Radiochemical studies on fission of actinides

Pram.~oa, Vol. 24, Nos 1 & 2, January & February 1985, pp. 137-153. © Printed in India.

Radiochemical studies on fission of aetinides M V R A M A N I A H

Bhabha Atomic Research Centre, Tromhay, Bombay 400085, India

Abstract. Since its discovery in 1939, nuclear fission has been extensively studied by various experimental as well as theoretical groups in several countries leading to an understanding of major aspects of this important and complex nuclear reaction. In Trombay, studies have been carried out in the last 25 years using both physical and radiocbemieal methods and significant contributions have been made towards a better understanding of this reaction. This paper presents highlights of radiochemieal studies on fission of actinides, particularly mass, kinetic energy and charge distribution and fragment angular momentum. Results of these studies brought out the important role played by deformation energy surface, spherical and deformed nuclear shells and nucleon pairing.

Keywords. Nuclear fission; radiochemical methods; mass; charge; kinetic energy distri- butions; fragment angular momenta; nuclear shells and nucleon pairing,

PACS No. 25-85

1. Introduction

The high sensitivity a n d specificity o f radiochemical m e t h o d s led to the discovery o f nuclear fission by H a h n a n d Strassmann in 1939. Since then, all aspects o f this c o m p l e x nuclear reaction have been studied extensively b y radiochemical as well as physical methods. S o o n after the discovery, B f h r a n d Wheeler (1939) put f o r w a r d a t h e o r y o f nuclear fission based on the liquid d r o p model (LDM), which was able to explain s o m e b r o a d features o f the reaction such as energetics o f fission process, fission p r o b a b i l i t y and fissionability. T h e m o s t striking feature o f fission, namely, a s y m m e t r i c m a s s distribution could n o t be explained by the LDM, according to which the m a s s distribution in low energy fission should be symmetric. This p r o b l e m e v o k e d great interest in several experimental and theoretical g r o u p s in the world. Within a b o u t a decade since the discovery o f fission, a massive a m o u n t o f experimental d a t a was collected on mass, charge and kinetic energy distribution as well as o t h e r aspects.

Considerable effort was directed towards understanding the variation o f p o t e n t i a l energy surface as a function o f symmetric a n d a s y m m e t r i c d e f o r m a t i o n for a wide r a n g e o f fissionability p a r a m e t e r s with the a i m o f providing an explanation for the o b s e r v e d mass a s y m m e t r y (Wilets 1964). Results o f extensive experimental w o r k covering mass, charge a n d kinetic energy distribution as well as p r o m p t n e u t r o n a n d g a m m a emission b r o u g h t o u t the i m p o r t a n c e o f nuclear shells.

Several theoretical approaches were m a d e i n c o r p o r a t i n g shell effects, p r o m i n e n t a m o n g t h e m being the statistical model (Fong 1956), a n d the nucleon exchange m o d e l ( R a m a n n a 1964). As discussed by K a p o o r and R a m a m u r t h y in a p a p e r to this volume, nucleon exchange m o d e l can explain one-, two-, a n d three-peaked mass distributions in terms o f exchange o f nucleons taking into a c c o u n t the influence o f f r a g m e n t nuclear shells. An i m p o r t a n t b r e a k t h r o u g h c a m e f r o m the w o r k o f Myers a n d Swiateeki (1967) 137

138 M V R a m a n i a h

and Strutinsky (1967). Incorporation of single particle effects over and above that of liquid drop potential by these groups resulted in a double-humped fission barrier in contrast to a single-humped barrier resulting from LDM consideration. Moller and Nilsson (1970) showed that in the vicinity of the second saddle point, asymmetric deformation of the fissioning nucleus results in the lowering of the fission barrier, which provided a qualitative explanation for the asymmetric mass distribution in terms of the double-humped fission barrier. The effect of washing out of nuclear shell effects with excitation energy on the observable quantities like the fragment angular distribution and fission probabilities in the case of nuclei with double-humped barrier was later worked out by Ramamurthy et al (1970). Mustafa et al (1973), based on the two-centre shell model, showed that the shell structure in the fragments influences the potential energy surface, explaining qualitatively the mass distribution of a wide range of fissioning nuclei. More recently, Wilkins et ai (1976) and Prakash et al (1979) had attempted to explain various features of low energy fission as a result o f recognising the importance of deformed nuclear shells in addition to spherical shells at scission in their model based on the quasi-statistical equilibrium near scission. A large volume of results of the theoretical and experimental studies of low-energy fission have been published in a number of excellent reviews and proceedings of International Conferences (Hyde 1966; Vandenbosch and Huizenga 1974; Proc. of the IAEA Symposia on Physics and Chemistry of Fission; 1965, 1969, 1973 and 1979).

At Trombay, work on nuclear fission was started by Dr Ramanna and it is because of his continued interest and strong support that basic research in this important field could be pursued and significant contributions made. Both physical and radiochemical methods have been employed in these investigations.

The areas of fission research to which a substantial contribution has been made by the Trombay group using physical techniques such as ionization chambers, scintillation detectors, semiconductor detectors and time of flight are the studies of fission fragment characteristics and secondary radiations emitted in fission. The early investigations concerned the mass, kinetic energy and angular distributions of fission fragments and the correlations among them (Kapoor et al 1965; Rekha Govil et al 1983), and the emission of neutrons (Ramanna et al 1961; Kapoor et al 1963), gamma rays (Kapoor and Ramanna 1964) and K-x-rays (Kapoor et al 1968, 1969, 1971; Kataria et al 1970) in coincidence with the fission fragments. In the last few years, a comprehensive programme to study the light-charged particles in fission has also been carried out (Ajitanand et al 1975; Choudhury et al 1976, 1980), the results of which have been reviewed elsewhere (Nadkarni 1982).

Radiochemical studies on the fission of actinides were initiated with the aim of understanding the systematics of low energy fission, particularly distribution of mass, charge, kinetic energy and angular momentum covering a wide range of elements. The results contributed to a better understanding of this interesting nuclear reaction, particularly the role played by both the spherical and deformed nuclear shells and the effect of nucleon pairing. In this article, we present a summary of the Trombay radiochemical work highlighting the important findings.

2. Mass distribution

At Trombay, mass distribution studies were carded out in the neutron-induced fission of a number of actinides ranging from 22~Ac to 24SCm. These studies involved

R a d i o c h e m i s t r y o f f i s s i o n o f a c t i n i d e s 139 radiochemical separations o f fission products followed by their estimation using b e t a or g a m m a c o u n t i n g or direct counting o f catcher foils on a high resolution g e r m a n i u m spectrometer. Several m e t h o d s such as absolute m e t h o d , relative m e t h o d a n d c o m p a r i s o n m e t h o d (Jain a n d R a m a n i a h 1973) were e m p l o y e d in these studies. S o m e relevant results are presented in table 1. O n e interesting feature which e m e r g e d f r o m the extensive d a t a o b t a i n e d at T r o m b a y a n d f r o m the literature d a t a covering a wide range o f fissioning nuclei f r o m 227Ac to 259Md is the transition f r o m t h r e e - p e a k e d distribution in the A c - T h - U region to two-peaked distribution in heavier actinides a n d a single-peaked mass distribution in the F m - M d region. T h e transition f r o m three- peaked to tWO-l~aked distribution in Ac-Th region (Jensen a n d Fairhall 1958) was explained on the basis o f t w o - m o d e fission hypothesis put f o r w a r d by T u r k e v i c h a n d N i d a y (1951) according to which the three-peaked mass distribution is a result o f superposition o f a s y m m e t r i c a n d symmetric mass distributions a n d transition to an a s y m m e t r i c mass distribution occurs rather sharply in going f r o m a c t i n i u m to thorium.

N e u t r o n - i n d u c e d fission o f 232Th (Iyer et al 1963) was studied at T r o m b a y a n d a small s y m m e t r i c p e a k was also observed besides the two large a s y m m e t r i c p e a k s indicating that the extent o f symmetric contribution m a y n o t strongly d e p e n d on the p r o t o n n u m b e r o f the fissioning nucleus. This was further c o n f i r m e d by the m a s s distribution in the n e u t r o n fission o f 232U ( M a n o h a r et al 1979) which s h o w e d a s y m m e t r i c p e a k similar to that in the n e u t r o n fission o f 232Th. T h e d e p e n d e n c e o f s y m m e t r i c c o n t r i b u t i o n on p r o t o n a n d neutron n u m b e r o f the fissioning nucleus was explained on the basis o f the influence o f variation o f the difference between barrier heights for symmetric a n d a s y m m e t r i c modes (Es-Ea) o b t a i n e d f r o m the w o r k o f Moiler a n d Nix (1974) as a function o f p r o t o n and n e u t r o n n u m b e r as s h o w n in figures l a a n d lb. It is seen that (Es-Ea) varies m o r e sharply with the n e u t r o n n u m b e r t h a n the p r o t o n n u m b e r o f the fissioning nucleus and the c o n t r i b u t i o n o f the s y m m e t r i c c o m p o n e n t increases as (Es-Ea) decreases. T h e observability o f the s y m m e t r i c p e a k in 232U could be u n d e r s t o o d as due to a decrease in (Es-Ea) with decrease in the n e u t r o n n u m b e r f r o m 143 to 141, which m o r e than compensates for the increase in (Es-Ea) with increase in the p r o t o n n u m b e r f r o m 90 to 92.

Table 1. The mass distribution characteristics for different fissioning nuclei studied at Trombay

Fissioning Most probable mass

nucleus Light Heavy VWTM P[V Remarks

22SAc 88"0 138"0 18"0 42 Three-peaked (')

23°Th 88-5 139-5 15-8 261 Three-peaked ~a)

2aaTh 93"0 137-5 21"0 111 Three-peaked to)

2aZPa 94"2 139-8 20-5 97 Two-peaked ~'~

2 a 3 U ' 94-1 138"9 21 "0 480 Three-peakea--~d)

234U 95-0 139"0 21"9 330 Three-peaked ('~

236U 95"5 139-5 21.2 620 Two-peaked ~'~

2aaNp 98"0 140-0 23"8 140 Two-peaked (~)

2'*°Pu 100-4 139.6 24-0 200 Two-peaked ( / )

2421~U ^{102"6 139"4 24"0 600} Two-peaked ~)

2 4 ~ C m 105"3 140-7 25"0 155 Two-peaked ~)

" Iyer et al (1965; b Singh et al (1982); c Iyer et al (1963); J Manohar et al (1979); ~ Chitambar (1984); : Jain et al (to be published in Radiochimica Acta); ~ Ramaswami et al (1979).

87

V [] N 146 0 N 14B • i t l . • • L = l t 91 95 99 PROTON NUMBER

> qu A o LU LU v

Figure la. Variation of(Es-Ea) as a function of proton number of the fissioning nucleus (Manohar et a11979; values of Es and Ea taken from Moiler and Nix 1974).

> o A o w I o w 0 P- 90 "" P - 92 0 P - 94 v P -96 140 144 143 152 NEUTRON NUMBER Figure lb. Variation of (Es-Ea) as a function of neutron number of fissioning nucleus (Manohar et a11979; values of Es and Ea taken from Moiler and Nix 1974).

w,w 4~ C~ ~v 6"

Radiochemistry of fission of actinides 141

I O O C

0 I 0 0

) - uJ

o

2 3 6 U

2 F

.

; i i ~ /

2 2 5 2 3 0 2 3 5 2 4 0 2 4 5 2 5 0 2 S 5 2 6 0

M A S S O F T H E F I S S I O N I N G N U C L E U S

Figure 2. Variation o f peak to valley ratio as a function o f mass o f fissioning nucleus in low energy fission (Manohar et al 1979).

l O !

1 0 ° 1 0 - 1 - g 1 0

1 0 " $

Io-4

0 J

~. 1o - s _ 1 0 " 6 u~ u l

~- 1o-'t

- 0 1 0

- 9 1 0

- 1 0 1 0

SO

2 0 P R O T O N S

;\

l . . | J l . I , I J | l l J l J l z ] l t i l t j i l l , j t ~ , !

? O 9 0 110 I ) 0 t $ O 1 7 0 t 9 0 ~1t3 2 3 0

M A S S N U M B E R

Figure 3. Mass yield curve in reactor neutron induced fission of 23sU extrapolated beyond A = 70 on lighter wing side and A = 161 on heavier wing side. Experimental points show the presence o f new "shoulders" or "humps" in highly asymmetric region due to 28 proton shell effect (Rao et al 1979).

142 M V R a m a n i a h

This dependence of (Es-Ea) on proton and neutron number of the fissioning nucleus was also able to explain the variation of the peak-to-valley ratio, P/V (the ratio of the highest yield to the yield corresponding to the symmetric mass split), with mass number of the fissioning nucleus as shown in figure 2. It can be seen that 236U has the highest P/V ratio, corresponding to the maxima in (Es-Ea) around Z = 92 and N = 146. For fissioning nuclei heavier than 236U, (Es-Ea) decreases again, but the symmetric peak is not observed any more as it is obscured by the broadening of the mass distribution and the shift in the position of light wing towards heavier mass.

Another interesting finding at Trombay is the influence of 28 proton shell in enhancing the yields of fission products at highly asymmetric mass region 66-67 and the complementary masses as shown in figure 3 (Rao et al 1979). The measured yields in the range 10- 3-10- 6 ~o are about 1-3 orders higher than those expected from a smooth curve.

3. Kinetic energy distribution

A major part of energy released in low energy fission appears in the form of fragment kinetic energy. Studies on kinetic energy distribution provide information on the influence of fragment nuclear shells, fragment deformation and scission point configuration of the fissioning nucleus. Extensive studies have been carried out in this area using physical methods and time-of-flight measurements. The physical methods have limited sensitivity in the low fission yield region and in the case of target nuclei with high alpha specific activity. Due to their high sensitivity, radiochemical methods have been widely used particularly where physical methods have limitations. In the radiochemical methods, kinetic energies of fission products are calculated from the measured recoil ranges in a suitable stopping medium such as AI, air, etc using empirical range-energy equations. The kinetic energies of fission products are converted into those of fission fragments by appropriate corrections for neutron evaporation. This procedure gives accurate kinetic energy values when range-energy equations are calibrated using kinetic energy data obtained by physical methods on high yield fission products.

Kinetic energy distribution in low energy fission shows a maximum around mass 132, but not at the symmetric mass split as expected from the LDM. The difference between maximum kinetic energy and the kinetic energy corresponding to symmetric split known as kinetic energy deficit (xeo), is explained on the basis of compact scission configuration of the fissioning nucleus for mass split corresponding to 132 (due to the presence of the doubly magic spherical shell with Z = 50 and N = 82) resulting in a shorter distance (D) between charge centres of the complementary fragments compared to that for a symmetric mass split.

Kinetic energy distribution in the neutron fission of 232Th, 23zu, 233U, a37Np, 239pu, 241pu, 241Am and 245Cm was studied leading to estimates of KEO and the average total kinetic energy (TKE) (Satya Prakash et al 1969, 1972a, b; Dange et al 1975;

Ramaswami et al 1977). A linear correlation was found to exist between KED and the difference of fragment mass for symmetric split from the doubly magic number 132 as shown in figure 4. An extrapolation of this correlation indicates that gEO for the fission of 264Fm tends towards zero and this trend was confirmed experimentally in the fission of 25SFm and 259Fm (Flynn et al 1978; Ragaini et al 1974).

Radiochemistry of fission of actinides

143

~E

h r~

(.9 W Z

o

W Z

50

4 0 3O 2 0 10

Figure 4.

1969).

A --232 T h o - 237Np n - 2 3 3 U ~ - 2 3 9 p u x - 2 3 5 U O - 2 4 1 p u

2 4 6 8 10 12 I/, 16 18

( 1 3 2 - ~ I )

Correlation of kinetic energy deficit (KED) with shell structure (Satya Prakash e t al

6 E

u 5

To

. J re"

. J Q

(o 2

E ₁ I

3 : Q

O

119

DL ] II

I0 E u

- 9 ~

t"°

_{= 8 c:~J}

7 ~ 6

I L ! I I , 1 ,

12b 13i 137 14__33 14__99

u 3 107 Iol 9 5 8 9

M A S S S P L I T

Figure 5. Variation of relative deformation parameter with mass split for fission of 237Np (Dange et al 1975).

The kinetic energy data from the large number o f fissioning nuclei mentioned a b o v e was used to calculate the relative deformation and d e f o r m a t i o n parameters o f various fission products to examine the dependence o f d e f o r m a t i o n parameter on the fissionability parameter X. F o r this purpose the D values for various mass splits were first calculated from the experimental values o f kinetic energies. The D values for a particular mass split was then apportioned between the complementary fragments on the basis o f the proximity o f their neutron and p r o t o n n u m b e r to the nearest closed shell. Figure 5 shows a typical plot o f deformations o f fragments as a function o f their masses. It was found that fragment deformation increases with increase in X for

1 4 4 M V R a m a n i a h

n,

z z ~ 3

i -

~ 2

o G .

I

0 8 0

. . . APALIN el. ol. E X P E R I M E N T A L DATA

~, . . . ~ USING MytrRaS M A S S F O R M U L A

= - USING WING-FONG'S M A S S F O R M U L A A

...,/ .,,:/

9 0 I 0 0 IIO 120 1 3 0 1 4 0 150

MASS NUMBER

Figure 6. Variation of prompt neutron multiplicity (v) with ma~s number; curve • . . . • is experimental curve (Apalin ^{et al} 1964); A - - - A is calculated curve obtained using mass formula of Myers and Swiatecki 1965 and calculated = • curve using mass formula of Wing and Fong 1964.

symmetric mass division, but does not change appreciably for asymmetric mass division. This difference could be explained on the basis o f cylindrical shape o f saddle point for nuclei with X ~> 0-7 which takes longer time to arrive at scission point with considerable stretching o f the neck with increasing X. Events leading to symmetric splits seem to be mainly governed by liquid drop behaviour o f the fissioning nucleus while asymmetric splits are influenced by fragment shells and hence remain insensitive to the variation o f X. F r o m the calculated fragment deformation, the total experimental kinetic energy and the calculated Q values, the deformation energies o f the fragments were calculated leading to estimates o f the p r o m p t n e u t r o n multiplicities as a function o f fragment mass. Typical results for thermal neutron fission o f 235U are shown in figure 6.

4. Charge distribution

Studies on charge distribution provide considerable insight into the influence o f nuclear shells and nucleon pairing and dynamical aspects o f descent o f the fissioning nucleus. The isobaric and isotopic yield distributions are o f Gaussian nature characterised by the most probable charge, Z r or mass Ap and the corresponding width parameters, tr z o r tr A.

Experimental investigations on charge distribution involve determination o f the fractional cumulative yields (vcx) or fractional independent yields (FLY) o f isobaric fission products or conversion o f the independent yields o f fission products to fractional isotopic yields making use of elemental yields. T h e physical methods involve on-line measurements o f x-ray or 7-ray intensities in coincidence with kinetic energies o f pairs o f c o m p l e m e n t a r y fission products or use o f mass separators, while

Radiochemistry o f fission o f actinides 145 radiochemical methods are off-line and involve separation of fission products of interest and their assay by fl/7 counting or direct gamma ray spectrometry. The necessity of the determination of the independent yields of fission products of short half-lives was a limitation of radiochemical methods in the past. However, the advent of fast and automated transport and radiochemical separation techniques during the last decade has attenuated this problem.

In our laboratories, isobaric charge distribution studies have been carried out in the mass region 100-105 and 130-140 in the neutron fission of 229Th,

239pu, 241pu

arid 245Cm (Rattan et al 1983; Datta et al 1980; Ramaswami et al 1982) and in the spontaneous fission of 252Cf (Manohar et al 1978; Srivastava et al 1984). In addition, investigations have also been carried out on the isotopic yields distribution of technetium in the neutron fission of 239pu and spontaneous fission of 252Cf and of iodine isotopes in 2s2Cf(sF) and in 30 and 40 MeV alpha-induced fission of 232Th (Reddy et al 1984).

Spontaneously fissioning nuclei are ideal to understand the role of potential energy surface of fissioning nucleus and fragment nuclear structure on charge distribution.

The FCV or FIr of a number of isobars obtained in our laboratory along with the data from literature (Wahl 1983) were analysed to obtain the values for Zp and tr z for mass chains 105, 131, 139, 140 and 141. It was found that the Gaussian distribution with a z = 0.60 + 0.06 represents most of the yields in 252Cf as shown in figure 7. It was

99-99 99"9 99 8 0 0 -- 99

>. 98 0 95

~ 9o

._1 3O

~_zo

'~o

~ 5

"" 2

- 0 . 5 0 . 2 0 . 1 0.05

0 0 1 - 2 , 0

O'Z =0

139C s I

135[ / ~ 2 - - 13 104Mo{ ~ 146 c 138Xe--~ . ~ --142Bo--103M°

134Te ~ 1 3 4 Te t05Mo ~ {/13l$b

139Xe -- t40xe

O'Z: 0 54

Figure 7.

s p o n t a n e o u s fission o f 2 s a C f ( S r i v a s t a v a et al 1984; S r i v a s t a v a 1984).

I i i t ~ t

-1"5 - I 0 -05 0 05 JO J 5 20 Z-Zp

A plot of fractional cumulative yields (FCf) as a [unction of (Z-Zp) in the

P. I0

146 M V R a m a n i a h

further observed that in the mass region 130-135, tr z value is on the lower side (i.e. tr z

= 0.50 to 0.55) indicating sharper charge distribution in this mass region, apparently due to preferential formation o f 82 shell fragments. An estimate o f p r o t o n pairing effect (-t- 12 ~o) was obtained based on our data on elemental yield o f iodine and literature data on other elements in the spontaneous fission o f 252Cf.

F r o m the data presented in figure 8 for 252Cf, it is seen that the deviation o f Zp from Z u c o (AZ) increases with mass asymmetry as expected from the m i n i m u m potential energy hypothesis. F r o m a similar analysis o f variation o f A Z with mass asymmetry in the n e u t r o n fission o f 233U, 2350, 239pu and 249Cf (Wahl 1983; Mariolopoulos 1981), it was n o t e d that the rate of increase o f AZ with mass asymmetry increases with fissionability parameter as shown in table 2. With increasing fissionability, the saddle

. r O . O

Z 0

~

^{- 0 . 5}

1"4 ff 0 .,I O . . 1.0 ULI Of:

-I-

',3 - I .5 [ , LIGHT 125 HEAVY 127

- H E A V Y

120 115 110

132 137 142

FRAGMENT MASS ( A' )

+ 1 . 0

, 1 , , 1.5

105 102 147 1~0

O 0 .J N <i

Z +0.5

&

.J

W C~

F i g u r e 8. Variation o f charge polarization with f r a g m e n t m a s s in the s p o n t a n e o u s fission o f 252Cf (Srivastava et al 1984).

Table 2. Charge polarization as a function of mass asymmetry (AZ/AM) in different fissioning nuclei.

Fissioning Fissionability

nucleus AZ/AM parameter X

23eU 0.010 + 0-005 0-772

234U 0-015 + 0-005 0-774

24°pu 0-015 -I- 0-005 0-790

25°Cf 0-025 + 0-002 0-824

252Cf 0-036 ± 0-006 0-821

Z2A

* X - -

w h e r e A and Z a r e t h e m a s s a n d charge o f t h e fissioning nucleus.

Radiochemistry of fission of actinides

147 point shapes becomes more compact (as pointed out in § 3) and the nuclear viscosity increases making the time of descent longer, permitting higher charge polarization (AZ) to achieve preferred configurations.

The elemental yields for technetium (Z = 43) in the neutron fission of 2 3 9 p u and spontaneous fission of 252Cf were deduced from the isotopic yield distribution data.

From a comparison of these data with the data in the neutron fission of 235 U, it is seen that technetium yield increases in the order of fissioning nuclei 236U < 24°pu < 252Cf as shown in table 3. The same table also shows that while the Z of complementary fragment recedes from magic shell closure at Z = 50 from 236U to 252Cf, the neutron number of complementary fragment approaches spherical neutron shell at N = 82 in the fissioning nuclei 24°pu and the deformed neutron shell at N --- 88 in 252Cf. It is also seen that the neutron-to-proton ratio of the complementary fragment lies close to that of the fissioning nucleus as one approaches 252Cf indicating that shell effect is most strongly manifested when it is in phase with liquid drop energetics.

The investigation o f isotopic yields of iodine (Z = 53) in 30--40 MeV 0t-induced fission of 232Th throws some light on the extent of mass/charge equilibration in fission.

Table 4 shows the data on isotopic yield distribution parameter, A~, and o n as obtained in 232Th (~t30_.40 MeV,/) and the same based on literature data in 23sU (nth, f ). With increase in excitation energy the A e value approaches the value expected from unchanged charge distribution hypothesis. The increase of a A with excitation energy was int.erpreted to be due to influence of temperature on mass/charge equilibration, after taking into account multichance fission, indicating that with increase of excitation energy the time o f descent is shorter permitting less time for acquiring the preferred configuration as seen at lower excitation energies.

Table 3. Most probable neutron ( N v) values for charge splits involving technetium and its complementary products in 23SO(nth,f), 239pu(nth,f) and 2S2Cf(SF).

Fissioning Yz

nucleus Element A~, Np percent Q*

zs~U Technetium (43) I09-14 :[:0.14 66.14+0-14 0-092+0-024 1.017 Indium (49) 126.86+0-14 77"86+0.14

24op u Technetium (43) 108.35 + 0.45 65-35 + 0.45 8.00 + 1-32 1-022 Antimony (51) 131-65 +0-45 80-65+0-45

2s2C f Technetium ( 4 3 ) 109.10-I-0-50 66.10-I-0-50 16-90 + 2.09 1-017 Cesium (55) 142.90-t-0-50 87.90-t-0-50

* Q = (Np/Z)fragment/(NIZ)f~ssioning nucleus.

Table 4. Iodine isotopic yield distribution parameters.

Fissioning system

Excitation o A Calc.

energy (MeV) A o value o.4 expt. (in 236U*) 2 3 s u + nth

232Th q" aP30 MeV 232Th --~- ~¢40 MeV

6-54 135"9 1.21 -t-0-12 I "30

23"4 135.09 1.60+0-16 1.51

33"2 134-8 2.37+0-24 1-71

148 M V Ramaniah

5. Angular momentum

Measurement of angular momentum of fission fragments provide information on scission configuration and the dynamics of motion past the second saddle as fragments acquire their angular momenta due to mutual coulombic torque for axially asymmetric scission configuration and thus depend on fragment deformation. Among the various methods for the estimation of fragment angular momenta, physical methods have certain limitations, e.o. measurements of prompt gamma angular anisotropy provide only the gross estimate of average angular momentum and measurements on prompt gamma multiplicity and energy are dependent on the choice of various parameters.

Radiochemical method is the most suitable as it provides fragment angular momenta as a function of their mass and charge and has much less number of adjustable parameters.

The radiochemical method involves determination of the independent yield ratios of the fission product isomers followed by statistical model based analysis (Vandenbosch and Huizenga 1960) to correct for fragment de-excitation to arrive at fragment angular momenta.

At Trombay angular momenta of fragments corresponding to the fission products isomeric pairs 95Nb and 1321 in the neutron fission of 233U, 131,133Te in neutron fission of 241pu and of 111Pd and 117Cd, 131'133Te and 134I in spontaneous fission of 25zCf have been estimated (Datta et al 1982; Guin et al 1983; Data 1984). Studies have also been carried out for 131Te and 133Te in the 30 to 40 MeV alpha induced fission of 232Th (Datta et al 1983).

Results of investigation in the neutron fission of 2330 (as given in figure 9) showed

12.0

IO.O

v I-- Z U.I =E 8 . 0 0 3E

r r

• --= 6 . 0

Z

u~ 4 . 0

=E

I - -

z

W =E 2 . 0

t.s.

0 . 0 5 0

F i g u r e 9.

N = 7 9

I I I I I

51 52 53 5 4 55

F R A G M E N T A T O M I C N U M B E R

Plot of fragment angular momentum vs fragment atomic number in 233U(n,f ) (Datta et al 1982).

Radiochemistry of fission of actinides

¹⁴⁹

that angular momentum of fragments around doubly magic shell region 132 (Z = 50, N = 82) decreases as corresponding atomic number deviates from 50 proton spherical shell contrary to expectation. This apparent anomaly is explained on the basis o f the presence of the deformed shell (Z = 38) in the complementary fragment that tends to reduce the deformation, thus lowering the angular momentum of the corresponding heavy fragment as atomic number of the latter approaches Z = 54 from Z = 50.

In the spontaneous fission of 2 5 2 C f , it was observed that there exists an inverse correlation between fragment angular momentum and elemental yield with odd Z fragments having high angular momentum and lower yield compared to neighbouring even Z elements as shown in figure 10. This implied that for fragments with higher angular momentum, larger amount of energy remains tied up as rotational energy reducing the intrinsic excitation energy and in turn their yield according to the statistical model. Further, for odd Z elements high angular momenta indicates higher scission point deformation compared to their even Z neighbours in the magic shell region arising due to polarization of even-even core of protons by the odd-proton since in the spherical shell region o f N = 82 nuclear deformation is more strongly affected by protons than neutrons as has also been concluded from recent theoretical calculations (Madsen and Brown 1984).

The observations on fragment angular momenta in the

252Cf(sF)

show that the fragment angular momenta are correlated to the scission point deformation dependent, in turn, upon fragment nuclear structure. As a consequence one would expect a correlation between fragment angular momentum and prompt neutron number.

However, lack of any such correlation as observed has been explained to be due to the

18-0

16 -0

14-0

12-0

10-0

8-0

6 . 0

4 . 0

2"0

0 50

t / /

I I I J J i

52 54 56 56 60 62

FRAGMENT ATOMIC NUMBER

18,0

16.0 l

t4-0 7 12.0

0 I0"0 • E

8"0

6'0 o 4.0 ~.

2 ' 0

0 64

Figure 10. Correlation o f elemental yield and angular m o m e n t u m in 2 s 2Cf (Datta et al to be

published).

150 M V Ramaniah

fact that the prompt neutron number depends on total excitation energy of fragment after shape relaxation.

Fragment deformation at scission has been deduced based on simple theoretical calculation in terms of bending mode oscillation of the fissioning nucleus and statistical model (figure 11). The Bohr-Mottelson deformation parameters (fl) for various fragments in the spontaneous fission of 252Cfcould be obtained. The values for x 4162DA--"

(N = 66) and 142v-54,,c (N = 88) are 0.63 and 0.72 respectively which are theoretically

-( ^{Ail,Zl ]} ~' FISSION AXIS

~= 0 ,I

P R E - SCISSlON CONFIGURATION (.NECK RAO|US C )

x s/

ONSET OF BENDING OSCILLATION . . . .

¢AI ~ z2)

NON-LINEAR SCISSlON CONFIGURATION

(BFNOING AMPLITUO( ~'10"2 I

J i

Figure 11. Schematic of origin of fragment angular momentum due to precision bending mode oscillations.

Table 5. Comparison of fragment angular momentum in 235U at various excitation energies.

Fissioning system

Excitation Initial angular Fragment angular Calculated

energy (E*) momentum momentum (B~) B~ value

(MeV) (12~ 1/2 ~ ]31Te 133Te for 133Te

23SU(nth,f) 232Th (el30 MeV, f ) 23ZTh (~t40 MeV, f )

6.54 3 4 6 . 0 ± 1 . ~ 5.9±1-5" ---

7 . 5 ± ~ 7 ~ 6.5±0-4 b - -

23.36 10.2 5.7±0-6 6.9±0.4 7.03

33.20 14.4 5.8±0.8 7.9±0-8 7-81

Sarantites et al 1965.

b Imanishi et al 1976.

Radiochemistry of fission of actinides 151 predicted deformation parameters for occurrence of deformed shells at these neutron numbers, in low energy fission. Investigations on 30 to 40 MeV alpha induced fission of 2a2Th indicated that the angular, momenta of fragments in the magic shell region remains unchanged with excitation energy as shown in table 5. These observations have been interpreted in terms of interplay between tendency of increase in angular momenta at higher excitation energy as against stiffness of compound nucleus at higher angular momentum towards bending oscillation and shorter time of descent. In order to analyse the influence of the fissioning nucleus excitation energy and angular momentum, calculations were carried out for evaluation of fragment angular momenta.

This calculation was based on retainment of angular velocity of Fermi gas type fissioning nucleus at saddle point and population of higher rotational states at higher excitation energy taking into account the effect of multichance fission. The agreements between calculated and observed angular momenta indicates that at higher energy fragment angular momentum is primarily dependent on the properties of fissioning nucleus at the saddle point.

6. Conclusion

Radiochemical studies of fission carried out at Trombay during the last 25 years have contributed to a better understanding of this highly interesting and complex nuclear reaction. Extensive investigations on mass distribution have shown that the one-, two-, and three-peaked mass distribution in low energy fission arise due to the relative contributions of the symmetric and asymmetric modes of fission which, in turn, depend on the difference in the barrier heights for these modes. It has been further shown that this difference strongly depends on the neutron number than the proton number of the fissioning nucleus and further, the variation of this difference with mass number of the fissioning nucleus explains the observed variation in the peak-to-valley ratio with the fissioning nucleus. Enhanced fission yields in the highly asymmetric mass could be understood as due to the influence of the 28 p-shell. Results of kinetic energy distribution demonstrated the influence of the doubly magic shell at mass 132 on the total kinetic energy and kinetic energy distribution. The fragment deformation calculated from the kinetic energy data has clearly shown that the symmetric mode is largely governed by the liquid drop behaviour. Results of studies on charge distribution a n d fragment angular momentum brought out the influence of 66 and 88 neutron deformed shells and further showed their greater effectiveness when in phase with liquid drop energetics. It was also shown that the extent of variation of charge polarisation with mass asymmetry depends on the fissionability parameter due to the influence of the saddle point shape and dynamics of descent. Angular momentum studies provided estimates of fragment deformation and showed that the odd Z fragments have high deformation due to the polarisation of even Z core by the odd proton. Results of studies on medium energy fission have shown the influence of the saddle point properties on charge distribution and fragment angular momentum due to higher excitation energy and shorter time of descent. Thus, our studies have contributed to a better understanding of the nuclear fission process particularly concerning the late stage of fission process and have brought out the importance of the deformation energy surface, spherical and deformed nuclear shells, nucleon pairing and the dynamics of descent past the second saddle point.

152 M V Ramaniah Acknowledgement

The author is grateful to the large number of his colleagues for their valuable help, suggestions and comments during the preparation o f the paper. Particular mention should be made of Drs S S Kapoor, S B Manohar, P R Natarajan, V S Ramamurthy, Satya Prakash and Tarun Datta.

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