mica surfaces was also obtained, providing they had not suffered too long an atmospheric exposure. The vacuum evaporations were carried out at a pressure of < 10 - s torr using a resistance-heated tungsten filament. Gold was deposited in the elemental state, while uranium was deposited as the tetrafluoride. The amount of material deposited was determined by weighing. The target thickness was such that a negligible effect was expected on the energies of the escaping fission fragments, and was typically of the order of 100/~g/cm 2. Calculations based on the data due to Northcliffe ~4) indicated that, for a particle of most probable mass (i.e. at the peak of the mass distribution) emitted at 10° to the target surface and traversing the entire thickness of the target, the energy loss in the target was less than 10% of the total kinetic energy in the worst case. Consequently, there should be a negligible effect on detection efficiency and on the mass distribution from this source. After irradiation with the appropriate projectiles, the sandwiches were wedged open with teflon plugs in order to expose the interior surfaces to the etchant. The target material was dissolved with aqua regia at room temperature. After an aqueous wash, the micas were then etched in 4 8 0 H F for 20 min at 20°C, conditions
previously found 1°) to be optimum for track formation. After several subsequent washes, the sandwiches were allowed to dry and the teflon plugs removed. Both detectors of the sandwich were then dry-mounted, together and in register, on standard glass microscope slides and under cover glasses. The micas were scanned using the system described previously~°). A 100 x oil immersion objective and an overall magnification of 1600x were used. The magnification factor was calibrated (with the other components of the system) using the stage micrometer as described previously1°). The stage of the microscope was fitted with three mechanical gauges, two of which measured displacements in two coordinates in the plane of the stage, and a third measured travel along the focussing axis. The gauges were calibrated using the stage micrometer and found to be accurate within +0.3 ~m. The projected track length along the viewing axis was obtained as the difference in gauge readings for sharp focus on each end of the track. (These were the most difficult measurements to make and are believed to be subject to the largest uncertainty, as will be discussed in a later section.) The three projected lengths were then, by a simple geometrical calculation, converted into a true track length and incident track angle. There were several criteria used for judging two tracks to be members of a coincident pair (i.e. arising from the same fissioning nucleus). First, it could readily be determined by inspection if they were in opposite hemispheres with respect to the stage plane, and if their projections in that plane had a common point of origin. Second, the two tracks had to be in the field of view simultaneously (area ~ 4000 pm2). This criterion may have caused elimination of events whose angle of incidence to the mica surface was small, because of the non-zero separation of the mica surfaces during irradiation. Third, the two track projections were required to be roughly colinear (i.e. within +__15 °) in the plane of the microscope stage. Since the scanning axis was identical to the incident beam axis, it was not expected that this criterion would cause rejection of a significant proportion of the events due to centre of mass motion effects; one could anticipate the direction of motion of the center of mass to be close to the beam axis, for the systems and energies employed here. In addition to these selection criteria, it was essential that the track density be sufficiently low to avoid significant numbers of accidental coincidences. A density of ~ 2000 events/mm 2 (or g 8 pairs simultaneously in view) seemed to be the maximum in terms of scanning convenience.
COINCIDENCE SPECTROSCOPY OF FISSION FRAGMENTS 3. Results and discussion
3.1. SINGLE TRACKS In order to determine the precision with which the measurements could be made, a mica detector containing tracks of known orientation formed by projectiles of known mass and energy was first scanned. This detector was one of those used in the calibration study detailed previously 1°) and was selected because it contained tracks of approximately the same lengths as those encountered in the case of fission fragments. Design of the calibration experiment geometry ensured that the angle of incidence of fragments on the particular mica segment examined was 30 ° to the surface, and two dimensional measurement of the track projections in the plane of the microscope stage plus knowledge of the angle of incidence yielded a true track length of ( 7 . 5 + 0 . 3 ) # m . The uncertainties expressed here and subsequently are generally the fwhm of the measured distribution, unless otherwise noted. Measurement of the track length projections in three dimensions led to an average true track length of (7.7+0.4)/~m and an angle of incidence of (32+6) °. It should be emphasized that the uncertainties quoted in this case should not be considered typical of those to be expected in the general case. Here the relative ease or scanning tracks at 30 °, as opposed to tracks at either very steep or very shallow angles, led to results of above average quality. 3.2. THERMALNEUTRON INDUCED FISSIONOF 2351.] This system was chosen, not only because it has been thoroughly investigated using other techniques, but
also because there was no center of mass motion which might complicate the analysis of the track length data. The track length distributions in the forward and backward hemispheres (relative to the direction of the incident neutrons) are shown in fig. I. It can be seen that they are considerably broader than those for the monoenergetic fragments of unique mass referred to above. This is to be expected, however, because of the asymmetry of the fission mass distribution and the width of the fragment energy distribution. It will be noticed that the distribution in the forward hemisphere is slightly wider than that for the backward. This is believed to result from a problem in the scanning, namely the fact that forward tracks are viewed through both sheets of mica. As a result, the image is not quite as sharp, and therefore the depth measurements are subject to a slightly greater uncertainty, than for tracks in the backward hemisphere. The track angular distribution is displayed in fig. 2. One would expect that the distribution with respect to the direction of view (since there was no preferred incident neutron direction in this case) would be isotropic in the laboratory for this fissioning system. There are however, several experimental problems which, it is believed, contribute to the shape observed in fig. 2: 1) Tracks which deviate from the beam axis < 20 ~ are quite difficult to measure accurately. These are tracks which enter the mica nearly normal to the surface, and, viewed end-on, are the most difficult to recognise as coincident track pairs. 2) The critical angle for mica (i.e. the minimum angle to the surface at which a particle may enter and still leave a recognizable track) has been determined 13) to be ~ 5 °. Therefore, most fission
90 ....
FORWARD BACKWARO
125
f
FORWARD
.....
8/ICKWARD
~__.I O 0 - -r
r ....
60 (/1 IZ hi > bJ
357
-,
l
.....
, t ....
i
+ 30 . . . .
" ..... l ..... :
J
.....
o
%
aJ
+
; TRACK
,i LENGTH
15
lS~-'~
'-21
. . . .
io
20 310 4B /o LABORATORY ANGLE (DEGREES) i
8'o
,
90
(/J.)
Fig. I. Track length distributions in mica from the fission of 2asU induced by thermal neutrons.
Fig. 2. Angular distributions of the tracks from '~35U+ thermal neutrons. The angle is measured with respect to the beam axis in each hemisphere.
358
E. M I C H A E L
KIELY
Jl
~Oi- I
z t~ 40
°I O
0
5
I~)
15 20 25 D~VERGENCE(DEGREES)
~
r~5
40
Fig. 3. D i s t r i b u t i o n o f t h e d e v i a t i o n s f r o m c o l i n e a r i t y f o r t h e
tracks from 2asU+ thermal neutrons. fragments emitted at 85-95 ~ to the beam will not leave recognisable tracks, while tracks at nearby angles will be difficult to recognise. 3) A third problem is that of the irreducible spacing between the mica sheets during irradiation. Such spacing will cause the members of a track pair to be separated by a distance related to this spacing and to the angle made with the mica surface (becoming rapidly larger for angles approaching 0 ° to the surface). Thus track pairs at such angles would be rejected by one of the scanning criteria mentioned earlier. The conclusion from the foregoing is that overall angular distribution data obtained from this kind of measurement may be so distorted as to be of doubtful utility. However the distribution in direction of one track of a pair with respect to the direction of the other could still be measured. Such a distribution is shown in fig. 3. The fwhm of this distribution is seen to be about +_2 °, which is well within the value expected from the calibration data on single tracks. This colinearity, incidentally, is not related to the colinearity criterion used in scanning the tracks. The latter was concerned with orientation of the track projections in a plane perpendicular to the beam axis, whereas the quantity
AND
BRIAN
D. P A T E
measured to produce the data of fig. 3 is the departure from colinearity in three dimensions. The track lengths of coincident pairs measured for the system 235U+ thermal neutrons were converted into data on fragment masses by the following procedure: Previous experimental studie¢ °) of the track lengths in mica of ions of known characteristics have indicated a rather systematic variation of track length with mass as well as with kinetic energy. Because of the small amount of experimental data available, however, and the present need for track length data for a complete range of masses and energies, the functional form of the variation of track length with such parameters was determined from the range-energy data of Northcliffe et al) 4) which were fitted to fourth degree polynomials. These equations were then normalized in such a way as to reproduce the existing experimental data for track lengths in mica ~°) as closely as possible. In the analysis of the present fission data, a trial mass was selected for one member of the track pair. The energy corresponding to this mass and track length was obtained from a table generated from the equations just described. A trial mass for the other track was then selected and the corresponding energy obtained from the table. An error function was then calculated according to =
+W~ Af
/
+ WI,(P'-P2"~ 2, \ Pl /
+
Ef
(1)
where subscript 1 refers to one track, subscript 2 refers to the other track, subscript f refers to the fissioning nucleus, A is the mass number, E is the kinetic energy in the laboratory, P is the corresponding linear momentum, and W is an arbitrary weighting factor. El, the fission energy, was calculated via the formulation due to Nix ~5) and was corrected for fission asymmetry. The masses selected for the second track were confined to within 50 units of the value corresponding to mass conservation based on the selected trial value for the first track. This latter was restricted to between 25 (the approximate detection threshold for mica) and (A i,,g~,-25). After trying all mass combinations within the limits just stated, the pair with the smallest error factor was then accepted as "correct".
COINCIDENCE
SPECTROSCOPY
The results of this calculation for the data from z3sU + thermal neutrons are shown as the histogram in fig. 4. The solid curve in the figure is derived from the radiochemical datatl). These data are expected, however, to correspond to an infinitely small mass resolution, whereas mass data from the present experiment (histogram) are known to contain effects from a poorer mass resolution derived from the track length uncertainties. Therefore each point on the radiochemical mass yield curve was replaced by a gaussian curve of width corresponding in mass to the width (in track length) of the track length distribution measured in the calibration studies 1°) for ions of unique mass and energy, and assuming a constant fission fragment velocity (in MeV/amu). These gaussians were then summed to yield the dashed curve shown in fig. 4. In view of the approximations and averaging techniques used, the agreement between the mass distribution obtained from the measured track length data and that derived from the known mass distributions is reasonably good. it should be noted that the weighting factors Win eq. (I) were initially assumed to be equal at a value of unity. It was found that this yielded results very similar
OF F I S S I O N
359
FRAGMENTS
to those presented here with the exception that the sum of the fission fragment masses was about 10 amu less than the mass of the fissioning nucleus. This was true, not only for the system 23SLr+thermal neutrons, but also the systems presented later. It was discovered that an increase in W A to a value of 5.0 removed this discrepancy, while very little else was affected (including the average kinetic energies of the fission fragments). Consequently, a value of WA = 5.0 was arbitrarily adopted for all subsequent calculations. 3.3. 14-MeV NEUTRON INDUCED FISSION OF URANIUM The track length distributions in the forward and backward hemisphere for this system are shown in fig. 5. As can be seen, the forward distribution again appears to be slightly the broader. The angular distribution, displayed in fig. 6 and expected to be nearly isotropic,
IOC - -
FORWARO
.....
EIACKWAR0
80
,,n6C
'9O
I-Z hi
4C
120
70
'I'°°
,
2C
3
6
8o ~
9 12 15 TRACK LENGTH (/.L)
18
-21
Fig. 5. Track length distributions for the fission o f 2asU with 14-MeV neutrons.
125
I
,; j ol
,
~/
f'
- -
FORWARD
....
BACKWARD
IOO 2O
Z
7s
---i
tJ,J
,
. l. . . . . . .
17'5
FRAGMENT
MASS
Fig. 4. Mass yield distribution for the fission o f 235U with thermal neutrons. T h e histogram was calculated from the mica track data. T h e solid curve was obtained from radiochemical experiments (ref. 11). T h e dashed curve represents modification o f the radiochemical data (see text). Both curves were normalized to the area u n d e r the histogram.
2
0
F ......
Io
1
20
3~3 4'0 5'o 6'0 7'0 LABORATORY ANGLE (DEGREES)
do
9o
Fig. 6. A n g u l a r distribution o f the tracks from '~3su+ 14-MeV neutrons.
360
F. MICHAEL
KIELY
AND
BRIAN
D. PATE
60-
30
i’l n
1
Ll\
01
I
I
0
5
IO
-mm x)
35
4
DI”kGENC%GR&
Fig. 7. Distribution
about colinearity for sssU + 14-MeV neutrons.
the
tracks
from
suffers from the same problems at angles near 0” and 90” as discussed earlier, (but perhaps to a lesser extent following a smaller separation between the mica detectors during this bombardment). The distribution about colinearity in fig. 7 again indicates a fwhm of +2”. The data of fig. 5 were subjected to the analysis detailed above in order to extract a mass distribution for this fissioning system; the result is displayed as the histogram in fig. 8. Again, the solid curve represents the result of radiochemical studies”) while the dashed curve displays the radiochemical data modified by the expected mass resolution of the present experiment. Again, the agreement may be considered fairly satisfactory, although the modified radiochemical mass distribution is somewhat broader than that derived from the track length data. The low mass peak of the latter distribution appears to be shifted somewhat towards higher masses relative to that in the radiochemical data. In a manner to be discussed below, the small center of mass motion of the fissioning nucleus was included in the calculation of the mass distribution in this case, and the results are depicted in fig. 9. As might have been anticipated, the effects of this correction are so
Fig. 8. Mass yield distribution for the fragments from sssU+ 14-MeV neutrons. The histogram represents the results of the present experiment, while the solid curve shows radiochemical data (ref. ll), and the dashed curve represents modification of these data (see text).
1
120
J 100
zb
5
I. 60
& 2 ;
%
I 602
?
2
40
0
I
25
50
I
75
I
loo 125 FRAGMENT
!
150 MASS
:\ 1-s
1
200
0 225
Fig. 9. Mass yield distribution from sssU + 14.MeV neutrons assuming compound nucleus formation prior to fission. The curves have the same significance as in fig. 8.
COINCIDENCE
SPECTROSCOPY
small as to be within the statistical uncertainties of the data. The solid and dashed curves are identical to those in fig. 8. 3.4. 80-MeV
ALPHA-PARTICLE INDUCED FISSION OF
GOLD
The track length distributions for this system are displayed in fig. 10. One can notice in these distribu-
FORWARD
60
.......
BACKWARD
45
i'
I---
r.J
OF F I S S I O N
361
FRAGMENTS
tions that the average track length at laboratory angles forward of 90 ° with respect to the beam direction is considerably larger than that in the backward direction (a difference of almost 3/~m). This evidently arises from substantial centre-of-mass motion of the fissioning nucleus in this case. The colinearity plot, in fig. 11, indicates a fwhm of +__15°, considerably wider than observed in the other systems studied. This lack of colinearity may also be partly responsible, in fig. 12, for the angular distributions having maximum intensities at different angles in the two hemispheres. Consequently, it became necessary to include a correction for center of mass motion in the calculation of the mass distribution. This was accomplished under the assumption that the kinetic energy and direction of motion of the fissioning nucleus were those corre-
~-~
-
-
FORWARO
......
15
OACKWARID
I00 0
Fig.
0
,r--,--r
,
3
6
,
~--'--'--,
,
9 12 15 TRACK LENGTH (/,t.)
18
8O
21 IZ
10. Track length distribution for f r a g m e n t s from the 80 MeV alpha-induced fission o f gold.
,>. , 6 0 LI.J
"
40
I!..... .....
-I .....=L
20 .....
0 25
i L ....
0
,b
I I .....
[
q ......
~o ~o 40 50 60 70 80 LABORATORY ANGLE (OEGREES)
90
Fig. 12. A n g u l a r distribution o f the tracks from 197Au-F 80-MeV
20 60 FORWARD ........ >
BACKWARD
15
~J
40 ;;'-
L
20
0
o o
,~
,£
~
2s
~
FI,FI 3~
40
0
"I ~
$
~-q-
J 6
; 9
f2
";
__r-1 ,
15
~-r--~, f8
2t
TRACK LENGTH (/1.)
DIVERGENCE (DEGREES)
Fig. I I. Distribution o f the deviations from colinearity for the tracks from 1 9 7 A u + 80-MeV ~'s.
Fig. 13. Track length distribution o f the tracks from 197Au+ + 8 0 - M e V ~ ' s corrected for centre-of-mass m o t i o n a s s u m i n g c o m p o u n d nucleus formation.
362
F.
MICHAEL
KIELY
AND
s p o n d i n g to c o m p o u n d nucleus f o r m a t i o n between the projectile and target. W h e n each mass pair was selected, the c o r r e s p o n d i n g kinetic energies were corrected for the centre-of-mass motion. The corrected energies were then used to calculate the error function o f eq. (1) and the calculation c o n t i n u e d as before. W h e n the " b e s t " mass pair was found, the corrected energies were used to determine w h a t the t r a c k lengths and angles w o u l d have been in the centre-of-mass system.
/00
- -
FORWARD
......
BACKWARD
BRIAN
D.
(~ I-
4
60 F ..........
60
I
48 °2/-
z > tLi
t
i
i
30[-
24i-
_1
80
PATE
4,8
i
w
F
z 60 > hi
-'112
40
ot6.....
2O
25
0 0
,0
20
.~0 ANGLE
4b
5'0
.....
60
.- . . . . . .
i
70
80
4C
0 0
I 5
I
/ I0
Lf--
15 20 25 DIVERGENCE (DEGREES)
n,-30
35
/ 75
I00 125 150 FRAGMENT MASS
17'5
200
225
90
(DEGREES)
Fig. 14, Angular distribution in the centre-of-mass system for the tracks from 197Au+ 80-MeV :~'s.
1
50
40
Fig. 15. Distribution about colinearity in the centre-of-mass system for the tracks from 197Au+ 80-MeV ~t's.
Fig. 16. Mass yield curve for fragments from the 80-MeV alpha-induced fission of Au. The histogram was calculated from the data of the present experiment assuming compound nucleus formation (see text). The solid curve was obtained from existing radiochemical data (ref. 12), and the dashed curve represents adjustment of those data (see text). The resulting track length and a n g u l a r distributions are displayed in figs. 13 and 14. The track length distributions now peak at a p p r o x i m a t e l y the same value in each hemisphere, while the a n g u l a r distribution now a p p e a r s to be symmetric a b o u t 90 ° . M o r e o v e r the colinearity distribution in fig. 15 has been n a r r o w e d to _+6 °. It is c o n c l u d e d that centre-of-mass m o t i o n has been satisfactorily taken into account. The mass distribution o b t a i n e d from this analysis a p p e a r s as the h i s t o g r a m in fig. 16 and is seen to be in excellent agreement with the unmodified and modified radiochemical d a t a 12) (shown as a solid and dashed curve, respectively). It might be a d d e d t h a t the mass distribution calculated with no correction for centreof-mass m o t i o n exhibited a very b r o a d m a x i m u m (almost two humped), with nearly all the a p p a r e n t l y heavy mass fragments coming from tracks in the forward hemisphere and the a p p a r e n t l y light mass fragments from tracks in the b a c k w a r d direction. Several other centre-of-mass m o t i o n s were tried, from 50% to 125% o f c o m p o u n d nucleus. The results did not seem very sensitive to this p a r a m e t e r within this range, although the colinearity distribution was the
COINCIDENCE SPECTROSCOPY OF FISSION FRAGMENTS narrowest (by a slight a m o u n t ) at 100% o f c o m p o u n d nucleus m o m e n t u m .
363
tion o f the two fragments may, in other words, tend to reduce the uncertainty which would exist for consideration o f a single fragment.
4. Conclusions F r o m the foregoing, two general conclusions m a y perhaps be drawn: 1) F o r the m e a s u r e m e n t o f f r a g m e n t a n g u l a r distributions in detail, the mica sandwich configuration is unsuitable; the technique o f d o u b l e measurement, one with the b e a m at 0 ° to the mica surface and a second with the beam, say, at 45 ° to the surface, may p e r h a p s suffice in some cases, and m a y generally p r o d u c e d a t a c o m p l e t e enough for a useful total crosssection m e a s u r e m e n t to be possible. 2) F o r f r a g m e n t - m a s s distributions the technique is m o r e useful, and should perhaps be c a p a b l e o f detecting an increasing mass distribution width as the fissility o f the target system is reduced t o w a r d s the BusinaroG a l l o n e point I s). It would be preferable, were it possible, to extract the mass-distribution directly from the track length distribution, rather than the present necessity o f c o m p a r i n g the measured track length d i s t r i b u t i o n with that expected for a series o f '~trial" mass distributions. W o r k is presently u n d e r w a y on this possibility. It is interesting that the experimental mass distributions seemed in slightly better agreement with the radiochemical d a t a before the separately d e t e r m i n e d mass-resolution was folded in. It is not c o m p l e t e l y clear why this could be. One possibility which suggests itself is that the t r a n s f o r m a t i o n o f track length uncertainty to mass n u m b e r uncertainty is c o m p l i c a t e d by the use o f the conservation laws in o b t a i n i n g the " c o r r e c t " masses for a p a r t i c u l a r t r a c k pair. C o n s i d e r a -
The a u t h o r s are indebted to Dr T. T. S u g i h a r a and Texas A & M University for their hospitality in providing cyclotron time, to M r H. Blok for carrying out the a l p h a irradiations and to M r T. Bennett for 14-MeV neutron b o m b a r d m e n t s . They also wish to t h a n k D r L. B a b b and the staff o f the University o f W a s h i n g t o n R e a c t o r for their kind assistance with the reactor b o m b a r d m e n t s , and the o p e r a t i n g staff o f the S F U C o m p u t e r Centre for c o m p u t a t i o n a l services. W o r k was p e r f o r m e d under N a t i o n a l Research Council o f C a n a d a , G r a n t N u m b e r A2510.
References 1) R. L. Fleischer et al., Phys. Rev. 133 (1964) A1443. ':) J. P~ter and M. Lecerf, Nucl. Instr. and Meth. 104 (1972) 189. ~) M. Monnin, Th/~se (Facult6 des Sciences, Universit6 de Clermont, France, 1969). 4) R. L. Fleischer, P. B. Price and R. M. Walker, Ann. Rev. Nucl. Sci. 15 0965) I. 3) H. Blok and B. D. Pate, to be published (1973). ~) S. Katcoff and J. Hudis, Phys. Rev. 180 0969) 1122. 7) B. D. Pate and J. P/~tcr, Nucl. Phys. A173 (1971) 520. 8) G. Remy et al., J. Phys. 31 (1970) 27. ~) M. Ait-Salem et al., Nucl. Instr. and Meth. 60 (1968) 45. 10) H. Blok, F. M. Kiely and B. D. Pate, Nucl. Instr. and Meth. 100 0972) 403. tt) H. R. Von Gunte, Actinides Rev. 1 (1969) 275. le) F. Plasil et aI., Phys. Rev. 142 (1966) 696. la) H. A. Khan and S. A. Durrani, Nucl. Instr. and Meth. 98 0972) 229. 14) L. C. Northcliffe and R. F. Schilling, Nucl. Data Tables A7 (1970) 233. 15) j. R. Nix, Nucl. Phys. A130 0969) 241.