Emission of 8Li fragments from interactions of 9 and 24 GeV protons with heavy emulsion nuclei

Nuclear Physics 58 (1964) 17--31; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

E M I S S I O N OF SLi FRAGMENTS FROM INTERACTIONS OF 9 AND 24 GeV P R O T O N S W I T H HEAVY E M U L S I O N NUCLEI W. GAJEWSKI, J. PNIEWSKI, J. SIEMII~SKA, J. SUCHORZEWSKA and P. ZIELII~ISKI

Institute of Experimental Physics, University of Warsaw and

Institute of Nuclear Research, Warsaw Received 14 February 1964 A full account of the work concerning 445 hammer tracks collected from 9 GeV and 24 GeV proton interactions with heavy emulsion nuclei is presented. The conditions of the routine work on hammer tracks are established. The frequency of emission o f SLi fragments for different Nn intervals was estimated. Taking into account the effect of the motion o f the nucleus the velocity fluctuations and nuclear recoil resulting from the fragment emission, the angular distribution and the energy spectrum were compared with the results of evaporation theory. The values of the parameters T, V and 8, representing the temperature, Coulomb barrier and average velocity of the emitting nucleus, were estimated on different assumptions. A high value of T and a low value of V were obtained.

Abstract:

1. Introduction The history of investigations of the emission of fragments from the interactions of high-energy particles with heavy nuclei is nearly twenty years old but the situation in this field is still ambiguous. The accumulated experimental material, not always consistent, has not yet been positively elaborated from the theoretical point of view. It has neither been definitely ascertained what is the extent of the applicability of the statistical model of the nucleus, so far the only model in this field giving quantitative results, although everybody agrees that at the present stage this model is not sufficient. It is not even known whether different processes are responsible for the fragment emission and if so, what are their features. The present work constitutes one more attempt 1-4) to provide experimental data concerning the emission of SLi fragments from the interactions of 9 and 24 GeV protons with heavy nuclei of nuclear emulsion and to compare these data with the basic results of the evaporation theory. In the case of fragments yielding characteristic hammer - like tracks in emulsion there exists a possibility to collect information on the whole energy spectrum and to obtain a nearly clean sample of well-identified fragments. Additional data on the other charged particles emitted from the interactions complement the picture of nuclear fragmentation. 17

18

w. GAJEWSKI el al.

2. Experimental Material

The experimental material was obtained f r o m two stacks of nuclear emulsion. The first one was composed of N I K F I R emulsion 10 c m x 10 em x 400 #m irradiated with a beam of 9 GeV protons in the synchrotron at Dubna, whereas the second one consisted of Ilford G-5 emulsion 5 em x 10 cm x 600/tin exposed to the beam of 24 GeV protons from the synchrotron at C E R N . Three samples of interactions of primary particles with heavy emulsion nuclei were obtained. The first sample consisted of 14800 stars with N h > 9 among which 188 hammer tracks were detected as the result of the scanning along the secondary tracks and ascribed to SLi fragments produced in the interactions of 9 GeV protons. The second sample contained about 12 000 stars with N h ~ 9 among which there were 198 h a m m e r tracks due to SLi fragments from the interactions of 24 GeV protons. The additional third sample consisted of 1340 stars with N h ~ 27, produced by the interactions of 9 GeV protons, which partially overlapped with the stars of the first sample. In all, 445 SLi tracks were collected of which 94 came from stars with N h > 27. SLi fragments found in stars with N h > 27 came mainly from the interactions with silver nuclei; in general, this was confirmed even by a rough estimation of charge. Details concerning all three samples m a y be found in refs. 5, 6). In this work, as well as in the earlier s, 6), particular attention was paid to the elimination, as complete as possible, of scanning biases affecting the emission picture, even at the cost of obtaining smaller statistics. The collection of samples, as clean as possible, of SLi fragments and the estimation of the remaining biases and losses made it possible to establish the conditions of routine work on hammer tracks. 3. Routine W o r k on H a m m e r Tracks 3.1. W R O N G Q U A L I F I C A T I O N O F T R A C K S TO T H E C A T E G O R Y O F H A M M E R T R A C K S

In a correctly processed emulsion with small background of random electron tracks there is a possibility to observe in 98 ~ of the cases tracks of ~ particles accompanying hammer tracks. This was checked on a sample of chosen hammer tracks with correctly registered ~t tracks of total length > 4/~m. Moreover, for every hammer track of this sample the atomic number Z of the fragment was established from track-width measurements s). At the same time in an emulsion with small background, not more than 2-3 % of tracks cannot be uniquely ascribed to the category of hammer tracks. This indeed happened in the case of the first stack. The higher background and the worse conditions of processing lowered the certainty of identification of electron tracks to 80 % in the case of the second stack and somewhat increased the percentage of tracks which could not be uniquely qualified as hammer tracks. 3.2. LOSS O F H A M M E R T R A C K S R E S U L T I N G F R O M T H E E N E R G Y A N D A N G U L A R D I S T R I B U T I O N S O F T R A C K S O F ct P A R T I C L E S C O M I N G F R O M T H E F R A G M E N T DECAYS

It was found that even in a careful and repeated scanning there was a loss of about 25 ~o of hammers with tracks of ,¢ particles short and steep or situated near the

EMISSION OF eli FRAGMENTS

19

fragment track itself. It is easy to lose up to 40 ~ of all hammer tracks in a less careful scanning. On the other hand, no definite loss was observed of hammers with even short ~ tracks if the latter were nearly flat and perpendicular to the fragment track. A random loss of tracks with favourably situated ~ tracks may be not higher than 5 ~ in a single scanning. These remarks may be applied to all hammer tracks and, in particular, to certain cases of hyperfragment decays. The ~ tracks of the lost 8Li fragments are limited mainly to the intervals: R < 8/~m, ~ < 30°, ~ > 45 °, where R is the range of an ~ track, ~0 and 9 are the azimuth and dip angles, respectively 5). 3.3. LOSS OF SHORT-RANGE FRAGMENTS As will be shown later, about 3 ~o of the total number of hammer tracks of the given energy spectrum are additionally lost. This is the result of the difficulties of observing short tracks with length less than 10 #m; such tracks are usually lost in about 30 ~ . This effect is partly connected with the difficulties of qualifying hammer tracks of this type and partly with the difficulties of detecting them in a high background of neighbouring tracks, in particular in stars with large N h or when the dip angles ill emulsion of the tracks are large. 3.4. S E L E C T I V E LOSS O F T R A C K S P A S S I N G TO N E I G H B O U R I N G E M U L S I O N S H E E T S

It was found that for the observed energy spectrum and angular distribution of fragments and for the vertical density distribution of parent stars in emulsion not much different from a uniform distribution, about 169/o of 8Li fragments leave the emulsion when it is 400/art thick and about 9 ~ when it is 600/lm thick. Ascribing a proper statistical weight to each track found one may, in principle, correct both the energy spectrum and the angular distribution of the emitted fragments. In fact, this can be done in that part of the energy spectrum where the statistics are large (e.g. E < 80 MeV). For the high-energy part of the spectrum (E > 80 MeV) the statistics are always poor and the introduced corrections strongly increase the fluctuation as can be seen from the distribution shown in the latter part of this work. An increase of the emulsion thickness does not essentially change the situation. One of the following two solutions may be considered: (i) following out of tracks passing to neighbouring emulsion sheets, (ii) a simultaneous scanning along the secondary tracks and an area scanning to detect passing tracks. Both these solutions, however, do not give a good efficiency. In this work, in the third sample (400/~m thick emulsion) all the secondary tracks were followed out whereas in the first sample (the same thickness) this was done only for half of the stars. The efficiency of this scanning was estimated to be 5 5 ~ due to the random loss and difficulties in making numerous followings. On the other hand, the efficiency of a similar scanning done by the same personnel within one emulsion sheet was 95 9/o. In this work all the results were corrected for the biases discussed here.

4. Identification of SLi Fragments Most of the B s fragments can be separated by the measurement of width of the hammer tracks when account is taken of the correction factors for dipping tracks.

W. GA,IEWSKI e t al.

"20

B y this method 90 % of tracks of the whole sample of hammer tracks with various dip angles can be identified. This solves the problem since the relative frequency o f emission of boron fragments is low. If follows from the attempts to estimate the content of 9Li fragments in the sample that the non-collinearity of tracks of ~ particles is an inappropriate criterion of identification of decays due to 9Li and SLi. Kinematic considerations of these decays lead to the conclusion that possible contamination of the sample with 9Li tracks is not larger than 39/0. Few events ( ~ 1%), consistent with the decay kinematics of 9Li and being interpretable in terms of 8Li on the assumption of little probability that the = particles suffered interactions, were excluded from the statistics.

5. Frequency of Emission of SLi Fragments The frequencies of emission of SLi fragments from the interactions of 9 and 24 GeV protons 5, 6) and 1.3 and 1.5 GeV/c K - mesons 7) for different intervals of N b are given in the quoted references. Fig. I illustrates these data and the lack of a

100 50"

°! 05

O4 03 02'

10

I

I

I

I

I

I

I

12

I4.

/8

f8

20

22

24

I

I

I

1

2S 28 3 0 3 2

~

I

38

.Nh

Fig. 1. Probability of the emission of SLi fragments per interaction for different Nh intervals. Primary beam: 1) protons: x 24 GeV, • 9 GeV, • 9 GeV (Nn :> 27) 2) K--mesons: A 1.5 GeV/c, O 1.3 GeV/c. definite relationship between the frequency of emission and the type or energy of the primary particle. A strong correlation of this frequency and the number of heavily ionizing particles emitted can easily be seen.

6. Angular Distributions The distributions in the laboratory system of angles of emission with respect to the primary beam for SLi fragments found in stars belonging to the three samples investigated are shown in fig. 2. These distributions are characterized by a certain

EMISSION OF SLi ]FRAGMENTS

21

anisotropy similar to that observed by S6rensen and Skjeggestad 9). These authors showed that such an anisotropy may be caused by the motion of the centre emitting fragments isotropically in its own system. Since the average velocity of the emitting centre may have only a longitudinal component, an attempt was made to find such a system moving with respect to the laboratory system with velocity/~ in which, independently of the energy of the fragments, the distribution of their momenta was isotropic or at least symmetric relative to the plane perpendicular to the direction

30

F=I47"-Q30

C

D

25 20 ~6

15

0 0

tO 5

f2

gGev Nh 26

0

lO

0

0 0

O8

75

0

06'

0

20

15 tO 9GeV

5 0 30

-~ ~5';~027

8 O o

o o

o

o

o

fO

NGeV

5 0 -~0 -Oa-06-0.,; -a2

0

82 t2~ Q6 08 ~0 COS ~)L OD

Fig. 2. Angular distributions of eLi fragments in the laboratory system. The shaded a r e a corresponds to the leaving hammer tracks found.

fOJ,,3 Fig. 3. Transformation to a system of the best isotropy of 8Li fragments. The Z2 and Kolmogorov-Smirnov tests of the hypothesis of isotropic emission for different values of velocity fl (primary 9 GeV protons).

of motion of the primary particle. An attempt was made to determine the optimum value of fl by three independent methods, i.e. by looking for a system in which (i) F / B = 1, (ii) there is the best isotropy for 20 intervals of the cosine of the emission angle in this system (see fig. 3) according to the X2 or Kolmogorov-Smirnov tests, (iii) the energy spectra of fra~nents emitted forwards or backwards have the least differences when considered separately.

22

w. OAJEWSKI e t al.

The following values of p were finally obtained: ]~ = 0.013-1-0.003 for the two samples taken from the interactions of 9 GeV protons and p = 0.015+0.003 for the sample from the interactions of 24 GeV protons. Similar indications concerning the values of ]~ were obtained from the analysis of the angular distributions of all black prongs belonging to large stars N h > 27 in ref. s) and from the analysis of the tracks of random stars. In the new systems the angular distributions o f SLi fragments are isotropic for all energies within the limits of 1 to 10 MeV/nucleon, independently o f N h of the parent stars. These distributions do not differ from isotropy by more than 1 standard deviation; even for the smallest stars an anisotropy that could have been expected for a large angular momentum of the emitting nucleus 1o) was not observed with the limits of the present statistics. The angular distributions of fragments of energy E < 1 MeV/nucleon in the moving systems are given in fig. 4. 7= 0015

p=~f3

24Ge V

0

0

t12.

a2

96eV

L2~

g"~

0~.

O~

ZO-

I.o

1.2-

z2

1.4

,

n ,

o ,

I o i

LO, -O.8 -OZ~ -0.4 -82

o

~,

a2

o,

tl4

o,

= ,

J

[1o OB I.O cos '#~s

1.~

a

" b ~o - ~ -d8 -fi4 -ae

.o

o%

de d4 d~ d8 ~o C05 ~15

Fig. 4. A n g u l a r distribution o f low energy SLi f r a g m e n t s in the system o f the best isotropy. T h e curves c o r r e s p o n d to the m o n o - e n e r g e t i c f r a g m e n t s in the l a b o r a t o r y system. Elab = 0.5 M e V / n u c l e o n c o r r e s p o n d s to t h e range 7.5 /~m. B = backwards, F = forwards.

The deviations from isotropy in these systems can easily be explained as the result of a loss in the scanning for tracks with ranges less than about 7 pro. The numbers of such tracks may be estimated from the curves drawn in that figure. The energy distributions were corrected for this bias; the frequencies of emission given in ref. 6) should be increased by about 3 ~o according to the remark given there. A similar effect was reported by Breivik et al. 1 ~). On the other hand, the situation in the energy region E > 10 MeV/nucleon requires to be checked on larger statistics. All 445 SLi fragments collected in this work are shown on fig. 5 in a representation in which the energy and longitudinal momentum of the fragments are plotted along the x and y axis, respectively. The points representing the tracks are situated inside the parabola (in the non-relativistic approximation). The axis of the parabola corresponds to the tracks of the fragments emitted at 90 ° in the laboratory system whereas the branches to those emitted at 0 ° and 180°, respectively. If the velocity of the centre-of-mass system of the excited nucleus has only a longitudinal component

23

EMISSION OF 8Li FRAGMENTS

/~, then in order to perform a transformation to this system the axes must be changed to the conjugate axes of the parabola. Simple relations between the two coordinate systems are shown in fig. 5. In a system of angular isotropy the distribution of experimental points in the strips parallel to the corresponding y axis is homogeneous and the density of the points gives the distribution function f ( E , p , ) d E d p , ; the eorrespondin~ x-axis divides the points into two groups so that the F I B ratio is equal

f

i

i j

1000

500 arc cm_

, '~..

\\

\

'\\ -500

.~ . ",

\

'\,

- 1500

Fig. 5. The energy spectrum and angular distribution of the whole sample of aLi fragments presented on the pst-E plane, where Pu is the longitudinal momentum and E the energy of the fragment. The curves correspond to the events having the same probability of registration in one pellicle. The numbers represent the percentage probabilities for 400 /~m and 600 /tin thick emulsions. Some passing tracks are marked by crosses. A new axis of the parabola and the conjugate diameters correspond to a moving system with velocity fl =0.014. to 1. However, the assumed value of/~ is only the average velocity of the centre-ofmass system and the distribution function f ( E , p , ) actually observed is diffused parallel to the x axis by the transversal motion of the centre-of-mass system and somewhat influenced by the different actual values of ~. The influence of these differences in the velocities of the centre-of-mass system on the energy spectrum of the emitted fragments and, in particular, on the values of the obtained parameters characterizing this spectrum, will bz discussed in the next section.

24

w . GAJEWSKI e t al.

On the plot of fig. 5 n o corrections were made for loss o f tracks passing to neighbouring emulsion sheets or of tracks o f low-energy fragments. The loss of the latter is clearly seen on that plot. The curves drawn in fig. 5 correspond to the events having the same probability of registration in one emulsion sheet (the figures give the percentage probabilities for the emulsion sheets of thickness 400 or 600/~m, respectively, calculated on the assumption of a uniform distribution o f primary stars in emulsion). The points marked with a cross correspond to the fragment tracks passing to the neighbouring emulsion sheets which were found by chance or in the special scanning mentioned above. About 55 passing tracks were expected in the three samples taken together, of which 19 were found. Although the smallest efficiency for registration of a fragment in one emulsion sheet corresponds to the high-energy part of the spectrum, most of the lost tracks fall in that region o f the spectrum where the statistics are large and can be easily corrected both in the energy spectrum and the angular distribution. The high-energy region is certainly distorted but the statistics are too small to allow the appropriate correction to be made.

7. Energy Spectra Fig. 6 shows the energy spectra of SLi fragments, belonging to the three samples, in the laboratory system and in the appropriate systems of optimum isotropy. The spectra were corrected for the loss of tracks passing to the other emulsion sheets. The possible losses of low-energy fragments were also taken into account for the spectra given in the systems of optimum isotropy. Since there were no pronounced differences between the spectra of fragments emitted from the interactions of 9 and 24 GeV protons in the following the spectra of samples 1 and 2 were analysed jointly. The comparison of the obtained results with the predictions of the evaporation theory present a number of difficulties, in the first place on account of the change of parameters characterizing a nucleus during the evaporation processes and our ignorance of the velocity of a nucleus at the moment of the fragment emission. The analysis of the influence of the motion of a nucleus on the shape of the energy spectrum of the emitted fragments was divided into three stages: the influence (i) of the average velocity, (ii) of its fluctuations, (iii) of the nuclear recoil. Then it was assumed that: (A) All the nuclei move in the direction of motion of the incident primary particle with the same average velocity ft. The excited nuclei acquire this velocity during the fast stage of the collision process. The influence of this motion on the spectrum of emitted fragments was eliminated by the transformation of the momentum of every fragment to the system of average optimum isotropy. (B) The velocities of individual nuclei at the moment of the fragment emission deviate by fluctuations from the average velocity both as regards the direction and the value. Fluctuations of this type are the resultant of fluctuations of the momentum acquired by a nucleus during the first stage of the interaction process and of fluc-

25

EMISSION OF 8Li F R A G M E N T S

tuations of the momentum transfers from the particles evaporated from a nucleus until the fragment emission. (C) In the process of fragment emission a nucleus acquires a recoil momentum. C.

30" ~5

>26

20

Nh :'28

gaC

9GeV

10 5 rl 3025-

n

bl #Gev

j ~

9GeV

bz

15. 10" '

0 -

n

~o. ~ ~. 20-

I'1

__

t8

20

at

~

248eV

,.,

NGeV

tO.

5" 0

4 6

,, 10 12 14

n~'~

8

lol)

t8

20

2

4

~

8

HeV/nuc!

10

f7

IS

I~

16

NeV/nuc(

Fig. 6. The energy spectra for three samples of SLi fragments in the laboratory system and the system of the best isotropy. 7.1. DISCUSSION OF THE I N F L U E N C E OF FLUCTUATIONS OF THE N U C L E U S VELOCITY A R O U N D THE A V E R A G E V A L U E ON THE E N E R G Y SPECTRUM OF THE EMITTED F R A G M E N T S

The influence of the fluctuations of the velocity of an evaporating nucleus on the energy spectra of the fragments was investigated in the system of optimum isotropy. It was assumed for simplicity that in such a system the fluctuations are distributed isotropically in space and that their distribution in a given direction has a Gaussian shape with a dispersion a. The shape of the energy spectrum of the fragments in the centre-of-mass system was taken to be given by the relation of the evaporation theory

P (E)dE - E-T 2V

exp

(

E T- -V )

dE,

where E is the fragment energy in the centre-of-mass system, T and V are respectively the mean temperature and Coulomb barrier of the evaporating nucleus. In

w . OASEWSKI e t al.

26

the system of best isotropy, this speetaum will be described by the relation IF

+.

+ f ( E ) } dE,

t where

can be approximated for small values of E by B

where t~ --- ~m~ 2,

r =

=

1

• (~) -- ~ - ~ exp (_½~z),

¢ _r4e-r4v,

F(~) =

;

o -- 4 e - 2 4 v

® O(x)dx.

The influence of the fluctuations of this type on the spectrum with parameters T = 10 MeV, V = 6 MeV is illustrated in fig. 7. It shows curves calculated for two values of the parameter a (0.007 and 0.009) apart f r o m a c o m m o n evaporation curve. These curves indicate that the probability of appearance of the "sub-barrier" particles is different from zero and that of the high-energy particles is increased. 7.2. DISCUSSION OF THE INFLUENCE OF THE NUCLEAR RECOIL RESULTING FROM THE FRAGMENT EMISSION A fragment gains only a part of the energy E released in the act of emission, namely E(1 + m / M ) - 1 . In the case of heavy fragment emission an effect on this kind changes essentially the shape of the energy spectrum of these fragments in the system of optimum isotropy as is also illustrated on fig. 7. It shows, as an example, successive deformations of a spectrum provided by the evaporation theory for T = I0 MeV and V = 6 MeV, first under the influence of the velocity fluctuations with a Gaussian distribution with a = 0.007, and then as a result of the nuclear recoil under the assumption of a mean mass of the nucleus M = 60. The influence of the nuclear recoil increases the probability of appearance of sub-barrier events and strongly decreases the probability of observation of high-energy particles. It should be stressed that the acceptance of M = 60 corresponds to the assumption that SLi fragments are emitted rather at the first stage of the evaporation processes. The decrease of the mean value of M leads to even clearer changes of the spectrum.

E M I S S I O N O F aLl F R A G M E N I " S

27

P[E)

I!

\~.

~

6rm=ooog

xx\ J r

d1"/3)=0007, .

M=60

I itl

f 2

3

4

j

6

7

8

.9

10

+l

me¢/nucl

Fig. 7. Successive deformation of the energy spectrum provided by the evaporation theory under the influence of the velocity fluctuations and the nuclear recoil (optimum isotropy system). The curve for tr = 0.009 is for clarity marked by crosses only (see text).

7.3. COMPARISON OF THE SPECTRUM OF 8Li FRAGMENTS WITH THE THEORETICAL CURVES It follows from the analysis of angular distributions that it is possible to find such a moving system in which the majority of the fragments, irrespective of their energy, are emitted isotropically. This might suggest that all or nearly all the fragments result from one process. Taking this into account work was started on an analysis of the energy distributions in the system of optimum isotropy by comparing the whole spectrum with the theoretical curve discussed above, calculated for the appropriate values of the parameters V and T. The theoretical curve was modified by accounting for the influence of the effects described above. At the moment no data are available on the velocity fluctuations of the evaporating nuclei and on their mass at the moment of the emission of aLi fragments. A f o r t i o r i not much can be said on the variations of these quantities with the magnitude of Nh; therefore, in the course of the following discussion it is assumed that tr = 0.007 and M = 60 for all the values of N h. By the method of best fit a corrected theoretical curve was chosen which best described the obtained experimental spectrum. It was found that the best fit was obtained for T = 12 MeV. This curve does not fit the group of highenergy events constituting about 2 % of the total number of fragments. It describes well the low-energy end of the spectrum for the parameter V = 3 MeV. The upper limit that might be indicated for the parameter V was 5 MeV, but in this case the

28

w. GAJEWSKIet

aL

respective curve did not contain the events of lowest energy constituting about 3 % of the whole sample. Some of the events could possibly be due to the residual nuclei remaining after the complete smashing of the most highly excited nuclei of Br and Ag. This analysis is illustrated on fig. 8.

50.

40.

30.

20-

10-

L

4

I g

I

8

|

,

~

f'~

~8

20

Me v/~cl

Fig. 8. The energy spectrum of SLi fragments in the system of best isotropy. Curves show the calculated evaporation spectra for a distribution of velocity fl characterized by e = 0.007 and the mass of the recoiling nucleus M = 60. 7.4. ENERGY SPECTRA OF THE FRAGMENTS FOR SUCCESSIVE INTERVALS OF Na FOR PARENT STARS In the present experiment a certain tendency was observed indicating changes in the energy spectra of the fragments with the variation of Nh of their primary stars. Fig. 9 presents the energy spectra for three different intervals of Nh. It was found that the spectra corresponding to the extreme intervals of N h differed by more than 2 standard deviations. With the increase o f Nh the width of the spectrum and the number of low-energy fragments increase. From the point of view of the evaporation theory this would correspond to an increase of the temperature and a decrease of the potential barrier. In the category of interactions with high N h one could expect increased velocity fluctuations and a decrease of the nuclear mass at the moment of fragment emission, both as a result of an increase in the number of the cascade particles and the number of the evaporated particles before the fragment emission. However, in these intervals o f N h we collect selectively more often or even mainly the fragmentation processes of silver nuclei and on the other hand the increased smashing

29

EMISSION OF 8Li FRAGMENTS

of the target nuclei, especially those of bromium, may cause the emission of 8Li fragments as residual nuclei. We can say with all reserve, especially due to the influence of these effects, that the energy spectra of the fragments collected from stars of the largest values of Nh may be described by a curve with a parameter T ~ 15 MeV.

~

~

Nh4/8

20

159 evil;t5 T=tZ2MeV V ~ n e V

10 . . . . f

2

3

4

5

6

7

8

g

tO

tl

f2

13

14

II . r"l I5

19

20

I5

17

t~

t8

f8 < ,vh~<25

20

~h~

! 78evon/s

10

1

2

3

4

5

6

?

8

9

10

f!

12

13

14

t5

Nh> 26 20 .

l~7evonts

t

z

3

4

5

6

z

a

9

to

n

t2

ts

t~

t~

HeV/nucl Fig. 9. The energy spectra for three different intervals of Nh (9 and 24 GeV protons).

The values of the parameter T obtained here and in the preceding section are too large to be consistent with those predicted by the evaporation theory. If in fact the evaporation theory describes the process of the fragment emission in high energy interactions the results obtained would indicate that in the relation between the temperature and the excitation energy U

=

kAT",

the values of the parameters k = 0.1 and n = 2 are not correct for the excitation energies approaching the binding energy of the target nucleus xz, 13).

30

W. GAJEWSKI e t al.

8. Conclusions (1) The experimental frequency of emission of aLl fragments increases with the increase o f N h of the primary stars. For a given Nh there is no evident dependence of the emission frequency on the energy of the primary protons. The results shown in fig. 1 indicate similar emission frequencies in the case of K - meson interactions. (2) The anisotropy in the emission of the fragments in the laboratory system was found to increase with the fragment energy. Assuming that the emitting centre moves with the average velocity fl = 0.014 one finds that in such a system the angular distribution of the fragments can be considered to be isotropic up to the fragment energy of 10 MeV/nucleon. The angular distribution of fragments of higher energy should be investigated with larger statistics. (3) The energy distribution of 8Li fragments from a random sample of stars may be described approximately by modified evaporation curves with the parameters T = 12 MeV and V = 3 MeV. The influence of the fluctuation of the nucleus velocity around the average value fl = 0.014 and the influence of nuclear recoil resulting from the fragment emission were taken into account. The value T = 10.5MeV is the lowest possible limit of temperature and V= 5MeV is the upper limit of the barrier. The magnitude of the barrier might be increased by about 1 MeV on the assumption that the fragments were emitted, on the average, from nuclei of mass number less than 60. Moreover, some small number of lowenergy aLl fragments from stars with a large prong number may be due to residual nuclei. The low value of the potential barrier seems to be striking. (4) By comparing the energy spectra of fragments from stars of different Na a tendency was found for T to increase and V to decrease with the increase of Ark. (5) A study of an additional sample of aLi fragments coming from interactions in which a large energy was transferred to a nucleus (Nh _>--27) did not show any quantitative differences in comparison with the fragments coming from smaller stars except those mentioned in (4). The character of the relation between Nh and the frequency of emission of 8Li fragments, as well as their angular distributions, are not inconsistent with the predictions of the theory of fragment emission from a moving excited centre. The energy spectra of the majority of the fragments can be described by the evaporation theory curves, after the transformation to the centre-of-mass system of the emitting nucleus. However, it is necessary to assume, as in other papers, values of the parameters that are inconsistent with those predicted by the evaporation theory. One obtains very low potential barriers and temperatures corresponding to very high excitation energies. All these results seem to indicate that a new approach to the interpretation of heavy fragment emission is required.

EMISSION OF 8Li FRAGMENTS

31

T h e a u t h o r s wish to t h a n k the team o f physicists o f the J o i n t Institute f o r N u clear R e s e a r c h at D u b n a , U S S R a n d o f C E R N , G e n e v a f o r the i r r ad i at i o n an d processing o f the stacks. T h e y t h a n k Mr. M i c h a l ~wi~cki a n d o t h er colleagues f o r help an d v a l u a b l e discussion a n d the scanning t e a m f o r very careful a n d tenacious w or k.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

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