The fission of gold by oxygen nuclei

Nuclear Physics 17 (1960) 74---88; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

THE FISSION

OF GOLD B Y O X Y G E N

NUCLEI

A. R. Q U I N T O N , H. C. B R I T T , W. J. K N O X a n d C. E. A N D E R S O N

Sloane Physics Laboratory, Yale University, New Haven, Connecticut, U.S.A. t Received 30 J a n u a r y 1960 T h e a n g u l a r d i s t r i b u t i o n a n d t h e energies of t h e fission f r a g m e n t s , e m i t t e d in t h e b o m b a r d m e n t of a t h i n gold foil b y 160 MeV o x y g e n nuclei, h a v e been e x p e r i m e n t a l l y d e t e r m i n e d b y t h e u s e of a p r o p o r t i o n a l c o u n t e r detector. B y a c o m p a r i s o n w i t h t h e t h e o r y of H a l p e r n a n d S t r u t i n s k i a n e s t i m a t e h a s been m a d e of t h e s h a p e of t h e fissioning n u c l e u s a t t h e saddle point. T h e t o t a l kinetic e n e r g y released was d e t e r m i n e d to be 150 MeV. I t is c l a i m e d t h a t t h e fissioning n u c l e u s h a s t y p i c a l l y a m a s s of 204 m a s s units. T h e possibility of t h e e m i s s i o n of c h a r g e d particles, as well as n e u t r o n s , in s o m e of t h e e v a p o r a t i o n c h a i n s p r e c e d i n g fission, is discussed. A fission cross section of 1.84-0.2 b was o b t a i n e d .

Abstract:

1. I n t r o d u c t i o n

In the last few years interest has developed in fission studies in the angular distribution of the fragments with respect to the direction of the incident projectiles. On the theoretical side this interest stems from the attempt of A. Bohr x) to explain the then existing experimental data 9.) in terms of the collective model of the nucleus. In the work referred to above the emphasis was on the state of the fissioning nucleus when excited Just above threshold. Later treatments due to Strutinski 3), and Halpern and Strutinski *) have concentrated on removing this energy restriction b y resorting to statistical model considerations. According to Bohr the fission fragments leave one another along the line of the nuclear symmetry axis and the relevant quantum number is K, the projection of the total angular momentum I on this same axis. In the statistical treatments the same postulates hold but now one is dealing with distributions in K and I. However, at high excitation energies, K is not a good quantum number but is to be regarded as the mean moment of the nucleons about the nuclear axis. Since the mean square value of K is related to the effective moment of inertia of the nucleus, which is in its turn determined b y the shape of the nucleus, it follows that angular distribution measurements could perhaps become a powerful technique for fission investigations. This would be especially true if, as expected, it is the mean value of K 2 at the saddle point shape which controls the angular distribution. H e a v y ions would appear to be suitable projectiles for these investigations t) T h i s w o r k w a s s u p p o r t e d b y t h e U. S. A t o m i c E n e r g y C o m m i s s i o n . 74

T H E FISSION OF GOLD BY O X Y G E N N U C L E I

75

and this paper describes an attempt to exploit this promising new tool using 160 MeV oxygen ions. The requirements of the statistical treatment are met rather well, the fission cross section with a gold target is a large fraction of the geometrical cross section s) and the anisotropy is large. Measurements of the energy spectra and angular distributions of the alpha particles e) and protons ~) from the oxygen bombardment of a nickel target strongly suggest the influence of the high angular momentum characteristic of high energy heavy ion reactions. This influence is expected to appear in the fissioning of heavy nuclei 8). Presumably it is just this effect which is responsible for the large anisotropy observed in the experiment under discussion, because the angular distribution is proportional to I/sin 0 in the classical limit, when I is large and K zero. This merely expresses the fact that fission fragments would be centrifuged off from a classical system, with constant probability in any direction in a plane perpendicular to I. Since the spin of Au 19~ is ~- and the maximum orbital angular momentum contributed b y the oxygen projectile is 85~, there is justification for the approximation that the projection M of the total angular momentum vector I is zero along the beam direction. One of the less satisfactory features of heavy ion bombardment for bringing about fission is that the A and the Z of the fissioning nucleus are not known. It is expected that the principal competing processes are neutron evaporation and fission, after compound nucleus formation, although the possibility of some charged particle evaporation cannot be ruled out completely. Hence the reaction can be symbolized, perhaps, as Au (0; xn, f) but the range of values of x and their relative probabilities are not known. Since evaporation cools a nucleus down it means that the temperature of the fissioning nucleus takes on a range of values. It is reasonable to assume, however, that most of the nuclei fission from states of high excitation and of high angular momentum, so that the statistical considerations 3, ,) should apply. 2. Method

A detailed description has been given elsewhere 9) of the equipment used in this experiment. The full energy 160 MeV O is beam was magnetically analysed and collimated to about 1° onto a thin self-supported gold target, 360/~g/cm * thickness. Occasionally 180/~g/cm 2 targets, supported b y 40 #g/cm * formvar, were used. The beam current was collected in a Faraday cup and integrated, and the number of incident particles calculated on the assumption of completely stripped oxygen nuclei. Monitoring was also done b y using a fixed cesium iodide scintillation counter at 20 ° with respect to the beam, and operating it so that only the elastically scattered oxygen ions were counted. Other measurements in this laboratory 10) have shown that the scattering follows closely the Rutherford scattering law at such an angle. Usually the two systems of moni-

76

A. R. Q U I N T O N , H. C. B R I T T , W. J .

KNOX AND C. E. A N D E R S O N

toring agreed to within 5 % and angular distributions from day to day never differed by more than 10 %. The fission fragments were detected in a simple proportional counter, through a 500 #g/cm 2 nickel window, with the counter operated at a pressure of 60 cm of mercury which provided a maximum gas path equivalent to 4 mg/cm ~ of aluminium. At angles of observation less than 40 ° the low energy side of the fission spectrum was contaminated by elastically scattered oxygen nuclei and by particles of rather low mass emitted probably in direct interactions. They were rejected on the basis of their range. Since they could pass through the proportional counter they would be counted by the cesium iodide scintillation counter which forms the back wall of the gas counter. Pulses from both counters were fed, after passing through amplifiers and discriminating circuits, to an anticoincidence circuit, the output of which was used to open the gate of a 20 channel analyser. The observed energy spectra of particles stopping in the proportional counter were independent of counting rate except at the extreme forward angles. At these later angles, where elastic scattering predominates, the counting rate was lowered to a safer level but the energy spectra were less reliable in this range ~). 3. C a l i b r a t i o n

A Cf25~ spontaneous fission source was used for the energy calibration of the proportional counter detector. Such a source proves to be extremely convenient for the following reasons: 1) the 6.1 MeV alpha particles allow the system to be checked for gain drifts very quickly; 2) the upper energy peak corresponds to a fission fragment mass close to that of the fragments expected in the experiment; 3) the energy resolution can be checked from the peak to valley ratio. Fig. 1 shows a pulse height spectrum taken in three pieces with a 20 channel analyser. The pulse heights are relative to that of a 6.1 MeV alpha particle passing through the counter and depositing 2.5 MeV. A similar curve displaced on the average 2 channels to the left was obtained when the gold foil, later used for a target, was put between source and counter window. In this way "half target thickness" corrections could be applied to the data. The results of Milton and Fraser 11) were used for calibration purposes. Their curve for the single fragment energy spectrum, obtained by the time of flight method, was first normalised to the same total number of counts as the proportional counter spectrum. There was no significant disagreement in the shapes of the spectra obtained by the two methods, time of flight and proportional counter ionization. Then, after assuming that there was a direct correspondence in the energies at the peaks of the two curves, a detailed point by point energy calibration was obtained by measuring off, away from the peaks, equal increments of area under the two curves. Such a procedure gave an energy calibra-

THE

FISSION

OF GOLD

BY OXYGEN

NUCLEI

77

tion from 55 MeV up to 115 MeV, sufficiently linear so that it could be extrapolated to higher energies if necessary. Heavy ion induced reactions involve, of course, a large centre of mass velocity. As a consequence the fission fragments emitted at backward angles in the laboratory frame can well be of such low energy that calibrations below 55 MeV are needed. The procedure used depends for its validity on the following assumptions: 1) a windowless proportional counter would have a linear pulse

I

b-

i o

z_ z

o.

o

o

5

Io

J5

20

25

30

35

4o

4,~

5o

5~

CHANNEL NUMBER

Fig. l. The s p e c t r u m of pulse heights from the detection of Cf 252 fission f r a g m e n t s in the proportional counter.

height versus energy response with a small intercept; 2) dE/dx is a constant for the fragments at the higher energies, say greater than 80 MeV. First a curve of pulse height versus air absorber thickness was determined for the upper peak of the spectrum, that is for the mass 100 fragment. The shape of this absorption curve indicated that dE/dx is a constant at the higher energies but decreases substantially at low energies. Then, by using a nickel foil of the same thickness as the counter window as an absorber it was possible to deduce the energy loss of a high energy fragment in the window. Hence the calibration from 80 MeV up could be corrected to give the windowless counter calibration. This curve when extrapolated to lower energies gave a small intercept of about 8 MeV corresponding probably, to our accuracy, to the ionization defect. Next, examination of the slope of the pulse height versus absorber curve at various

78

A. R. QUINTON, H. C. BRITT, W. J. KNOX AND C. E. ANDERSON

pulse heights indicated the correction to apply for an absorber of the thickness of the window. Then the assumed linear windowless curve could be moved back to give the final calibration curve (fig. 2) from 20 MeV upwards. The intercept on this curve corresponds to the most energetic particle which after passing through 160/~g/cm 2 of gold and 500/~g/cm * of nickel could enter the gas of the counter but not produce a detectable number of ion pairs. 3(1

il

I

20

i-

~20t~J

3:

I ,u 15

t

g

j" J,

J

J i

20

4O FISSION

J [

~

60

F R A G M E N T ENERGY

J !

80

I00

120

(MeV)

Fig. 2. The p r o p o r t i o n a l c o u n t e r e n e r g y c a l i b r a t i o n c u r v e for fission f r a g m e n t s of A ~ 100. The e n e r g y scale refers to t h e f r a g m e n t k i n e t i c e n e r g y o u t s i d e t h e c o u n t e r w i n d o w . The p u l s e h e i g h t s are r e l a t i v e to t h e pulse h e i g h t p r o d u c e d b y a 6.1 MeV a l p h a p a r t i c l e d e p o s i t i n g 2.5 MeV in t h e c o u n t e r .

4. Results and Transformations In fig. 3 is shown the angular distribution in the laboratory frame of reference, illustrating the rather striking preference for emission of fragments along or against the beam direction. Each point represents a summation of the number of particles of all energies for a selected laboratory angle. Typical spectra for three angles are presented in fig. 4(a). These curves, which are, of course, normalised to the same number of incident oxygen ions, also demonstrate the large centre of mass velocity of the collision as evidenced by the lowering of the peak energy as the angle of observation increases in the backward direction. In order to make a transformation to the collision centre of mass coordinate system it is necessary to know the velocity of the fragment whose energy has been measured, or in other words, the fragment mass has to be known. In this respect we surmise that the reaction under consideration is similar to that studied radiochemically by Tarantin et al. z2). The result of that investigation was that the fissioning of gold by 115 MeV nitrogen ions proceeded by symmetric

THE FISSION OF GOLD BY OXYGEN NUCLEI

~9

---

800

[ "tO0

L

600--

500-----~ 400 .

--.

.

.

.

-~T

~- ~ 0 0 -

°

I

o 200---

I

I00

0 ,,

20

4o~

~

=o

ioo"

,,o

i,to"

t6o"

~LAB F i g . 3. T h e a n g u l a r d i s t r i b u t i o n

of f i s s i o n f r a g m e n t s

in the laboratory

f r a m e of r e f e r e n c e .

701 60

_

50

!~

1

o 3o ~ 20-

7\rl

--7

o

I

,'°"

7'7,/k~,J~ +X

20

40

115

"~ 8C

X'3°

I10

60

107

80

I00

: 120

140

Eio b (MeV)

105 104 103 102

~cm

6c

•~

40

bl~zc t

20

40

gO

80

I00

120 140 Ecm (MeV)

F i g . 4. (a) T y p i c a l f i s s i o n f r a g m e n t e n e r g y s p e c t r a a t 6 0 °, 9 0 ° a n d 1 3 0 o i n t h e l a b o r a t o r y (b) T h e 9 0 ° d a t a t r a n s f o r m e d t o t h e c e n t r e of m a s s e n e r g y .

frame.

80

A.R.

QUINTON,

H. C. BRITT,

W.

J. K N O X

AND

C. E. A N D E R S O N

division with the mass yield curve peaked at A m I00, and about 20 mass units wide at the points of half m a x i m u m yield. Accordingly, the energy spectra for this system of gold plus oxygen were transformed assuming that the d e t e c t e d fragment always had a mass of 100 units but was e m i t t e d from a system m o v i n g t h r o u g h the l a b o r a t o r y with the velocity of the centre of mass of the collision system. I n h e r e n t l y , the assumption is that, on the average, the e v a p o r a t e d particles leave behind a fissioning nucleus of net u n d i s t u r b e d velocity. In fig. 4(b) is shown the result for the 90 ° l a b o r t o r y spectrum, as an 4.o,

.... !

[

i

t

j

2,

tl

'o: "o ! I

/~.rJ

i / i

i II g

o

~

|i Iso

,o

I

°

i 2o l ~,o i ,o mo

J4o

tzo

itl

I ~,o] too

(~cm Fig. 5. Centre of m a s s a n g u l a r d i s t r i b u t i o n s for 75, 60 a n d 90 MeV f r a g m e n t s .

mo

mo

J4o

lao

Ioo

I~cm Fig. 6. Centre of m a s s a n g u l a r d i s t r i b u t i o n s for 50, 70, 80 a n d 100 MeV f r a g m e n t s .

illustration, with centre of mass e n e r g y and angle scales. F r o m sixteen such curves one can proceed to unfold the l a b o r a t o r y spectra and construct curves of the centre of mass angular distributions. This has been done for fragment energies from 50 to 100 MeV in 5 MeV steps. The results d e m o n s t r a t e s y m m e t r y of the angular distributions a b o u t 90 °, and s y m m e t r y of the e n e r g y spectrum, at a n y angle, a b o u t 75 MeV. The second s y m m e t r y follows because, to within the a c c u r a c y of the d a t a points, one curve can be drawn t h r o u g h the 70 and 80 MeV points, one through the 65 and 85 MeV points, etc. F o r this reason such pairs of energies have been coupled together in the presentation of the d a t a (figs. 5---7). The error shown for each point is estimated from the error of the nearest point on the s m o o t h curve from which it was extracted.

T H E FISSION OF GOLD BY OXYGEN NUCLEI

81

At this stage of the analysis it is possible to construct, from the angular distributions for various fragment energies, a centre of mass spectrum at any desired centre of mass angle. Actually closer inspection shows that, for each curve in figs. 5--7, a factor can be found which, within the experimental statistics, makes each curve coincide with the 75 MeV curve. In other words the angular distributions are not dependent upon fragment energy. The reciprocal of each factor has been plotted in fig. 8 to yield the centre of mass energy spectrum and so this plot represents a best determination of the energy spectrum, taking into account the data at all angles.

3.0

0'-90"

'

70

I

9 0 * - 180 °

2.0

g

o 50 1.0

Z

_o l-

o

o

u) ~0

i

0 3O

~1_~

7-- 0.5 . . . . .

-

U ..J

---

u.

a

I

,i! o

55and95MeV i

[

~,!0 180

160

)

140

120

I

~ zo W {1:

--

tO

40

60

80

IOO

120

I00

Ocm F i g . 7. C e n t r e o f m a s s a n g u l a r d i s t r i b u t i o n s f o r 55, 65, 8 5 a n d 9 5 M e V f r a g m e n t s .

£CM (MeV) F i g . 8. T h e b e s t d e t e r m i n a t i o n centre of mass energy spectrum

of the (see text).

As a check some of the data has been transformed assuming, first of all, a fragment mass of 90 units and secondly a mass of 110. In the first case the resulting spectra decrease in energy as the angle of observation increases. For the transformation assuming a mass of 110 units the reverse trend is seen, namely an increase in energy at the backward angles relative to the forward. Now it is certainly to be expected that the fission takes place from a compound system and hence that tile centre of mass spectra should not be angle dependent. Furthermore if a laboratory spectrum contained fragments of say mass 90 and

82

A. R .

QUINTON,

H.

C. B R I T T ,

W.

J.

KNOX AND

C. E .

ANDERSON

mass l l 0 , with the same shape of the s p e c t r u m for the two masses, t h e n the t r a n s f o r m e d s p e c t r u m would show a t e n d e n c y to double hump. B u t as one proceeded from small to large angles the two peaks would merge and cross over. So the s p e c t r u m shape would be angle d e p e n d e n t and, most significantly of all, linear m o m e n t u m would not be conserved in the r e c o n s t r u c t e d fission events. The claim is m a d e therefore t h a t the fission process observed in this e x p e r i m e n t is s y m m e t r i c with a r a t h e r narrow range of masses a r o u n d mass n u m b e r 100. Actually the procedure outlined above can give crudely the most probable fragment mass e m i t t e d in s y m m e t r i c fission, if one demands a unique centre of mass energy spectrum. Some slight trends in our t r a n s f o r m e d d a t a would

220 2

I

io _ _ , L _ _ I

200

__ :

r

i

190 ------L

=

i

---4

.

~_ ,,o ~ --

15o"

130 I I00

C'm242

l

i

....1

I

I

/

i

!

I

,

l ~

~--~'--r.7...~

~

, 1200

CmZ4¢T /

o~

.

.

.

~:. -Tin + n

.

fI

:~(......-.r-~ P°+n

1I/--"t'

z33

229

. . . . .

|1

Th +n

i

L,

1300

1400

ZVAil3

F i g . 9. T h e t o t a l k i n e t i c e n e r g y r e l e a s e d i n f i s s i o n a s a f u n c t i o n of

1500

Z~/Ai.

see ref. in).

suggest t h a t a mass of 101 units would fit this criterion b e t t e r t h a n the trial value of 100 mass units. If an allowance is m a d e for the liberation of 2 neutrons at fission, t h e n the conclusion is reached t h a t the fissioning system has an A ~ 204. A useful empirical curve is available is), which correlates the kinetic energy released in fission with the p a r a m e t e r Z2/A½~If the assumptions are made t h a t this relation is valid when e x t r a p o l a t e d to 150 MeV total kinetic energy released and t h a t the parent nucleus has a mass of 204, t h e n it follows t h a t the most probable fissioning nucleus is an astatine isotope (fig. 9). This in its turn would m e a n t h a t some charged particle emission was competing with the neutron e v a p o r a t i o n before fission. Some preliminary investigations of the alpha particle spectra and angular distributions have been made. It is r a t h e r clear t h a t most of these particles came from the c o m p o u n d s y s t e m prior to fission (or as an alternative to fission) because the peak e n e r g y corresponds closely to the barrier of a Z ~ 80 nucleus r a t h e r t h a n a Z ~ 40 nucleus. The ratio of alpha particles to fission events is r o u g h l y 2 : 3. P r o t o n emission is e x p e c t e d to

THE

FISSION

OF GOLD

BY OXYGEN

NUCLEI

83

be at least equally significant. Another possibility is that some stripping reactions can leave a system with a fragment of the oxygen projectile amalgamated with a gold target nucleus and this system subsequently fissions. Such a mechanism tends to lower the average Z and A of the parent suggested by the experimental results presented here. However without the elaboration of coincident counters it is difficult to see how these "stripping plus fission" reactions could be measured in sufficient detail to permit a valid centre of mass transformation. The cross section for fission was determined by a direct comparison, using the same proportional counter, target and geometry, of the elastic scattering counting rate of oxygen ions at a few forward angles with the fission counting rate, and allowing for the presence of two fragments in the later case. McIntyre and co-workers 10)have measured the differential scattering cross section for 160 MeV oxygen ions on a gold target and hence the laboratory angular distribution of fig. 3 is calibrated in this fashion. A cross section of 1.8+0.2 b is the result. The fraction of the total compound nucleus cross section represented by this value is not known. Polikanov and Druin 5) report that the formula

where B is the Coulomb barrier and E the available kinetic energy in the centre of mass system, fits the measured cross sections with r 0 = 1.5 × 10-13 cm. This same formula would give a fission cross section of 2.3 b and so it is seen that the agreement between formula and experimental result, at this higher bombarding energy, is only fair. The quoted probable error comes mainly from the uncertainty in the value of the scattering angle of the elastically scatt~.red oxygen nuclei, which are counted by the fixed monitor.

5. D i s c u s s i o n In this section we attempt an interpretation of the angular distribution of the fragments of all energies. Fig. 10 shows this distribution with a plot of 1/sin 0 for comparison and it is clear that from 40 ° to 140 ° the curves are coincident to within the accuracy of the measurement. Beyond 140 '~, and presumably further forward than 40 °, the observed distribution is significantly lower than 1/sin 0. Following the analysis of ref. a), the claim is made that the data enable the mean square value of K to be obtained. At the saddle point shape of the fissioning nucleus the projection K of the total angular momentum I along the symmetry axis is "frozen in". Fission is achieved a short time later and no other parameters other than I and this particular value of K affect the direction of

84

A. R. QUINTON, H. C.

BRITT,

W.

J.

KNOX

AND

C.

E.

ANDERSON

fragment emission. For a given K and I the angular distribution from an elementary geometrical averaging procedure,

is found to be,

Fig. 10. The angular distribution of fission fragments emitted in the reaction Au’~~+O~~. The departure from I/sin 7 and the fit to the curve p = 5 are illustrated.

Hence the distributions in K and I determine the angular distribution. The usual classical treatment of impact parameters leads to an I distribution, linear in 2I+ 1, up to a maximum I, given by

In this formula ,u is the reduced mass of the system, (r,+r,) the sum of the radii of the target and projectile nuclei, B the Coulomb barrier energy and E the kinetic energy in the centre of mass. If a formula Y = r,Af is assumed with yO = 1.5~ IO-l3 cm and distortions of the nuclei are ignored, I, = 875 for the reaction under consideration.

THE

FISSION

OF GOLD

BY OXYGEN

NUCLEI

80

The distribution P ( K ) in K will be governed by a Boltzmann-factor exp(--Erot/T), leading to the expression P(K) c c e x p t - - - - ~ T -

~--)~

,

where T is the nuclear temperature and/'u and/'± are the moments of inertia of the nucleus, about axes parallel and perpendicular respectively to the nuclear symmetry axis. Then defining Tjen 1 __ 1 1 K02-- ?/2 with ieff ~'11 ~'.1. ' the fission angular distribution is determined by the parameter p where 4)

(mF p = \2Ko ! •

For example if p = oo the distribution follows the relation 1/sin O, but as p ~ 0 the distribution becomes increasingly isotropic. In the use of this relation allowance should be made for the change in angular momentum of the nucleus brought about by the departure of evaporation products. It is expected that the plane of emission of these particles is strongly correlated with the angular momentum. Furthermore, because of the increase in level density with decreasing spin, the tendency will be for the emerging particles to lower I. Consider four possible chains of evaporation prior to fission: 1) 9n; 2) 8 n + p ; 3) 7 n + 2 p ; 4) 5n+~. At the prevailing excitation energies and potential barriers an evaporation neutron could carryoff a maximum of 37/, a proton 47i and an alpha particle 127/. These values correspond to emission with the maximum impact parameter but with the average particle energy. In making these estimates for the neutron case, twice the nuclear temperature was taken for the average energy with the nuclear temperature averaged along a chain of evaporation; in the case of charged particles, quantal penetration was considered and the classical barrier was taken for the average energy. This last consideration is in more accord with our experience than to regard the barrier energy as the most probable particle energy. Using these values one might guess that the 87 units of angular momentum are reduced to 671i. As shown in fig. 10 the data can be fitted satisfactorily with p = 5 and suggest that the root mean square deviation in the Gaussian K distribution is given b y K o = 15.0. In carrying out the nuclear temperature calculations above the assumption was made that the Fermi gas model is applicable and hence that A Eex c ~ -T 2 ~ 20 T 2 10

8()

A. R. QUINTON, H. C. BRITT, W. J.

KNOX AND C. E. ANDERSON

For calculating excitation energies (Eexc), published tables of atomic masses 14) were used. Again, with the same assumptions about the energy removed by an evaporated particle as above, the excitation energy of the nucleus at the end of each of the postulated evaporation chains can be estimated. The results are shown in table 1. The same table lists the final nuclear temperature, the TABLE I

Nuclear t e m p e r a t u r e s and other quantities for different evaporation chains Evaporation Chain 9n

8n+p 7n+2p 5n+e

Eexc (MeV)

T (MeV)

8.9 8.2 4.2 38.4

0.66 0.63 0.14 1.36

X

--

(Z2/A) (Z2fA)cm 0.805 0.788 0.770 0.770

/(x) 0.0054 0.0070 0.0091 0.0091

Ef

(MeV) 2.8 3.6 4.7 4.7

values of the fission parameter x and the corresponding function is) /(x) together with the fission barrier. For these purposes (Z2/A)ertt-----46 and 4nro'°a---- 15 MeV were used with Ef = 4~ro2aA~/(x).

It should be remarked that the theory leading to this result is for nuclei which are spherical in their equilibrium forms and that rotation is not considered. As shown by Pik-Pichak 18) the fission barrier is lowered by rotation. His analysis when applied to the cases under consideration predicts that Ef would be close to 1 MeV. It should also be mentioned that for the typical fissioning nucleus some 6.5 MeV of energy is in the rotational form if it is assumed that the saddle point shape can be approximated by a rigid ellipsoid with a 2 : 1 axis ratio. An examination of the table suggests that the nucleus formed by the evaporation of 5 neutrons and an alpha particle might still continue to evaporate neutrons, or other particles, rather than fission. In other words 8 n + ~ is an extreme possibility. It is possible to suggest then that evaporation to around A = 204 with Z = 85---87 is feasible since at that point the excitation energies left to the nuclei are greater than the fission barriers but not enough energy is available to evaporate particles. Recently calculations of the Monte Carlo type have been carried out by Dostrovsky et al. 17) on fission-spallation competition. These calculations apply to high energy proton bombardment of heavy nuclei so the initially excited nuclei are not the same as in this experiment. However the energy ranges are similar, and an examination of the theoretical predictions shows them to be qualitatively in accord with the suggestion here of the evaporation of about 9

THE

FISSION

OF GOLD

BY OXYGEN

NUCLEI

87

nucleons prior to fission, including some charged particles. The expectation is also t h a t the charged particles are emitted early in the evaporation chain. Now combining the K 0 estimate of 15.0 with an estimated temperature of T = 0.66 MeV there results a value of 2.30× 10 -46 g • cm 2 for Jeff. Presumably also the nucleus can be considered to be behaving as a rigid body at the prevailing excitation energies so t h a t the corresponding nuclear dimensions can be estimated. Let us assume t h a t the nucleus can be represented by a prolate ellipsoid at the saddle point shape with a > b ~-- c, and further t h a t the distortion from spherical shape takes place at constant volume with no thermal expansion. Then a2@b 2

Jeff =- { M b 2

a2

b2

and ab 2 = r a --_ roa A .

Calculation shows that, if a = 9.1× 10 -13 cm and b = c----6.8×10 -13 cm, the value of Jerr estimated from the experimental results is obtained. This axes ratio of 1.35 : 1 can be compared with the saddle point shape calculations of Swiatecki 15). When x is approximately equal to 0.8, he predicts a 1.90 : 1 at the saddle. Qualitatively then there is fair agreement between theory and experiment. The theory however ignores the effects of rotation. Considerations of the energy of a uniformly charged liquid droplet, including a rotational energy term, show t h a t a rotating drop can reach the saddle point shape with less distortion (i.e. a / b smaller) t h a n a non-rotating drop, under otherwise the same conditions. References 1) A. Bohr, Proceedings of the International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1955, Vol. 2 (United Nations 1956) 151 2) J. E. Brolley and W. C. Dickinson, Phys. Rev. 90 (1953) 388; 94 (1954) 640; R. L. Henkel and J. E. Brolley, Phys. Rev. 103 (1956) 1292 3) V. M. Strutinski, J. Nuclear Energy 7 (1958) 239 4) I. Halpern and V. M. Strutinski, Second United Nations' Conference on the Peaceful Uses of Atomic Energy, Geneva, 1958, Vol. 15, 398 5) S. M. Polikanov and V. A. Druin, J E T P 36 (1959) 522 6) W. J. Knox, A. R. Quinton and C. E. Anderson, Phys. Rev. Letters 22 (1959) 402 7) W. J. Knox, A. R. Quinton and C. E. Anderson, to be published 8) Proceedings of the Conference on Reactions between Complex Nuclei, Gatlinburg, Tennessee, 5--7 May, 1958, ORNL-2606, p. 159 9) C. E. Anderson, A. R. Quinton, W. J. Knox and R. Long, Nuclear Instruments and Methods, to be published 10) J. A. McIntyre, private communication 11) J. C. D. Milton and J. S. Fraser, Phys. Rev. 111 (1958) 877 12) N. I. Tarantin, Iu. B. Gerlit, L. I. Guseva, B. F. Miasoedov, K. V. Fillippova and G. N. Flerov, J E T P 34 (1958) 220

88

A. R. QUINTON, 14. C. BRITT, W. J. KNOX AND C. E. ANDERSON

13) J. Terrell, as p r e s e n t e d b y R. B. L e a c h m a n , Second U n i t e d N a t i o n s ' Conference, G e n e v a , ]958, Vol. 15, p. 331 14) A. G. W. Cameron, A R e v i s e d S e m i - E m p i r i c a l A t o m i c M a s s F o r m u l a , Chalk River, Ontario, CRP-690, A.E.C.L. 433, D e c e m b e r 1958 15) W. J. Swiatecki, P h y s . R e v . 104 (1956) 993 16) G. A. P i k - P i c h a k , J E T P 3 4 (1958) 238 17) I. D o s t r o v s k y , Z. F r a e n k e l a n d P. R a b i n o w i t z , Second U n i t e d N a t i o n s ' Conference on t h e Peaceful Uses of A t o m i c E n e r g y , G e n e v a , 1958, Vol. 15, p. 301