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c protons with heavy emulsion nuclei
Nuclear Physics 79 (1966) 449--458; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photnprint or microfilm without written permission from the publisher
ON THE RESIDUAL NUCLEI O B S E R V E D I N T H E I N T E R A C T I O N S O F 25 G e V / c P R O T O N S WITH HEAVY EMULSION
NUCLEI
E. MAKOWSKA, J. SIEMII~ISKA, M. SOLTAN and J. SUCHORZEWSKA Institute of Experimental Physics, University of Warsaw and Institute of Nuclear Research, Warsaw
and S. J. ST. LORANT t CERN, Geneva Received 21 July 1965 Abstract: The kinematical analysis of the residual nuclei in the interactions of 25 GeV/c protons
with heavy nuclei in low sensitivity nuclear emulsion was made for a sample of 354 stars containing aLi fragments. The average velocity component in the direction of the beam is fix = 0.0044-0.002 for recoils and fix = 0.0154-0.003 for SLi fragments. The average mass number of residual nuclei is found to be about 30. In 30 % of all the stars the masses of residual nuclei are comparable to those of other fragments. A correlation of the directions of motion of the residual nucleus and the emitted SLi fragment is found. I E
Interactions of 25 GeV/c protons with Ag and Br nuclei; aLi fragments, recoils; fix = 0.004:]:0.002 for recoils; fix = 0.0154-0.003 for aLi.
I
1. I n t r o d u c t i o n
R a d i o c h e m i c a l m e t h o d s 1 - 3 ) a n d the nuclear e m u l s i o n technique 4 - 6 ) have often been u s e d to investigate the recoiling residual f r a g m e n t s o f the t a r g e t nuclei p r o d u c e d in high-energy interactions. This w o r k describes the analysis o f the kinematics o f recoils o b s e r v e d in high-energy interactions in a s s o c i a t i o n with SLi fragments. T h e l o w sensitivity e m u l s i o n u s e d in the e x p e r i m e n t m a d e it possible to resolve the s h o r t t r a c k s o f the recoils n e a r the centre o f a star a n d to o b t a i n some i n f o r m a t i o n on their charge. 2. E x p e r i m e n t a l
Procedure
A s t a c k o f 600 # m I l f o r d K1 n u c l e a r e m u l s i o n pellicles i r r a d i a t e d in the 25 G e V / c p r o t o n b e a m f r o m the P r o t o n S y n c h r o t r o n at C E R N was used. Since the p r i m a r y p r o t o n s are n o t registered in K1 e m u l s i o n t t the direction o f the b e a m was o b t a i n e d t Present address: Stanford Linear Accelerator Center, Stanford University, Stanford, California. tt The standard Ilford K1 emulsion when normally processed does not register protons with energies above 7 MeV. 449~
450
E. M A K O W S r J L
e t aL
from K5 emulsion pellicles irradiated jointly with the main stack. To reduce the background of secondary interactions, an area 1 cm wide, lying near the beam entrance edge of the pellicle was scanned for stars with more than two prongs. All the prongs were followed in one pellicle in search for hammer tracks. The length of the u-particle tracks, their colinearity and ionization were used for the qualification of hammer tracks. Only well discernable hammerlike tracks were accepted. The majority of the 9Li fragments was probably eliminated in this way and the possible SB fragment contamination can certainly be neglected. The collected sample may be considered to be a reasonably pure SLi sample. Stars with SLi fragments were further examined for the presence of black tracks, that is tracks having an ionization greater than that of boron. While the selection of such tracks implied no maximum range criterion, the lower limit on range was taken to be 1 /zm. In practice such tracks proved to be shorter than 30 pro. These tracks will be termed "residual nuclei tracks" or "recoils" in the following. To eliminate interactions with light nuclei only stars with more than four tracks, excluding the recoil, were considered. Here this selection rule replaces the selection criterion Nh > 8 usually adopted with high sensitivity emulsion. The sample consists of 354 stars containing hammer tracks. In 176 such stars one black track with a large ionization was also found and in 19 stars two such tracks appeared. In 25 stars the presence of a residual nucleus track was uncertain. In the subsequent analysis these stars were included in the class of stars without residual nucleus track. If two black tracks were observed in one star neither of them was used to estimate the range or the angular distribution of the residual nuclei. One of them may be due to a heavy fragment 4) or possibly both are fission fragments ~3). A number (not exceeding 10 ~o), of single black tracks might also be due to heavy fragments. This percentage was estimated from the known frequency of stars with two black tracks. In the analysis a sample of 205 featureless stars with N ~ 5 found in the scanned area was also considered. 3. Biases
The efficiency of the scanning for stars was estimated from the results obtained in three successive scannings. This efficiency depends on the number of visible prongs and it increases from the value of 60 ~o for five prong stars to 85 ~o for stars with a prong number above 8. Within statistical errors the efficiency of the scanning is independent of the presence of a residual nucleus track or of a short hammer track in a star. The scanning efficiency affects the range distribution of the residual nuclei since these ranges depend on the prong number of each interaction. 4. Results 4.1. RANGE DISTRIBUTIONOF THE RESIDUAL NUCLEI
The observed range distribution of residual nuclei in stars containing a SLi track
451
RESIDUAL NUCLEI
is shown in fig. la; the shaded portion of the distribution represents the correction introduced by taking scanning efficiency into account. The mean range of the corrected sample is 5.3 #m and this figure increases with the prong number (fig. 2). This is thought to be due to the decrease in the mass of the residual nuclei with a
/'o )
30
25
20
10
1 2
~
i
i
6
8 ID IZ 14, 16 18 20 Z2 30 Rgnqe in,~m (/_7)
~0
30
i
I
i
I
i
i
-10 -QS-Q6-Q4 -Q2 O" 02 O~ 06 08 ZO
cos (r,p) Fig. I. Range and angular distributions of residual nucleus tracks in stars with hammer tracks. (a) Range distribution; the shaded area corresponds to the residual nuclei from the lost stars with 5 ~ N < 8. (b) The distribution o f the angle between the direction of flight of the residual nucleus and the incident beam.
452
~. t,tAKOWSrd~ et al.
concomitant increase in the momentum transfer to this residue. The velocity distribution of the residual nuclei in stars with SLi fragments (fig. 3) was obtained from the range-velocity relation for heavy ions of mass number 20 < A < 40 calculated on the basis of data given by Heckmarm et aL 7). The distribution obtained for the velocity component in the direction of the beam
~mj 85
8O
20
65
GO 55 50 45 tO .
3
4
5
.
6
7 8 Number o//racks
ff
lO
l!
I2
Fig. 2. The dependence of the average range of the residual nucleus on the prong number in stars containing hammer tracks. is also shown in fig. 3. The mean value of this component is different from zero. The shape of the distribution has been compared with the Gaussian distribution which may be expected in the approximation of the two stage model discussed below. The distribution has been normalized to the number of events in the external parts o f the distribution where no loss of tracks is to be expected (Ivxl > 0.016 c). The mean value fix = 0.004_+0.002 and the dispersion a(vx) = (0.016_+0.002) c of the
453
RESIDUAL NUCLEI
Gaussian distribution give the best fit to the unbiased parts of the estimated distribution. With this assumption 75 + 13 9/0 of all the recoils are registered, producing tracks of the range above 1 #m. The dispersion of the distribution of the velocity component in the direction perpendicular to the beam and the percentage of invisible recoils were found to be similar. Taking into account the stars with 8Li fragments containing one or two black prongs we conclude that residual nuclei are present in about 70 9/0 of all interactions considered here. These considerations derive further support from the comparison of the mean prong number of stars containing both a hammer
60
50
?5
?o
30
20
10
\½ 14
30
V1 78 V -~.8
-~2
-~6
0
I6
37
48
6.~ ?)x
Veloc~tq m umt5 o[ ROlc
Fig. 3. The velocity distribution of the residual nucleus tracks from stars containing hammer tracks and the distribution of the velocity component in the beam direction. The continuous line represents the best fit of the Gaussian distribution in the region [Vx[> 16× 10-8c. The best fit values of the parameters are given. The shaded area corresponds to the residual nuclei from the lost small stars. track and a recoil track * (N = 8.0+0.2) and a hammer track only (N = 9.3+0.2). Prong multiplicity in stars without a recoil should be smaller than in stars with a recoil if the lack of a recoil track is due to a too small velocity of the residual nucleus for this track to be registered (fig. 2). If, on the other hand, the residual nucleus is lost by being indistinguishable from the other light fragments, the prong multiplicity should be larger. It is seen that the latter effect may be significant. A similar result is obtained from the Nh prong number distribution for stars containing hammer tracks observed in normal emulsion s). From the analysis of t Recoils were excluded f r o m the p r o n g n u m b e r , as c o n t a m i n a t i o n by u n o b s e r v a b l e residual nuclei o f very s h o r t range is t h o u g h t to be present.
454
E. MAKOWSKA e t al.
the charge carried by particles emitted from stars with Nu _~ 26 it follows that such stars possibly correspond to the disintegration of nuclei in which there is no heavy residual nucleus left at the end of the process 15). The average mass number of the residual nucleus taken over all interactions was found to be 30_+ 10. This was estimated from the total charge of all the particles emitted in the first and second stage of the collision assuming appropriate relative emission probabilities for different particles 12). A similar value was obtained from the comparison of the experimentally estimated velocity distribution of the recoils with the calculated distribution of the resultant velocity transferred to the residual nucleus. 4.2 A N G U L A R DISTRIBUTION O F R E S I D U A L N U C L E I
The angular distribution of residual nuclei with respect to the beam direction for stars containing a SLi fragment is shown in fig. lb. The forward-to-backward ratio is 1.4_+0.2. The forward,to-backward ratio of the residual nuclei in a sample of stars with SLi fragment emitted in the forward hemisphere is equal to 0.8_+0.2 whereas for stars with 8Li fragment emitted backward it is as high as 3.0_+0.8. ~0
s0
L
[ . |
,
..... cos (c,h)
Fig. 4. The distribution of the angle between the directions of flight of the residual nucleus and the
fragment. The correlation between the direction of the fragment track and that of the residual nucleus is shown in fig. 4. In 74_+4 ~o of all events the angle between these two tracks is greater than 90 °. 4.3. A V E R A G E STARS
In a sample of 205 stars a single short black track was observed in 95 events. The following results were obtained: (i) The average length of the black tracks (R ~ 1 #m) is equal to 5.3_+0.4 #m.
RESIDUAL NUCLEI
455
An increase in the average length of the r~oils with increasing prong number in a star was observed. (ii) The forward-to-backward ratio is 1.8±0.4. (iii) The upper limit of the fix value has been estimated to be 0.006. The average number of prongs in stars with and without a visible recoil is equal to 7.3 ± 0.2 and 7.5 ± 0.3, respectively. This taken in conjunction with the prong number distribution in similar stars in emulsion of normal sensitivity s) indicates that in a small fraction of average interactions no massive residual nucleus is left. The frequency of occurrence of two black tracks in a star is equal to about 4 ~o. 5. Discussion
Assuming independent, isotropie emission of slow particles from a nucleus which is moving as a consequence of an earlier stage of the process, the velocity of the residual nucleus will be the vector sum of the velocities of the emitting nucleus and of the emitted constituent particles. This resultant velocity should have a Maxwellian distribution while its longitudinal and transverse components will have a Gaussian distribution with a dispersion depending on the number and the momenta of the . emitted particles. The Monte-Carlo approach to the intranuclear cascade can give the form of the velocity distribution of the emitting nucleus; the calculations of Porile 11) at lower energies of the primary protons however do not lead to a Gaussian shape. This may be due in part to the kinetics of the emission process; if the number of particles emitted in the second stage of the cascade is large then it may critically influence the velocity distribution of the residual nuclei. A reasonable approximation to the dispersion of the distribution as obtained by considering the second state of the process only is given by 1
a(v)=(m)V~=lp2
,
(1)
where n denotes the number of subsequently emitted slow particles, m the variable mass of the nucleus in the second stage of the process and Pi the momentum of the Rh emitted particle. In the equation the decrease in the mass of the nucleus during the emission process was taken into account approximately. It was assumed that the composition of the emitted particles and their mean momenta are consistent with those considered in refs. 1o, ~2). The dependence of the probability of emission of particles on the cooling down of the nucleus has been neglected. The experimental value of the quantity a(Vx) is consistent with that calculated using eq. (1) under the assumption (l/m) = ~o, corresponding to an average value of about 30 for the mass of the residual nucleus. The relation between the forward-to-backward ratio of the residual nuclei and the longitudinal component of the momentum of the SLi fragment has been calculated on the basis of the model (fig. 5). Previous experimental values of the mean velocity
456
E. MAKOWSKAet aL
/~x a n d d i s p e r s i o n a(vx) are consistent with this calculation p r o v i d e d t h a t in the s e c o n d stage o f the process the nucleus is a s s u m e d to have an initial m a s s M o n the average equal to 50-80. T h e o b s e r v e d c o r r e l a t i o n o f the direction between the t r a c k o f the residual nucleus a n d t h a t o f the SLi f r a g m e n t (fig. 4) is consistent with the p r e d i c t i o n s o f the m o d e l for the same values o f the p a r a m e t e r s M a n d a. 7
5
/7
2
i
-600
300
t
200
i
0
J
ZOO
i
400
600
Fig. 5. The dependence of the forward-to-backward ratio of the visible residual nuclei on the momentum component of the fragment in the beam directions. The crosses are the experimental points, the theoretical continuous lines are calculated for the following parameters: (i)/~, = 0.010, a(v,) = 0.016, M = 70; (ii)/~x = 0.005, a(Vx) = 0.016, M = 50; (iii)/3x = 0.005, a(vx) = 0.019, M = 70, where M denotes the mass of the nucleus after the emission of the 8Li fragment. Fig. 6 shows the results o f the calculation o f the r e l a t i o n between the f o r w a r d t o - b a c k w a r d r a t i o o f the residual nuclei a n d the average c o m p o n e n t o f the velocity /~x o f these nuclei in the direction o f the b e a m . T h e curves are c a l c u l a t e d for different values o f the dispersion. T h e e x p e r i m e n t a l value F I B = 1.4_+0.2 for stars c o n t a i n i n g a 8Li f r a g m e n t is also i n d i c a t e d in fig. 6. T h e c h a r a c t e r o f the d e p e n d e n c e
457
RESIDUAL NUCLEI
shows that only low values of fix are consistent with experimental results. Taking into account a possible admixture of fragments among the residual nuclei not exceeding 10 ~o of all the events we come to the conclusion that the previously obtained value of fix might probably be slightly underestimated. Nevertheless the corrected value would be about 0.005, which would not affect the results of the analysis.
6=~2008c
6=QOlbc
5
~
3
~
!
2
3
4
t
i
h
i
i
i
i
5
6
7
8
9
10
11
I2
i
i
t
t
t
t
i
I3
14
I5
/6
17
I8
1g
Veloc/tt/ /n units o~ 0001c
Fig. 6. The calculated relation between the forward-to-backward ratio of the residual nuclei and the average component of the velocity fix of these nuclei in the direction of the beam for different values of the dispersion. The experimental value FIB = 1.4-4-0.2 for visible recoils is indicated.
6. Conclusion The estimated average velocity component fix = 0.004+0.002 of the residual nuclei is much lower than the corresponding value fix = 0.015+0.003 usually obtained for fragments (see e.g. ref. 9)). The same high value of fix was obtained from SLi fragment data in this experiment. Thus the velocity of a system of isotropic emission of the fragments cannot be identified with the velocity of the whole system of nucleons in thermodynamic equilibrium. The estimated frequency of heavy recoils with ranges below 1 /~m is 17___9 ~ . In about 30 ~ of the cases the mass of recoil is comparable with the masses of other fragments. In about 4 ~ of the stars, two short black tracks have been found. The tracks are interpreted as being due to fission fragments or to a recoil accompanied by a fragment. The estimated average mass number of the residual nucleus in all interactions here considered is 30___10.
458
E. ~O.KOWSr.~et aL
The average range of the recoils registered as black tracks (R > 1/~m) is 5.3/am. This average range increases with the increasing prong number in a star. A correlation is observed between the direction of the recoil track and that of the 8Li fragment as well as a dependence of the F I B ratio for the recoils on the direction of 8Li emission. N o t e added: After this paper was completed, an article by Breivik, Jacobsen and S6rensen 16) appeared devoted to the analysis of residual nuclei in interactions of 4.5 GeV negative pious with heavy nuclei in emulsion. Some of the results reached by these authors are similar to ours.
We wish to express our indebtedness to Professor J. Pniewski and Dr. P. Zieli~ski for their help and valuable advice. We wish to thank also Drs. B. D. Hyams and G. Vanderhaeghe of CERN, Geneva, for permission to use the beam and the processing facilities respectively and the scanning team in Warsaw for careful scanning and measurements.
References 1) J. B. Cummings, R. J. Cross Jr., J. Hudis and A. M. Poskanzcr, Phys. Rev. 134 (1964) B167 2) J. B. Cummings et aL, Phys. Rev. 134 (1964) B1262 3) L. Winsberg, Phys. Rev. 135 (1964) Bl105 4) P. A. Goritchev, O. V. Lozhkin and N. A. Perfilov, JETP 45 (1963) 1784 5) O. V. Lozhkin and N. A. Perfilov, JETP 31 (1956) 913 6) V. I. Ostroumov, JETP 32 (1957) 3 7) H. H. Heckman et al., Phys. Rev. 117 (1960) 544 8) W. Gajewski et aL, Nuclear Physics 45 (1963) 27 9) W. Gajewski et aL, Nuclear Physics58 (1964) 17 10) E. W. Baker and S. Katcoff, Phys. Rev. 123 (1961) 641 11) N. T. Porile, Phys. Rev. 120 (1960) 572 12) D. H. Perkins, Phil. Mag. 41 (1950) 138 13) E. W. Baker and S. Katcoff, Phys. Rev. 126 (1962) 729 14) N. Metropolis et aL, Phys. Rev. 110 (1958) 204 15) R. Kaczarowski and E. Makowska, Nuclear Physics 74 (1965) 348 16) F. O. Breivik, T. Jacobsen and S. O. SOrensen, Nuclear Physics 61 (1965) 321
ON THE RESIDUAL NUCLEI O B S E R V E D I N T H E I N T E R A C T I O N S O F 25 G e V / c P R O T O N S WITH HEAVY EMULSION
NUCLEI
E. MAKOWSKA, J. SIEMII~ISKA, M. SOLTAN and J. SUCHORZEWSKA Institute of Experimental Physics, University of Warsaw and Institute of Nuclear Research, Warsaw
and S. J. ST. LORANT t CERN, Geneva Received 21 July 1965 Abstract: The kinematical analysis of the residual nuclei in the interactions of 25 GeV/c protons
with heavy nuclei in low sensitivity nuclear emulsion was made for a sample of 354 stars containing aLi fragments. The average velocity component in the direction of the beam is fix = 0.0044-0.002 for recoils and fix = 0.0154-0.003 for SLi fragments. The average mass number of residual nuclei is found to be about 30. In 30 % of all the stars the masses of residual nuclei are comparable to those of other fragments. A correlation of the directions of motion of the residual nucleus and the emitted SLi fragment is found. I E
Interactions of 25 GeV/c protons with Ag and Br nuclei; aLi fragments, recoils; fix = 0.004:]:0.002 for recoils; fix = 0.0154-0.003 for aLi.
I
1. I n t r o d u c t i o n
R a d i o c h e m i c a l m e t h o d s 1 - 3 ) a n d the nuclear e m u l s i o n technique 4 - 6 ) have often been u s e d to investigate the recoiling residual f r a g m e n t s o f the t a r g e t nuclei p r o d u c e d in high-energy interactions. This w o r k describes the analysis o f the kinematics o f recoils o b s e r v e d in high-energy interactions in a s s o c i a t i o n with SLi fragments. T h e l o w sensitivity e m u l s i o n u s e d in the e x p e r i m e n t m a d e it possible to resolve the s h o r t t r a c k s o f the recoils n e a r the centre o f a star a n d to o b t a i n some i n f o r m a t i o n on their charge. 2. E x p e r i m e n t a l
Procedure
A s t a c k o f 600 # m I l f o r d K1 n u c l e a r e m u l s i o n pellicles i r r a d i a t e d in the 25 G e V / c p r o t o n b e a m f r o m the P r o t o n S y n c h r o t r o n at C E R N was used. Since the p r i m a r y p r o t o n s are n o t registered in K1 e m u l s i o n t t the direction o f the b e a m was o b t a i n e d t Present address: Stanford Linear Accelerator Center, Stanford University, Stanford, California. tt The standard Ilford K1 emulsion when normally processed does not register protons with energies above 7 MeV. 449~
450
E. M A K O W S r J L
e t aL
from K5 emulsion pellicles irradiated jointly with the main stack. To reduce the background of secondary interactions, an area 1 cm wide, lying near the beam entrance edge of the pellicle was scanned for stars with more than two prongs. All the prongs were followed in one pellicle in search for hammer tracks. The length of the u-particle tracks, their colinearity and ionization were used for the qualification of hammer tracks. Only well discernable hammerlike tracks were accepted. The majority of the 9Li fragments was probably eliminated in this way and the possible SB fragment contamination can certainly be neglected. The collected sample may be considered to be a reasonably pure SLi sample. Stars with SLi fragments were further examined for the presence of black tracks, that is tracks having an ionization greater than that of boron. While the selection of such tracks implied no maximum range criterion, the lower limit on range was taken to be 1 /zm. In practice such tracks proved to be shorter than 30 pro. These tracks will be termed "residual nuclei tracks" or "recoils" in the following. To eliminate interactions with light nuclei only stars with more than four tracks, excluding the recoil, were considered. Here this selection rule replaces the selection criterion Nh > 8 usually adopted with high sensitivity emulsion. The sample consists of 354 stars containing hammer tracks. In 176 such stars one black track with a large ionization was also found and in 19 stars two such tracks appeared. In 25 stars the presence of a residual nucleus track was uncertain. In the subsequent analysis these stars were included in the class of stars without residual nucleus track. If two black tracks were observed in one star neither of them was used to estimate the range or the angular distribution of the residual nuclei. One of them may be due to a heavy fragment 4) or possibly both are fission fragments ~3). A number (not exceeding 10 ~o), of single black tracks might also be due to heavy fragments. This percentage was estimated from the known frequency of stars with two black tracks. In the analysis a sample of 205 featureless stars with N ~ 5 found in the scanned area was also considered. 3. Biases
The efficiency of the scanning for stars was estimated from the results obtained in three successive scannings. This efficiency depends on the number of visible prongs and it increases from the value of 60 ~o for five prong stars to 85 ~o for stars with a prong number above 8. Within statistical errors the efficiency of the scanning is independent of the presence of a residual nucleus track or of a short hammer track in a star. The scanning efficiency affects the range distribution of the residual nuclei since these ranges depend on the prong number of each interaction. 4. Results 4.1. RANGE DISTRIBUTIONOF THE RESIDUAL NUCLEI
The observed range distribution of residual nuclei in stars containing a SLi track
451
RESIDUAL NUCLEI
is shown in fig. la; the shaded portion of the distribution represents the correction introduced by taking scanning efficiency into account. The mean range of the corrected sample is 5.3 #m and this figure increases with the prong number (fig. 2). This is thought to be due to the decrease in the mass of the residual nuclei with a
/'o )
30
25
20
10
1 2
~
i
i
6
8 ID IZ 14, 16 18 20 Z2 30 Rgnqe in,~m (/_7)
~0
30
i
I
i
I
i
i
-10 -QS-Q6-Q4 -Q2 O" 02 O~ 06 08 ZO
cos (r,p) Fig. I. Range and angular distributions of residual nucleus tracks in stars with hammer tracks. (a) Range distribution; the shaded area corresponds to the residual nuclei from the lost stars with 5 ~ N < 8. (b) The distribution o f the angle between the direction of flight of the residual nucleus and the incident beam.
452
~. t,tAKOWSrd~ et al.
concomitant increase in the momentum transfer to this residue. The velocity distribution of the residual nuclei in stars with SLi fragments (fig. 3) was obtained from the range-velocity relation for heavy ions of mass number 20 < A < 40 calculated on the basis of data given by Heckmarm et aL 7). The distribution obtained for the velocity component in the direction of the beam
~mj 85
8O
20
65
GO 55 50 45 tO .
3
4
5
.
6
7 8 Number o//racks
ff
lO
l!
I2
Fig. 2. The dependence of the average range of the residual nucleus on the prong number in stars containing hammer tracks. is also shown in fig. 3. The mean value of this component is different from zero. The shape of the distribution has been compared with the Gaussian distribution which may be expected in the approximation of the two stage model discussed below. The distribution has been normalized to the number of events in the external parts o f the distribution where no loss of tracks is to be expected (Ivxl > 0.016 c). The mean value fix = 0.004_+0.002 and the dispersion a(vx) = (0.016_+0.002) c of the
453
RESIDUAL NUCLEI
Gaussian distribution give the best fit to the unbiased parts of the estimated distribution. With this assumption 75 + 13 9/0 of all the recoils are registered, producing tracks of the range above 1 #m. The dispersion of the distribution of the velocity component in the direction perpendicular to the beam and the percentage of invisible recoils were found to be similar. Taking into account the stars with 8Li fragments containing one or two black prongs we conclude that residual nuclei are present in about 70 9/0 of all interactions considered here. These considerations derive further support from the comparison of the mean prong number of stars containing both a hammer
60
50
?5
?o
30
20
10
\½ 14
30
V1 78 V -~.8
-~2
-~6
0
I6
37
48
6.~ ?)x
Veloc~tq m umt5 o[ ROlc
Fig. 3. The velocity distribution of the residual nucleus tracks from stars containing hammer tracks and the distribution of the velocity component in the beam direction. The continuous line represents the best fit of the Gaussian distribution in the region [Vx[> 16× 10-8c. The best fit values of the parameters are given. The shaded area corresponds to the residual nuclei from the lost small stars. track and a recoil track * (N = 8.0+0.2) and a hammer track only (N = 9.3+0.2). Prong multiplicity in stars without a recoil should be smaller than in stars with a recoil if the lack of a recoil track is due to a too small velocity of the residual nucleus for this track to be registered (fig. 2). If, on the other hand, the residual nucleus is lost by being indistinguishable from the other light fragments, the prong multiplicity should be larger. It is seen that the latter effect may be significant. A similar result is obtained from the Nh prong number distribution for stars containing hammer tracks observed in normal emulsion s). From the analysis of t Recoils were excluded f r o m the p r o n g n u m b e r , as c o n t a m i n a t i o n by u n o b s e r v a b l e residual nuclei o f very s h o r t range is t h o u g h t to be present.
454
E. MAKOWSKA e t al.
the charge carried by particles emitted from stars with Nu _~ 26 it follows that such stars possibly correspond to the disintegration of nuclei in which there is no heavy residual nucleus left at the end of the process 15). The average mass number of the residual nucleus taken over all interactions was found to be 30_+ 10. This was estimated from the total charge of all the particles emitted in the first and second stage of the collision assuming appropriate relative emission probabilities for different particles 12). A similar value was obtained from the comparison of the experimentally estimated velocity distribution of the recoils with the calculated distribution of the resultant velocity transferred to the residual nucleus. 4.2 A N G U L A R DISTRIBUTION O F R E S I D U A L N U C L E I
The angular distribution of residual nuclei with respect to the beam direction for stars containing a SLi fragment is shown in fig. lb. The forward-to-backward ratio is 1.4_+0.2. The forward,to-backward ratio of the residual nuclei in a sample of stars with SLi fragment emitted in the forward hemisphere is equal to 0.8_+0.2 whereas for stars with 8Li fragment emitted backward it is as high as 3.0_+0.8. ~0
s0
L
[ . |
,
..... cos (c,h)
Fig. 4. The distribution of the angle between the directions of flight of the residual nucleus and the
fragment. The correlation between the direction of the fragment track and that of the residual nucleus is shown in fig. 4. In 74_+4 ~o of all events the angle between these two tracks is greater than 90 °. 4.3. A V E R A G E STARS
In a sample of 205 stars a single short black track was observed in 95 events. The following results were obtained: (i) The average length of the black tracks (R ~ 1 #m) is equal to 5.3_+0.4 #m.
RESIDUAL NUCLEI
455
An increase in the average length of the r~oils with increasing prong number in a star was observed. (ii) The forward-to-backward ratio is 1.8±0.4. (iii) The upper limit of the fix value has been estimated to be 0.006. The average number of prongs in stars with and without a visible recoil is equal to 7.3 ± 0.2 and 7.5 ± 0.3, respectively. This taken in conjunction with the prong number distribution in similar stars in emulsion of normal sensitivity s) indicates that in a small fraction of average interactions no massive residual nucleus is left. The frequency of occurrence of two black tracks in a star is equal to about 4 ~o. 5. Discussion
Assuming independent, isotropie emission of slow particles from a nucleus which is moving as a consequence of an earlier stage of the process, the velocity of the residual nucleus will be the vector sum of the velocities of the emitting nucleus and of the emitted constituent particles. This resultant velocity should have a Maxwellian distribution while its longitudinal and transverse components will have a Gaussian distribution with a dispersion depending on the number and the momenta of the . emitted particles. The Monte-Carlo approach to the intranuclear cascade can give the form of the velocity distribution of the emitting nucleus; the calculations of Porile 11) at lower energies of the primary protons however do not lead to a Gaussian shape. This may be due in part to the kinetics of the emission process; if the number of particles emitted in the second stage of the cascade is large then it may critically influence the velocity distribution of the residual nuclei. A reasonable approximation to the dispersion of the distribution as obtained by considering the second state of the process only is given by 1
a(v)=(m)V~=lp2
,
(1)
where n denotes the number of subsequently emitted slow particles, m the variable mass of the nucleus in the second stage of the process and Pi the momentum of the Rh emitted particle. In the equation the decrease in the mass of the nucleus during the emission process was taken into account approximately. It was assumed that the composition of the emitted particles and their mean momenta are consistent with those considered in refs. 1o, ~2). The dependence of the probability of emission of particles on the cooling down of the nucleus has been neglected. The experimental value of the quantity a(Vx) is consistent with that calculated using eq. (1) under the assumption (l/m) = ~o, corresponding to an average value of about 30 for the mass of the residual nucleus. The relation between the forward-to-backward ratio of the residual nuclei and the longitudinal component of the momentum of the SLi fragment has been calculated on the basis of the model (fig. 5). Previous experimental values of the mean velocity
456
E. MAKOWSKAet aL
/~x a n d d i s p e r s i o n a(vx) are consistent with this calculation p r o v i d e d t h a t in the s e c o n d stage o f the process the nucleus is a s s u m e d to have an initial m a s s M o n the average equal to 50-80. T h e o b s e r v e d c o r r e l a t i o n o f the direction between the t r a c k o f the residual nucleus a n d t h a t o f the SLi f r a g m e n t (fig. 4) is consistent with the p r e d i c t i o n s o f the m o d e l for the same values o f the p a r a m e t e r s M a n d a. 7
5
/7
2
i
-600
300
t
200
i
0
J
ZOO
i
400
600
Fig. 5. The dependence of the forward-to-backward ratio of the visible residual nuclei on the momentum component of the fragment in the beam directions. The crosses are the experimental points, the theoretical continuous lines are calculated for the following parameters: (i)/~, = 0.010, a(v,) = 0.016, M = 70; (ii)/~x = 0.005, a(Vx) = 0.016, M = 50; (iii)/3x = 0.005, a(vx) = 0.019, M = 70, where M denotes the mass of the nucleus after the emission of the 8Li fragment. Fig. 6 shows the results o f the calculation o f the r e l a t i o n between the f o r w a r d t o - b a c k w a r d r a t i o o f the residual nuclei a n d the average c o m p o n e n t o f the velocity /~x o f these nuclei in the direction o f the b e a m . T h e curves are c a l c u l a t e d for different values o f the dispersion. T h e e x p e r i m e n t a l value F I B = 1.4_+0.2 for stars c o n t a i n i n g a 8Li f r a g m e n t is also i n d i c a t e d in fig. 6. T h e c h a r a c t e r o f the d e p e n d e n c e
457
RESIDUAL NUCLEI
shows that only low values of fix are consistent with experimental results. Taking into account a possible admixture of fragments among the residual nuclei not exceeding 10 ~o of all the events we come to the conclusion that the previously obtained value of fix might probably be slightly underestimated. Nevertheless the corrected value would be about 0.005, which would not affect the results of the analysis.
6=~2008c
6=QOlbc
5
~
3
~
!
2
3
4
t
i
h
i
i
i
i
5
6
7
8
9
10
11
I2
i
i
t
t
t
t
i
I3
14
I5
/6
17
I8
1g
Veloc/tt/ /n units o~ 0001c
Fig. 6. The calculated relation between the forward-to-backward ratio of the residual nuclei and the average component of the velocity fix of these nuclei in the direction of the beam for different values of the dispersion. The experimental value FIB = 1.4-4-0.2 for visible recoils is indicated.
6. Conclusion The estimated average velocity component fix = 0.004+0.002 of the residual nuclei is much lower than the corresponding value fix = 0.015+0.003 usually obtained for fragments (see e.g. ref. 9)). The same high value of fix was obtained from SLi fragment data in this experiment. Thus the velocity of a system of isotropic emission of the fragments cannot be identified with the velocity of the whole system of nucleons in thermodynamic equilibrium. The estimated frequency of heavy recoils with ranges below 1 /~m is 17___9 ~ . In about 30 ~ of the cases the mass of recoil is comparable with the masses of other fragments. In about 4 ~ of the stars, two short black tracks have been found. The tracks are interpreted as being due to fission fragments or to a recoil accompanied by a fragment. The estimated average mass number of the residual nucleus in all interactions here considered is 30___10.
458
E. ~O.KOWSr.~et aL
The average range of the recoils registered as black tracks (R > 1/~m) is 5.3/am. This average range increases with the increasing prong number in a star. A correlation is observed between the direction of the recoil track and that of the 8Li fragment as well as a dependence of the F I B ratio for the recoils on the direction of 8Li emission. N o t e added: After this paper was completed, an article by Breivik, Jacobsen and S6rensen 16) appeared devoted to the analysis of residual nuclei in interactions of 4.5 GeV negative pious with heavy nuclei in emulsion. Some of the results reached by these authors are similar to ours.
We wish to express our indebtedness to Professor J. Pniewski and Dr. P. Zieli~ski for their help and valuable advice. We wish to thank also Drs. B. D. Hyams and G. Vanderhaeghe of CERN, Geneva, for permission to use the beam and the processing facilities respectively and the scanning team in Warsaw for careful scanning and measurements.
References 1) J. B. Cummings, R. J. Cross Jr., J. Hudis and A. M. Poskanzcr, Phys. Rev. 134 (1964) B167 2) J. B. Cummings et aL, Phys. Rev. 134 (1964) B1262 3) L. Winsberg, Phys. Rev. 135 (1964) Bl105 4) P. A. Goritchev, O. V. Lozhkin and N. A. Perfilov, JETP 45 (1963) 1784 5) O. V. Lozhkin and N. A. Perfilov, JETP 31 (1956) 913 6) V. I. Ostroumov, JETP 32 (1957) 3 7) H. H. Heckman et al., Phys. Rev. 117 (1960) 544 8) W. Gajewski et aL, Nuclear Physics 45 (1963) 27 9) W. Gajewski et aL, Nuclear Physics58 (1964) 17 10) E. W. Baker and S. Katcoff, Phys. Rev. 123 (1961) 641 11) N. T. Porile, Phys. Rev. 120 (1960) 572 12) D. H. Perkins, Phil. Mag. 41 (1950) 138 13) E. W. Baker and S. Katcoff, Phys. Rev. 126 (1962) 729 14) N. Metropolis et aL, Phys. Rev. 110 (1958) 204 15) R. Kaczarowski and E. Makowska, Nuclear Physics 74 (1965) 348 16) F. O. Breivik, T. Jacobsen and S. O. SOrensen, Nuclear Physics 61 (1965) 321