A study of the de-excitation of primary fission fragments from the neutron-induced fission of 235U

]

2~.J

NuclearPhysics A205 (1973) 488--512; (~) North-Holland Publishino Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout writtenpermissionfrom the publisher

A STUDY OF THE DE-EXCITATION OF PRIMARY FISSION FRAGMENTS F R O M T H E N E U T R O N - I N D U C E D F I S S I O N O F 23Su TASNEEM A. KHAN t, D. HOFMANN*t and F. HORSCH

lnstitut fiir Anyewandte Kernphysik, Kernforschungszentrum Karlsruhe Received 10 January 1973 Abstract: Two separate three-dimensional experiments have been performed in which the energies of coincident fragment pairs and ),-rays or internal conversion electrons, emitted within ,~ 1.6 nsec of the thermal-neutron-inducedfission of 2a5U, were recorded event by event. The fragment kinetic energies were used for mass identification. The self-consistency of the values of electron energy, ~,-ray energy and fragment charge, and its agreement with X-ray selection data, were used to identify the atomic numbers of the fragments. The analysis of the )'-ray and conversion electron spectra resulted in the assignment of many transitions to new isotopes as well as improvement in or confirmation of many assignments from the 252Cf spontaneous fission data. Limited information on the multipolarities of the transitions in even nuclei is presented. The relative yield of electrons per fragment indicates softness to deformation in the mass region 100-110. Data are presented supporting the assignment of a 193 keV transition as the 2 + --> 0 + transition in 9aSr. An examination of the 2 + -~ 0 + level systematics of neighbouring even nuclei suggests a transition from vibrational to rotational behaviour in the light fragments between neutron numbers 58 and 60. NUCLEAR FISSION 23SU(n,f), E = th; measured fragment kinetic energies, E~, I,~, Ecc, (fission) ~'-, (fission) ce-coin; deduced fragment mass, charge, K/L, ce yields per fragment.

1. Introduction There is a n increasing interest in the study of nuclei far from the stability line. Such studies help to explore the new regions of nuclear deformations a n d to extend nuclear theory to regions which have hitherto been inaccessible. P r i m a r y fission fragments, with their large excess of neutrons, 6 to 10 h units of a n g u l a r m o m e n t u m a n d moderately high excitation energies, form a special class of nuclei far from the stability line. Moreover they cover two very significant regions of nuclear deformation. The study o f their nuclear properties is therefore of considerable interest. Experimentally the study of the de-excitation of the p r i m a r y fission fragments within the first few n a n o s e c o n d s after fission is rather difficult, due to the fact that there is n o way to study one isotope without interfering r a d i a t i o n from n u m e r o u s others. However, with present day techniques it is possible to measure the energies o f the fission fragments, as well as the energy of a n y r a d i a t i o n emitted by the fragments, for individual fission events. C o n s i d e r a t i o n o f m o m e n t u m a n d mass c o n s e r v a t i o n t h e n t Present address: Pakistan Atomic Energy Commission, PINSTECH, Nilore, Rawalpindi. t* Institut for Kernphysik, Universittit Frankfurt/Main. 488

FISSION F R A G M E N T

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489

enable one to obtain the mass of the fragment giving rise to the radiation. Experiments of this type have been performed to study the y-rays t,[2) and conversion electrons 3) from the fragments of 252Cf(sf)" It was felt desirable to extend these measurements to thermal-neutron-induced fission, firstly to investigate those nuclei whose yield in the spontaneous fission of 252Cf is low and secondly to obtain more information on the mass region accessible to both 252Cf(sf) and 235U(n, f) and compare the results of the two fissioning systems.

Gamma- roy detector cm 5

L

0 6Li2CO 3

Gammer- ray cotlimator with sawtooth- shaped inner surtoce

0.,.o,or,

-" 1~ ,~__,...~,

n-'~-ae am

[-

ment

/

/

Poll(ethylene collimator

I Fig. I. Schematic d i a g r a m o f the a r r a n g e m e n t for the),-ray experiment.

The present work summarizes the results of the investigations of the spectra of gamma rays 4, 5) and internal conversion electrons 6) associated with intervals of fragment mass using the neutron-induced fission of 235U. Whereas the y-ray experiments explored the relatively higher-energy transitions ( > 150keV) the electron measurements were mainly concerned with the large number of low-energy transitions. An attempt was made to obtain the electron spectra with high enough resolution to obtain the K/L ratios of the strongest transitions and thus assign multipolarities to

490

T.A.

KHAN

et

al.

them. By c o m p a r i n g the electron line energies with the energies o f the corresponding y-rays, assignment o f the charge o f the fragment was in m a n y cases possible. I

I

~I o00

i

. ;,~

f:~C t

". ,

r .f.

:

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H H

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.

-.

:x

800

600 -~

/.00

~ • .:. . ~ :

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~.

200

I

I

I

I ENERGY

(keV]

Fig. 2a. Prompt ?'-ray spectra for the fragment mass ranges A L = 88-90 and An = 143-145. The spectra demonstrate the dependence of the ?'-ray energy on the velocity and direction of the fragment motion. The pair of spectra represent the two cases: light fragments moving towards the ?'-ray detector (upper spectrum) and heavy fragments moving towards the ?'-ray detector (lower spectrum). The letters L and H indicate some assignments to the light and heavy fragments respectively.

2. Experimental procedure 2.1.

GAMMA-RAY

MEASUREMENTS

A detailed description o f the experimental procedure is given elsewhere 7); therefore only the basic principles o f the procedure will be outlined. The experimental set-up was designed in such a way that the assignment o f single ?-ray lines to specific fragments on the basis o f the direction o f the Doppler shift was possible. A schematic view o f the experimental arrangement is shown in fig. 1. A well-collimated and filtered neutron beam f r o m the F R 2 reactor was made to strike a 50/~g. cm -2 target o f

FISSION FRAGMENT

DE-EXCITATION

491

2asu on a 30/~g. cm -2 VYNS backing. The mass of the fragment giving rise to the radiation was determined from the kinetic energies of the fission fragments as measured by two Si surface-barrier detectors. The y-rays emitted by the fragments were

800

6OO

oo

=o

t

." •

-"

:..

,~

~

8 s~ 0

loo

0

~ :"

I

ioo

200

300

I

I

I

I

I

I

~oo

soo

600

~oo

eoo

9oo

""

looo

ENEROY(kW).

Fig. 2b. T h e pair o f p r o m p t 7-ray spectra for the f r a g m e n t m a s s ranges AL = 102-104 a n d A . = 130-132.

detected by a 28 cm a Ge(Li) detector which had a resolution of 3.5 keV for the 1332 keV y-ray of 6°Co. A NaI(TI) anti-Compton shield reduced the Compton distribution and the fast-fission neutron-induced lines in the y-ray spectra. The y-ray collimator was designed in such a way that the Ge(Li) detector could see both the fragments in flight, from their origin at the target to an average distance of about 1.6 cm. The actual fragment flight paths seen by the detector ranged between 1 and 2 cm. By this arrangement it was possible to assign a specific line to a particular member of each fragment pair by the sign of the observed Doppler shift in the y-ray energy caused by the moving fragments. The three analog pulse heights in each triple coincidence event were digitised and stored event by event in a 256 x 256 x 2048 channel matrix and processed via the Karlsruhe multiple input data acquisition system (MIDAS). The masses of the frag-

492

T . A . KHAN et al.

,ER LD

)URCE

Fig. 3. Schematic diagram of the arrangement for the electron experiment.

r

I,

-~

&

&

: IPl 1

1

O.-eATE 1

GATING

FEEDBACK

Z--L Fig. 4. Block diagram of the electronics for the electron experiment.

FISSION FRAGMENT DE-EXCITATION

493

ments were calculated from the measured energies. The method used is outlined in the appendix. Final post neutron-emission masses were calculated off-line using experimental neutron numbers to correct for the emission of prompt neutrons. Gammaray spectra associated with fragment masses in 2 amu wide mass intervals were obtained by sorting the three-parameter data. Each of these spectra was then analysed to give quantitative energies and intensities of individual transitions. Four typical examples of the mass-sorted ~-ray spectra are shown in fig. 2. 2.2. ELECTRON MEASUREMENTS The precise measurement of electron energies requires not only the elimination of any window for the electrons to penetrate that would seriously degrade their resolution, but also the mitigation of the Doppler broadening of the electron lines by the moving fragments. The manner in which these problems were resolved may be seen in fig. 3. A well-collimated neutron beam impinged on a target of 23SU. The energies of the fission~fragments were measured by two silicon surface-barrier detectors which were collimafed to 20 m m in diameter and operated at ' -~ 5..0~C. .... The internal conversion electron~ emitted by one of the fragments during the first 1.8 cm of its flight path were focussed on to an i0n'implar/ted detector by~'megns 0f a ~dodbly focusing magnetic field. The magnetic field steered the electrons round a lead shield which protected the detector from the intense prompt ~-ray background. The 200 mm 2 X 2 mm electron detector was operated at liquid nitrogen temperatures and had a resolution of about 3 keV in the region of interest. The length of the fragment flightpath was chosen to beas close as possible to the flight path of [the fragments in the v-ray experiment so that the resuRS of the two experiments could be compared. However, unlike the ~-ray set-Up, electrons from only one of the fragments could arrive at the electron detector. The angles of emission of the electrons With respect to the fragment path were restricted.to very nearly 90 °. The serious losses of energy resolution due to Doppler broadening by the moving fragments were thus mitigated at the expense of a much lower count rate~ However, by using a target of thickness 100 pg. cm -2 on a 30 pg" cm -2 backing of VYNS and a neutron flux of 109 n- cm -2 • sec -1 a count rate of 20 events per rain was possible. Since only those electrons within a certain energy window were focussed on the electron detector for a particular value of the magnetic field, the field was made to sweep back and forth continuously throughout the experiment. A block diagram of the electronics is shown in fig. 4. The pulses from the three detectors were amplified by low-noise preamplifiers and routed to the three ADC units of the MIDAS system through linear and variable-gain amplifiers. The three ADC units were gated by a timing system which required a threefold coincidence of events in the fission fragment and electron detectors. The coincidence resolving time was 80 nsec and any pile up of pulses in the fission detectors generated a veto signal in the gating circuit. As the measurements were made over several months, digital stabilisation was used

494

T . A . K H A N e t al.

528 484

~ 440

~ 396

T

nW 352

,++

Z 308

"~;e

2~ 0 U 26/.,-

•

220 176 ' 132

J

88 44

4.

~o

40

60

80

100 120

140

160 1110 200

220 2t,O 260 280 E N E R G Y ( k e V)

Fig. 5. A mass-sorted energy s p e c t r u m of internal conversion electrons from a mass interval in the light-fragment group.

528 •'J 484, ILl Z Z 440,

U

396

ILl

n 352 (/1 i.Z 308 0

264 220 176 132 88 MASS INTERVAL 147-149

44 0

o

2'0 4'0 6'0 8; 1;o 1~o 1;.o 1~o 1~o 2~o 2~o 2;.o 2~o 2~o E N E R G Y ( k e V)

Fig, 6. A mass-sorted energy spectrum o f internal conversion electrons from a mass interval in the heavy-fragment group.

FISSION FRAGMENT DE-EXCITATION

495

on all three detectors to avoid any possible gain shifts. The DC levels of the three detectors, as well as the gain of the electron detector were stabilised by monitoring precision pulsers. The gains of the fragment detectors were stabilised by monitoring the energies of the light fragment peaks. At the end of every 24 h of measurement calibration checks were made for stability by sliding the built-in calibration sources of 137Cs and STCo under the electron detector and observing the positions of the 129 keV and 624 keV electron lines. A two-parameter experiment to obtain the correlated energies of the two fission fragments was also performed at this time. This enabled one to obtain a set of calibration constants for the fragment detectors for each 24 h period and to monitor the quality of these detectors continuously. The events accumulated daily in the two-parameter experiments were summed over the entire period of measurement and used to obtain the mass-yield curve for the neutroninduced fission of 23SU. At the end of each reactor period a calibration of electron energy v e r s u s channel number was made by means of ta~Ba, s 7Co and 137Cssources, which gave a number of lines over the entire region of interest. During the course of the measurements a total of 1 million events for the threeparameter electron experiment and a similar number for the two-parameter experiment were accumulated. Part of the three-parameter data was accumulated during subsequent runs confined to the 200 to 350 keV region of electron energies. The data was processed by procedures similar to those described for the v-ray experiment and electron spectra associated with fragment masses in 2 amu mass intervals were obtained. Two examples of such mass-sorted spectra accumulated during the first half of the measurements are shown in figs. 5 and 6, The former is from the light- and the latter from the heavy-fragment groups. 3. Results 3.1. GAMMA-RAY MEASUREMENTS In table 1 54 v-rays have been assigned to individual fragments. The masses were obtained by plotting the peak intensities as a function of mass. The first moments of these distributions then identified the mass of the fission fragment and the widths established the mass resolution. The magnitude of the widths is determined by the dispersion introduced in prompt neutron emission and by the inherent energy resolution of the fission-fragment detectors. In the present case the mass resolution ranged from 4 to 7 amu FWHM. Only those v-transitions have been included in table 1 for which both Doppler-shifted members were well enough resolved to be identified on the basis of a congruous intensity v e r s u s mass distribution. The absolute uncertainties in the mass determination are mainly due to systematic errors in the calibration procedure and the neutron corrections. The most probable charges Z v were taken from the tables of Wahl e t aL s) starting from the original non-integral mass values derived. Due to the small width of the charge distribution for a given mass (,,~ 1.5 charge units F W H M ) the true charge

T . A . K H A N et al.

496

TABLE 1

A s s i g n m e n t o f p r o m p t 7-rays to individual f r a g m e n t s f r o m n e u t r o n - i n d u c e d fission o f 2a sU Fragment Most mass probA able charge Zp

884-1 914-1

35 36

934-1 954-I

38 38

96+1 964-1 964-1 984-1 994-1

38/39 39 39 40 40

1004-1

40

100_+~ 1014-1 1024-1

40 40/41 41

1034-1

41

10312 104±2 1044-1

41 41/42 41/42

1314-1 1324-1 1344-I

42 51 51 52

1354-1 1384-1 1394-1

52/53 53/54 54

1404-1 141±1

54/55 55

141 4-2 1414-1 1424-1

55 55 56

),-ray ~) energy E~, (keV)

8694-5 7064-4 9564-5 1444-2 249=[=2 8344-4 8134-4 376+3 ( 4 2 7 ! 4 ) b) *193i2 "1234-2 "1574-2 * 984-2 "2124-2 "351 4-3 4954-3 6224-5 12244-5 *3254-3 1744-2 •275+2 136±2 • 2964-2 518±3 581±4 "157±2 "1914-2

Relative Interpretation Interpretation Interpretation intensity based u p o n based u p o n close based u p o n close experimental systematics o f agreement of agreement of per 2+ ~ 0+ energy a n d m a s s energy a n d m a s s fission a n d transitions in a s s i g n m e n t with a s s i g n m e n t with 2s2Cf d a t a (t, p) a n d 16 n i m neighbouring flight p a t h doubly even nuclei fl-decay d a t a

< 25 70 =[=23 ( ° ° K r 2 + - * 0 +) 32 4-11 ( 9 2 K r 2 + - > 0 +) 14.54- 7.5 6 . 9 ± 3.5 61 + 2 0 C * S r 2 + ~ 0 +) 80 4-27 (9~Sr 2 + - ~ 0 +) 25.5112.5 ( > 32) 13.04-4.5 38 -t-19 21 4- 7 > 18 37 4-13 56 4-28 55 4-18 50 4-25 29 4-15 16 4- 8 7.74- 2.6 7 . 6 ± 2.6 7.84- 2.7 8.84- 2.9 15 4- 7.5 15 ± 7.5 5.44- 1.8 12 4- 4 (5564-3) ~) (12 ± 6) 3664-3 15.5 4- 7.5 12224-5 12.34- 6 (la°Sn 2 + - + 0 +) 9654-5 19.54-10 la2Te 2 + - + 0 + 11804-5 21 ± 1 0 12784-5 34 ± 1 7 la4Te 2 + --~ 0 + 4254-3 40 4-13 585±4 106 4-60 *373±3 70 ± 3 5 4824-3 112 4-37 723±4 47 4-23 *2834-2 16.54- 5.5 303±3 12 4- 6 • 3574-3 36.54-12 475±3 51 4-17 6294-4 38 4-19 4294-3 55 ± 2 7

*OlZr ~OOZr lOOZr ,OOZr (,OOZr

2 + --> 0 + 4 + .->2 + 6 + -+4 + 8 + - . 6 +) 9 8 Z r 2 + .--> 0 +

lO2Zr 4 + -->2 +

lO2Mo 2 + - ~ 0 + 'O*Mo 6 + --> 4 + lOZZr 8 + --> 6 + l O 4 M o 2 + --> 0 +

'O*Mo 4 + -+ 2 +

la*Te 2 + --~ 0 + laSXe 2 + --~0 + l*OXe

2 + -> 0 +

('*°Cs) ~42Ba

2 + -> 0 +

(' 4°Cs)

FISSION F R A G M E N T DE-EXCITATION

497

TABLE 1 (continued) Fragment Most mass probA able charge Zp

y-ray ' ) energy E~ (keV)

1434-1

"115±2 • 1984-2 • 3304-3 3434-3 4924-4 5074-3 8204-5 "1834-2 5024-3 *2944-2

56

1434-2 1434-1

56 56

1444-2 1464-2 1474-1

56 57/58 58

Interpretation Interpretation Interpretation Relative based upon based upon close based upon close intensity agreement o f agreement o f experimental systematics o f 2+ -*0 + energy and mass energy and mass per transitions in assignment with assignment with fission and neighbouring 252Cf data (t, p) and 16mm flight path doubly even nuclei fl-decay data > 18 36 4-12 57 4-19 23.54- 8 31 5:15 27 i 9 45 4-22 12 4- 4 17.54- 6 14 4- 5

144Ba 2 + --~0 + 144Ba 44- ~ 2 +

14'*Ba 6 + - * 4 +

l'~SCe 4 + -->-2+

") Derived from the tables given in ref. a). b) The high-energy Doppler-shifted member is partly screened by another line. c) The spectra permit the alternative interpretation: A = 130-t-1, Zp = 50, Ey : 5854-4 keV, rel. int. = 134-7.

should generally lie within __+1 unit of Zp since only transitions in fragments with fairly high yield ( > 0.5 %) are resolved in the present experiment. The y-ray energies are the mean values of the Doppler pairs. The error bars are based on both uncertainties in the determination of the peak positions and systematic errors. For fission fragments travelling in the direction of maximum detection efficiency, i.e. approximately towards the centre of the fragment detectors, the flight path viewed by the y-detector was 16 mm. This corresponds to about 1.1 nsec for the light fragments and 1.7 nsec for the heavy fragments. Therefore the experimental intensity values represent the relative number of quanta emitted within these times after fission. A large number of transitions may be identified on the basis of the close agreement in energy, charge and mass assignment with those observed in fragments from the spontaneous fission of 252Cf [refs. 1,2, 9)]. Other interpretations are based upon the systematics of 2 + --, 0 + transitions in neighbouring even nuclei or upon close agreement of energy and mass assignment with (t, p) [ref. 1o)] and fl-decay data 13). The interpretations are also supported by the results of the electron measurements as well as the fact that the intensities of transitions assigned as 2 + ~ 0 ÷ in doubly even nuclei in the present work follow the calculated independent yields of the isotopes, as discussed in subsect. 4.2. Many of the lowenergy y-rays observed could be related to conversion electron lines seen in the electron experiment. These lines are indicated by an asterisk before the line energy in table 1, Further information on these lines is given in the table 2 which summarises the results of the electron experiment.

498

T.A. KHAN et al.

3.2. ELECTRON MEASUREMENTS A total of 131 lines have been analyzed in the electron spectra out of which 63 belong to the light-fragment group and 68 to the heavy fragments. The masses of the fragments were determined from the centroid of a plot of electron peak intensities as a function of mass as discussed in subsect. 3.1. The energies of the electron lines were determined by a least-square analysis of the electron spectra using the calibration methods outlined in subsect. 2.2. In calculating ),-ray transition energies from the conversion electron energies, account has to be taken of the increase in electron binding energies due to the high states of ionization of the fragments. This correction, which is nearly constant and about 0.9 keV over the range of elements produced in fission a), has been made in the present data, and therefore the electron energies are compatible with 7-ray energies from stopped fission fragments. The electron energies in the present experiment are estimated to have an error of _+1 keV. In order to determine the charge of the fragments two procedures were adopted: (i) The results of the present experiment were compared with the work of Hopkins et al. 11.12) in which they studied 7-rays in coincidence with X-rays from stopped fission fragments of 252Cf" In their experiment the energies of a large number of lowenergy ?-rays are measured accurately and the coincident X-ray is used to give information regarding the charge of the fragment. The experiment restricts the possible origin of the v-rays to a pair of complementary fragments. In the present work, since we observe conversion electrons from only one of the two fragments and sort the spectra according to fragment mass, by a comparison of the results of the two experiments, it is possible to determine whether the electron (and v-ray) line originated from the heavy or light fragment, and to assign a mass number to the fragment. The procedure was to obtain the K-electron energies from the ?-rays using the binding energies of both the fragments. By comparing the K-line energies with the electron lines observed it was possible to determine not only which of the two fragments the electron line belonged to but also to ascertain that it was not from a neighbouring element. (ii) As a further check on the above procedure and for those electron lines whose corresponding ?-rays were not observed in the work of Hopkins et al., the binding energies of the elements around the most probable charge were used to calculate the corresponding ?-ray energies for the electron lines observed. The results were compared with the energies of v-rays measured in the v-ray experiment of the present work and the work on 2 S2Cf fission [refs. 1.2. 9)], and the element with the binding energy which gave the best fit was assigned. In the atomic numbers assigned in the present work, all the v-ray energies calculated from the electron energies were in agreement with the most accurate ?-ray measurement within experimental error. This error is estimated to be less than or equal to the difference in K-electron binding energies of neighbouring elements in most cases. The good agreement of the charge assignments with 252Cf(sf) fourparameter experiments in which X-ray selection was used for charge assignment l - a)

FISSION F R A G M E N T DE-EXCITATION

499

TAnLE 2 Assignment of prompt electrons to individual fragments Atomic number

Electron energy (keV)

89 91 93 94 94 94 94 94 94 95 95 95 95 96 96 96 96 96 97 97 98 98

35/36 36/37 37/38 38 37/38 37/38 37/38 37/38 37/38 38 38 38 39 Y 39 Y 39 38/39 38/39 38/39 39 Y 39 39/40 39/40

165 182 143 68 177 264 268 312 347 48 100 110 113 42 71 92 165 210 62 332 131 157

98

38

98

39/40

184

D

98 98 99 99+_I 99 99 99 99 99 99 99 99 99 100 100 100 100 100

39/40 39 40 Zr 40_+~ 41 Nb 41 Nb 39 Y 39/40 39 Y 41 Nb 39/40 40 Zr 39/40 41 Nb 41 N'b 41 Nb 40 41 Nb

338 362 38 46 55 78 84 87 105 119 126 147 170 64 100 108 135 139

122.3 ¢' c. t) 138 J)

105.2 119

165.3 d)

147.3

84.0 ~) 119.1 °) 126.4 ~)

65.0 100.1 107.4

159.0 TM)

140.0

D D B C B A B D A A D B D B B C D A

100

41

153

172.0 a)

153.0

B

Mass number

Sr

Nb

177

y-ray energy (keV)

K-line Assignenergy ment with category assigned Z

130.2 c) 58.2 ~) 87.6 c)

113.2 41.2 70.6

79.9 c)

62.8

193 ©)

55.0 ~) 64.3 ~) 73.8 c) 97.0 c, j) 100.6 ~)

176.9

37.0 46.3 55.0 78.0 83.6

D D D D D D D D D D D D B B C D D D C D D D B

Observations

probably from Sr since not seen in 2s2Cf (sf) suggested assignment 9SSr 2 + -~ 0 + probably from Sr since not seen in 2s2Cf (sf)

d) assigns to a complementary fragment (La)

500

T. A. K H A N et al. TABLE 2 (continued)

Mass number

Atomic number

100 100 100 101 101 101 101 101 101 102 102 102 102 104 104 105 105 106 106 108 133 134 136 136 136~ 136 137~ 137~ 137~ 137 137 138 138 139 139-4-2 140 140 140 140 141 141 141~ 141 141 141 141~

41 40 40 40 39 40 40 41 40/41 40 40 42 41 41 42 43 43 42 42 44 53 53 53 53 53 53 54 54 54 54 54 55 55 54 54 55 55 55 55 55 55 55 55 56 55 54

142

55

Nb Zr Zr Zr Y Zr

Electron energy (keV)

Xe Xe Xe Xe Cs Cs Xe Xe Cs Cs Cs Cs Cs Cs Cs Cs Ba Cs Xe

192 195 334 36 74 81 110 257 264 133 309 275 279 122 173 116 138 152 165 220 196 84 55 123 226 256 71 100 135 275 361 103 119 38 105 42 44 183 251 36 46 49 53 65 280 340

Cs

55

Nb Zr Zr Mo Nb Nb Mo Tc Tc Mo Ru I I I I 1 1

7-ray energy (keV)

212.0 212.7 352.1 53.4 91.0 98.2

d) b,¢,d.c) b.e) ¢) c:) ¢,c.g)

K-line Assignenergy ment with category assigned Z 193.0 194.7 334.1 35.4 74.0 81.2

276.0 e, j)

257.0

151.9 b) 326.6 b.~) 296.0 b, e) 297 J) 140.9 c,~) 192.3 b,©) 138 J) 159 ~,J) 171.7 b)

133.9 308.6 276.0 278 121.9 172.3 117 138 151.7

242.3 b) 228.5 ¢.1) 116.8 ~) 87.4 ~"s) 155.1 c,f) 261.0 c'~) 288.4 ~.f) 108.6 ~) 138.3 ¢) 172.0 ¢) 314.1 a.f) 400*0 d,f) 138.3 ¢'h) 154.1 ¢,h.I) 74.2 ¢) 143.0 c) 78.6 c.s) 80.0 c' h) 219.0 ~.f. I) 287.4 ~'*) 71.5 c,h) 81.7 ¢,h) 84.2 ¢) 89.0 ~'h) 102.5 c,~) 315.3 ~) 376.8 "' ~)

220.2 195.3 83.6 54.2 121.9 227.8 255.2 71.2 100.9 134.6 276.7 362.6 102.3 118.1 36.8 105.6 42.6 44.0 183.0 251.4 35.5 45.7 48.2 53 65.1 279.3 339.4

91.4 c'h)

55.4

B A A B A A D A D A A A A A A C C A D A B B B B B B C B B A B A A B B A B A B B A B A B B B A

Observations

lOOZr 2 + ~ 0 + lOOZr 4 + ~ 2 +

tO2Zr 2 + -+ 0 + lO2Zr 4 + --_>2 + lO2Mo 2+ -_~0 +

lO4Mo

2 + ~

0 +

lO6Mo

2 + ~

0 +

lOSRu 2 + --~ 0 + I) assigns to m a s s 132

f) assigns to m a s s f) assigns to m a s s f) assigns to m a s s mixes with 143Cs

137 :i:0 135+°x 136+° line at 69 keV

f) assigns to m a s s 138+_~

l) assigns to m a s s 139

p r o b a b l y l * ° X e 2 + ~ 0 + mixing with a n o t h e r line

FISSION F R A G M E N T D E - E X C I T A T I O N

501

TABLE 2 (continued) Mass number

Atomic number

Electron energy (keV)

7'-ray energy (keV)

96.9 ~'t) 191.8 c'''k) 231.6 d'''k) 335.8 d.h) 359.7 a.o.~) 106.0 c. a) 112.4 c'©'''h)

60.9 155.8 192.7 298.4 322.0 70.0 75.0

A A A

80.0

A

137.9 c.h) 212.4 o) 77.6 c)

100.5 174.6 38.7

B

84.0 c)

45.1

C

199.4 ,.d.,) 270.5 d)

161.9 231.6

A C

293 349 357 62 66 78 lll 114 128 130 201 43 91 144

331.0 a.,) 388.5 d. t) 397.5 ~.d) 100.3 c.#) 104.3 c.f) 117.8 ¢) 150.4 c) 153.8 ~) 167.7 ~'f) 171.9 d) 240.6 d) 82.2 ~' t) 130.5 c.t,.) 181.4 .... c.t.,)

293.6 349.8 357.2 61.4 65.4 77.4 111.5 115.1 128.8 131.6 200.2 43.3 91.7 144.0

A B

218 296 159 242 118 255 346 94 102 58 170 32 121

258.4 a.d) 333.0 *) 199.8 d) 283.8 o. t) 158.8 ~.o,f) 295.6 ,.a.,) 386.2 a) 134.0 c,t) 142.7 ¢'f'~) 97.7 a.~) 209.0 ") 75.9 ~) 164.7 *)

218.2 295.6 159.4 243.4 118.4 255,3 345.8 93.6 102.3 57.3 168.6 32.3 121.1

A A C A A A

142 142 142 142 142 143_+oz 143

55 55 57 54 56 55 56

Cs

Cs La Xe Ba Cs Ba

60 156 192 300 322 69 75

143

56

Ba

81

143 143

Ba Ba

144+~

56 56 57

101 175 40

144+~

57

45

144 144

56 57

Ba

162 232

144 144 144 145 145 145_+~ 145 145 145 145_+2 145+~ 146 146 146

56 57 58 57 57 58 57 57 57 58 58 57 57 56

Ba La Ce La La Ce La La La

146 146 1474-2 147 148 148 148 149 149 150 150 152 152

58 56 58 58 58 58 58 58 58 58 58 60 60

Ce Ba

a) ReL 2). r) Ref. 9).

La La Ba

Ce Ce Ce Ce Ce Ce Ce C.c Nd Nd

K-line Assignenergy ment with category assigned Z

b) E e L x). s) Ref. 3).

117.4 c.f.h)

~) Ref. ix). h) Ref. ~3).

Observations

B

A B B

B C

A A

l`*2Ba 2 + --~ 0 + mixing with laVXe line at 71 keV ' ) assigns to mass 144; h) to mass 141 t) assigns 1444-1; a) assigns to mass 142 h) assigns to mass 141 interference from 139Xe line at 38 keV interference from ~4°Cs line at 44 keV 144Ba 2+ --~0 + interference from another line near mass 137 144Ba 4 + -+ 2 + 14`*Ce 2 + --,0 +

B B B B B

C C A A A

14eBa 2 + ~ 0 + ; s..) assign mass 1444-1. t) assigns 1454-I x`*eCe 2 + ~ 0 +

X4SBa 4 + ~ 2 +

B

t4SCe 2 + --~ 0 + x,,SCe 4 + ~ 2 + l,,SCe 6 + ~ 4 +, weak line

A A A A A A

s) assigns to l,,gPr xsoce 2 + ~ 0 + lSOCe 4 + - - , 2 + 152Nd2+ -->.0 + XS2Nd 4+ - , 2 +

d) Ref. 12). l) ReL 1,,).

") Table 1. J) Ref. is).

k) ReL 16).

502

T.A. KHAN et al.

gives confidence in the above procedure, which is based on self-consistency in the results of three- and two-parameter y-ray and X-ray experiments and the electron measurements. The method used is particularly useful for cases where the isotopic or X-ray yields are low or background problems severe. The results of the analysis of the data are given in table 2. Columns 1 and 2 give the mass and charge assignment for each electron line, or the most probable charge if no corresponding v-ray line has been observed previously. Column 3 gives the energy of the electron line. Column 4 gives the best value of the corresponding v-ray energy and refers to other observations of the v-ray. Column 5 gives the calculated K-line energies using the v-ray energies of column 4 and the charge assignments of column 2. The electron line assignments are graded in four categories in column 6. Explanatory information pertaining to the various categories is as follows: Category A. In this category are those transitions whose mass and charge assignments appear to be established. The mass assignments in this category are based on two criteria. First, that the lines were well resolved and their masses could be well determined in the present experiment. A second restriction was that the masses so determined were either in good agreement with the mass assigned to the corresponding v-ray in the present or a previous work, or that the neighbouring masses could be excluded on physical grounds. For example, certain assignments could be ruled out on yield considerations. In other cases the fact that a relatively intense electron line clearly did not fit into the ground state rotational bands of adjacent even nuclei provided additional support for its assignment to an odd-mass nucleus in between. The charge assignments are based on the comparison of the calculated and experimental values of the y-ray energies and good agreement with an X-ray selection experiment 11,12, 1, 2) as outlined above. Category B. In this category the charge assignments are expected to be correct and are based on the same restrictions as for category A. The mass assignments have an error of + 1 amu or as specified in column 1. The mass assignments are based only on the mass determination of the present work. Category C. In this category the mass assignments are expected to have an error of + 1 amu or as specified. The atomic numbers have been assigned based on v-ray measurements but may be uncertain by _+ 1 units of charge or as specified, due to mixing with another line or other ambiguities. Category D. In this category are those transitions for which no corresponding Vray lines could be found. The mass assignments for these lines are expected to have an error of _ 1 amu or as specified and the atomic number values are those for the most probable charge s) starting from the original, non-integral mass values derived. The observations in column 7 include interpretations of certain lines, any mass or charge assignments proposed previously which differ from the present assignments, and other information of interest.

FISSION F R A G M E N T DE-EXCITATION

503

4. Discussion of results 4.1. G E N E R A L FEATURES

As 8 result of these measurements a large number of transitions has been observed in both the lower and upper energy regions. While the T-ray measurements revealed transitions predominantly in the 150 to 800 keV of T-ray energies, the electron measurements were particularly selective of low-energy transitions with electron energies from 30 to 300 keV. In fig. 7 the energies of the T-ray transitions are averaged over

1200 1000 ^ 800 I

I 400f 200t 0"

I

88

90 92 94 96 98

i

I

I

f

I

I

f

I

I

I

!

l

I

f

f

f

I

100 102 104 A 130 132 134 136 138 140 142 144 146

Fig. 7. Averaged energies of the observed ~-ray transitions as a function of mass A. The length of the horizontal bars gives the magnitude of the averaging interval.

~ .24. ~ .22,

7

~ . 20. ~ .18 _~.• 16

N=82

~ -14. ~ -12 o

]'/

u.I N'08 W

>.06. Lu 04. ,_1,

•

02"

i I

8'0

9'0

I00

Ii0

120

130

Ii0

150

160

POST NEUTRON EMISSION FRAGMENTMASS Fig. 8. The relative yield of internal conversion electrons as a function of fission-fragment mass.

504

T.A. KHAN et al.

certain mass regions and plotted as a function of mass. The gross energy tendency is consistent with what one would expect if the observed de-excitations of the primary fragments involved predominantly collective transitions. On physical grounds, it seems likely that the majority of the lines observed in the present measurements are linked with cascades from levels near the ground state since a necessary condition for the existence of high-intensity transitions is that there be a high probability of populating the same levels each time a particular fission product is formed. Such conditions are unlikely to exist at high excitation energies. The proposed interpretations of table 1 show that the more intense ~-ray lines belong to transitions in the ground state bands of the even nuclei. In the electron measurements the situation is slightly different since the observed transitions are selective of low energies. In regions away from nuclear deformation the level spacing near the ground state in the even nuclei is not low enough to give rise to highly converted transitions. For this reason a large number of the observed transitions, particularly away from the regions of deformation, arise from the odd or odd-mass nuclei. However, near regions of nuclear deformation, where the level spacing in the ground state bands of the even nuclei is low enough, the corresponding lines stand out clearly in the electron spectra. A further observation with regard to fig. 7 is that if the average energy of ~-rays may be regarded as an indication of nuclear stiffness over the averaged mass regions, then certain regions of hard nuclei e.g. around masses 88-90 and masses 130--132 and o f soft nuclei e.g. near mass 100 and beyond mass 142, are clearly apparent. Very similar features may be seen in fig. 8 which shows the relative yield of electrons per fragment. The curve was obtained by summing the events in each mass-sorted electron spectrum over energy and dividing by the respective mass yields as obtained from the two-parameter experiment described in subsect. 2.2. The error bars indicate the statistical errors in the yield curve. The gross features of the yield as a function of mass may be understood in terms of the nuclear detormations beyond mass 144, of the postulated 17) deformations of neutron-rich nuclei near mass 107, and the closed-shell properties of nuclei near mass 132. In the regions of deformation, with low-level spacing in the ground state rotational band one would expect low-energy transitions which are highly converted and therefore high electron yields, as seen in the yield curve. The reverse would apply in the closed-shell regions. Moreover, there appears to be evidence of softness to deformation also around mass 100, in agreement with the low average ~-ray energies observed in this mass region. This is of particular interest in view of the calculations of Arseniev e t al. 18) which predict deformation in this region. 4.2. TRANSITIONS IN THE EVEN NUCLEI A general feature of both the electron and ~-ray spectra was the existence of certain very prominent lines which were often an order of magnitude stronger than the neighbouring lines. In most cases they could be assigned to the ground state bands of even

FISSION F R A G M E N T DE-EXCITATION

505

n u c l e i . M a n y o f t h e s e t r a n s i t i o n s h a v e a l s o b e e n o b s e r v e d in t h e 2 s Z C f ( s f ) e x p e r i m e n t s [refs. 1 - 3 ) ] . A p a r t f r o m t h e i n d i c a t i o n s f r o m t h e i r m a s s a n d c h a r g e a s s i g n m e n t s , there are several other features which confirm their assignment to the ground state b a n d s o f t h e e v e n nuclei. T h u s f o r e x a m p l e , t h e r e l a t i v e i n t e n s i t i e s o f t h o s e t r a n s i t i o n s TAnLE 3 Ground state band transitions in the doubly even fission products of 23s U (n, f) Isotope

Interpretation

~,-ray energy (keV)

9°Kr 9ZKr ~4Sr 96Sr 9SSr 9llZr l°°Zr l°°Zr lOZZr l°ZZr l°2Mo 1°4Mo 1°4Mo

(2 + --~ 0 +) (2 + -->0 +) (2 + "-~ 0 ÷) (2 + ~ 0 +) (2 + ~ 0 +) 2 + --~0 + 2 + ---~0+ 4 + --~ 2 + 2÷ ~ 0+ 4 + --* 2 + 2 ÷ "-~0 + 2 + --~0 + 4 + ---~2+

7064-4 956-t-5 8344-4 8134-4 193-4-2 1224-4-5 212+2 351 + 3

lO6Mo

2 + -~0 +

13°Sn laZTe la4Te laSXe 14°Xe l'~2Ba X44Ba l'~4Ba l'*eBa ~46Ba 1'*6Ce 14aCe 14aCe

(2 + -~ 0 +) 2 + -+ 0 + 2 + --* 0 + 2 + --~0 + 2 + --~0 + 2+ ~0 + 2+ -~0 + 4+ ~2 + 2 + --~0 + 4+ ~ 2+ 2 + --> 0 + 2 + --.0 + 4 + -~2 +

1 ~OCe

2 + _+ 0 +

l~OCe

4 + .-~2 +

3254-3 2964-2 1914-2 3664-3 12224-5 9654-5 1278+5 5854-4 3734-3 357-t-3 1984-2 3304-3 1834-2

294=[=2

Relative intensity Experimental exp. per predicted K-line L-line fission and including energy energy 16 mm correction (keV) (keV) flight path for int. conversion 70 32 61 80 13 29 37

4-23 4-11 4-20 4-27 -4- 4.5 4,15 4-13

8.8+ 2.9 12 4" 4

55 28 59 25 8 45 52

12 12

12.34- 6 19.54.10 34 117 106 4-60 70 -4-35 36.54-12 36 4-12

16 16 82 43 49 43 38

12 4. 4

7

K/L ratio

177

191

6

suggest E2 transitions

195 334 133 309 275 173

210

7

suggest E2transitions

150

6

suggest E2 transitions

188

5.6 consistent with E2

152

170

5

356 195

5.2 consistent with E2 3.7 consistent with E2

176

2.7 consistent with E2

252 153 290 91

4.0 consistent with E2 2.8 consistent with E2

34o 322 162 293 144 296 218 118 255 58 170

consistent with E2

1.8 consistent withE2

w h i c h w e r e a s s i g n e d a s 2 + ~ 0 +, a f t e r t h e y h a d b e e n c o r r e c t e d f o r i n t e r n a l c o n v e r s i o n , w e r e f o u n d t o b e p r o p o r t i o n a l t o t h e i n d e p e n d e n t yields o f t h e i s o t o p e s t o w h i c h t h e t r a n s i t i o n s w e r e a s s i g n e d . T h i s is t o b e e x p e c t e d s i n c e it is k n o w n t h a t d e - e x c i t a t i o n i n d o u b l y e v e n f r a g m e n t s , s t a r t i n g f r o m h i g h a n g u l a r m o m e n t u m , is c h a n n e l e d through the 2 + ~ 0 + transitions and therefore the intensity of these transitions should b e s i m i l a r t o t h e i s o t o p i c yields o f t h e f r a g m e n t s c o n c e r n e d . R e c e n t l y a n a n a l y s i s h a s

506

T . A . K H A N e t al.

been performed by Wilhelmy et al. t g) based on the statistical nature of the deexcitation of the fission fragments and the removal of their primary spin which confirms that 95-98 9/00of the isotopic yield will be represented as 2 + ~ 0 + ground state band transitions. Confirmation of the assignments of a number of the transitions was N=50 o !

°----~Kr

ne2ooo

tO Z 14.1

isotopes

Sr °. . . . . Zr a--~-----Mo +. . . . . . . . . Ru x

50 |

isotopes isotopes isotopes isotopes

1500

~N=58 1000

°~ 500 !2÷)CRIT Sr 0

82

8'6

9'0

9'4

Zr

Ru

Mo

1;o MASS NUMBER A

Pig. 9. The systematic variation of the first 2 + excited states in the doubly even isotopes of Kr, Sr, Zr, Mo and Ru. The unbroken line is a plot of (E2+)c,it. in this region (see subsect. 4.3).

also provided by the K / L ratios observed, which were consistent with E2 transitions. Table 3 lists the electron and 7-ray lines assigned to the ground state bands of the doubly even isotopes. The measured K / L ratios and relative intensities of the 7-ray lines are also given in the table. The "predicted intensities" given in column 5 are the calculated independent yields s) corrected for converted transitions 2 o). The units are arbitrary since it is the relative variation of the experimental and predicted intensities which is of interest. The discrepancy between the experimental and predicted intensities for 134Te(2+ ~ 0 +) transitions is due to the fact that an appreciable feeding of the 1278 keV level proceeds via a 162 nsec isomeric state 9). Many of the transitions listed in table 3 have been observed previously in the 2 52Cf(sf) experiments of Cheifetz et al. 1, 2). The present 235U(n, f) measurements

FISSION F R A G M E N T DE-EXCITATION

507

support their proposed assignments in all cases and the observed K/L ratios provide additional confirmation. 4.3. SPECIAL FEATURES

An interesting aspect of the present results is their relation to the deformed regions in the light- and heavy-fragment groups. Of particular interest is the region of transition from undeformed to deformed nuclei. The transition from spherical to deformed behaviour is characterised by a rapid drop in the energy of the first 2 + level and an increase in the E4+/E2÷ energy ratio. As this ratio approaches 3.33, the value for a rigid rotator, the energy of the first 2 + state changes less and less from isotope to isotope. Although it is not possible to determine the existence of static deformations from observed energy levels alone, studies of such systematics are good indicators of nuclear softness. The first 2 + levels for the nuclei in the region of postulated deformations in the light fragments are shown in fig. 9, which is based on present results and previous determinations 21). Also plotted are the values of (E2 ÷)crit. ( = 13 h2/Jrigid) for each mass value for purposes of comparison. This quantity is proposed as an approximate criterion of deformation by Alder et al. 22). According to this criterion nuclei having E2 + > (E2 +)¢rit. are to be assumed as spherical and those with E 2 + < ( E 2 +)erR. as deformed. If strong changes in the energy of the first 2 + levels may be regarded as indicative of transition from the vibrational to rotational modes and of a strong change in nuclear softness, then it appears that this transition occurs between neutron numbers 58-60 for the light fragments. This conclusion is also supported by the (E2+)¢rit. criterion. Furthermore, although the transition in nuclear behaviour is analogous to that observed in the heavy-fragment region 2) between neutron numbers 88 and 90, in the light fragments it is far more drastic. The most striking case is that of the zirconium isotopes (Z = 40) first observed by Cheifetz et al. 1). The energy of the first 2 + level changes from 1223 keV for 9aZr to 213 keV for l°°Zr. In the neighbouring Mo(Z = 42) and Sr(Z = 38) isotopes the changes in the first 2 + level energies between N = 58 and 60 are much less abrupt and in R u ( Z = 44) the transition to rotational behaviour is relatively smooth and gradual. Sheline et al. 23) have recently suggested that the drastic changes in nuclear characteristics in the Zr and Mo isotopes may be due to a highly deformed secondary minimum (associated with the deformed shell structure at Z = 40) which moves down in energy with increasing N and becomes the ground state minimum at N = 60. Present results suggest that the behaviour of the Sr isotopes in the transition region may be similarly interpreted. The theoretical calculations 23) however, have so far been unsuccessful in producing a second minimum for nuclei in the vicinity of i°°Zr. Two transitions of particular interest are the 2 + ~ 0 + transitions in 96St and 9aSr. The two isotopes have a very low yield in 252Cf(sf), however, in 23SU(n, f) they are produced in more significant quantities. The transitions are of importance for several

508

T.A. KHAN et aL

reasons. The change from 96Sr to 9SSr is across the transition region (N = 58-60) and it is interesting to see how the first 2 + levels of these isotopes fit into the systematics of fig. 9. Moreover the nuclei lie at the boundary of the deformed region and help to m a p the borderlines of the regions of deformation. Lastly, the calculations of Arseniev et al. as) predict that the strongest deformations should be in the heavier isotopes of strontium (98-102) and it is of interest to compare the results with their predictions. TABLE 4 D e f o r m a t i o n indicators for the transition nuclei in the light-fragment group

Nucleus Neutron number 9aSr ~°°Zr 1O2Mo I°4Ru I ~aGd

60 60 60 60

E2+ (keV) 193 213 296 358 ~) 79.5 a)

(E2+)¢,,. (keV)

E(2+)¢,lt.--E2+ (keV)

422 408 395 383 192

229 195 99 25 112

Z 0.92 0.80 0.56 0.45 1.0

fl' 0.30 0.28 0.23 0.21 0.24

fl(theor.) b) fl(exp.)¢) --0.3l --0.29 (--0.28) d) (--0.26) d)

0.364 0.348 0.24

~) Ref. 21). b) Ret: Is). c) Ref. 1). a) Deduced from fig. 4 of ref. ~s).

In the present electron data, three different lines have been assigned to mass 9 8 _ 1 amu, their electron energies being 157, 177 and 184 keV. The fact that corresponding lines have not been observed in ZSZCf(sf) experiments suggests that they originate from Sr rather than from Y or Zr which have a higher yield for 252Cf(sf) ' The best candidate for the assignment as the 2 + ~ 0 + line in 9SSr out of these appears to be the 177 keV electron line. This is so because a corresponding ?-ray line at 193 keV and mass 9 8 + 1 has also been observed in the ~-ray experiment of the present work, whose energy is in agreement with the assignment of the electron line to Sr (see table 2). Moreover, the relative intensity of the corresponding ?-ray is compatible with its being the 2 + ~ 0 + line in 9SSr as may be seen in table 3. In accordance with current theory it would be preferable t o characterize a nucleus on the basis of the V M I [ref. 14)] model but for this a knowledge of at least two experimentally determined parameters (e.g. E 2 + and E4+) is necessary. In the case of 985r the only information available at present is the energy of the first 2 + level in the ground state band, if the assignment proposed for the 193 keV 7-ray is valid. Nevertheless, considerable understanding of the behaviour of a nucleus may be obtained by means of a number of indicators based on the energy of the first 2 + level. It is therefore of interest to compare such indicators for neighbouring transition nuclei (i.e. nuclei with N = 60) in the light-fragment group. One such indicator of deformation is the parameter g[ = (79.51/E2 +)(158/A) t] which gives an approximate mass independent comparison of the energies of the first 2 + states using the deformed nucleus l~8Gd as a comparison. Another useful comparison might be to obtain a

FISSION FRAGMENT DE-EXCITATION

509

relative value of the deformation (if) for the neighbouring transition nuclei 9aSr, l°°Zr, t°2Mo, l°4Ru, using the centrifugal stretching model of Diamond et al. 25) in which the moment of inertia J is assumed to be equal to 3Bfl 2. A final indicator might be the energy difference between E2÷ and (E2+)crit. mentioned above. The values of these indicators for the four transition nuclei as well as t SaGd are given in table 4. The fl' values were arrived at by calculating the moment of inertia J for each nucleus from the E 2 ÷ value and then obtaining the value of fl' from the curve of j / ( 2 A M R 2) versus fl of Diamond et al. Also given in table 4 are theoretical values of the deformation parameter fl from the calculations of Arseniev et al. is), whose reported eo deformation has been converted to fl by the relation fl ~ e0/0.95. The negative sign in the theoretical values implies oblate deformations. The last column of table 4 shows the experimental values of fl as derived from the B(E2) data for those nuclei whose B(E2) values are available 1). An examination of table 4 shows that the values of the deformation indicators for the nuclei in the postulated region of deformation in the light fragments are quite comparable with the values for lSaGd which is known to be a good example of a deformed nucleus in the rare-earth region. Furthermore, all three indicators suggest that of the four transition nuclei (N - 60) 9aSr has the strongest tendency towards deformation, the tendency decreasing monotonically in the N = 60 nuclei as one moves towards 10,Ru" This is in good agreement with the theoretical predictions of Arseniev et al. Moreover the fl' values derived in accordance with the procedure outlined above are very similar in magnitude and, more important, in variation to the calculated values for fl of Arseniev et al. However, the actual values of fl as obtained from the B(E2) values are somewhat higher in magnitude. A final point of interest is the lack of transitions from the isotopes of technetium in the present work in comparison with the 2S2Cf(sf) data. This is particularly significant in the electron data which cover the low-energy transitions. The lack of transitions from Tc isotopes may be connected with nuclear shell effects in fission. Thus, if there is a tendency to conserve 50 protons in the heavy fragments, then the primary yields of indium isotopes (Z = 49) and of their complementary fragments should be low. In 2aSU(n, f) these complementary fragments consist of the technetium isotopes (Z = 43). 5. Conclusion

The experiments described have demonstrated that despite additional experimental difficulties the multiparameter measurements of the prompt radiations from primary fragments can be successfully extended to neutron-induced fission. This makes it possible to investigate the mass region where the yield in spontaneous fission is low. It appears especially promising to use 23~U in such investigations since the mass regions covered in 23aU(n, f) partly overlap those reached in (t, p) reactions. Thus a large and continuous region of neutron-rich nuclei in the nucleide chart is accessible for investigations.

510

T.A. KHAN et al.

Moreover, as a result of the present work and previous investigations it is now possible to assign a number of transitions to specific isotopes although in other cases some ambiguities in mass or charge assignments remain. The ground state bands of many of the doubly even fragments have been constructed 1, 2). The more complex but important decay schemes of the odd and odd-mass nuclei remain to be tackled. This is a difficult task since the structure is complicated and the number of nuclei is large. However, a start has been made by the assignment of a large number of lines and it remains to perform y-y, y-e and other coincidence studies in depth. The authors would like to express their appreciation to Dr. John Wood, Dr. F. Dickmann and several colleagues from the Institut fiir Angewandte Kernphysik for stimulating discussions. We are also thankful to Miss I. Piper for experimental assistance. One of the authors (T.A.K.) wishes to express his thanks to the Gesellschaft fiir Kernforschung mbH, Karlsruhe and the Pakistan Atomic Energy Commission through whose collaboration his contribution to this work was made possible.

Appendix METHOD OF CALCULATION OF THE FISSION FRAGMENT MASSES It seems worthwhile to outline briefly the mass assignment procedure used here which is based upon some simplifications applied to the usual method. The simplified procedure saves computer time and the excellent agreement of the results with those from 252Cf [refs. t, 2)], where no simplifications were applied, has proved its feasibility. The energies of the fission fragments in detectors 1 and 2 were calculated from the channel numbers xi, using the equations for the mass-dependent pulse-height calibration: Ei

=

(ai+a;mi)xi+bi+b;mi,

i = 1, 2,

(A.1)

where m~ is the post-neutron emission mass. The calibration constants a~, a'~, b~, b~, were deduced from the fragment energy single spectra in the well-known manner 26). According to ref. 26) provisional masses p~ were defined on the basis of the following relationships: piE1 = #2E2,

(A.2)

At,

(A.3)

]A 1 "{-,/,/2 =

where ,'If is the mass of the fissioning nucleus. In the event by event calculation random numbers between - 0 . 5 and +0.5 were added to each pulse height xl in order to smoothen the pattern of the A D C channels. In addition in eq. (A.1) mi was replaced by/z~. This introduces only a small error of about 0.2 MeV due to the small coefficients of the mass-dependent terms. Using eqs. (A.1)-(A.3) the provisional

FISSION F R A G M E N T DE-EXCITATION

511

mass #1 and #2 were calculated f r o m the relations #1 = AfE2/(E1 + E 2 ) ,

(A.4)

~2 = A f - - ~ l .

Instead of applying the neutron correction to each single event, the data were sorted according to the provisional mass p yielding 48 ?-ray spectra. The correlation between the provisional masses and the final masses ml and m 2 was then calculated using the equations 27)

Af] ml = m*-vl,

~I = vl mI

m* +

v2 ,

(A.6)

(A.7)

/'B2

= A,,

(A.8)

where m* and m* are the pre-neutron-emission masses and v1 and v2 the mean number of prompt neutrons from fragments 1 and 2 respectively. These were taken from ref.2s) for the ?-ray work and from ref. 29) for the later electron work. In this procedure the variation of v with the kinetic energy of the fragments was neglected. This seemed to be justified by the observation that in 235U(n, f) the mean number of prompt neutrons varies by less than +0.5 amu for total kinetic energies within the double variance around the average total kinetic energy 26, 2s). This deviation is small compared to the typical mass resolution in this experiment of about 5 amu F W H M . References 1) E. Cheifetz, R. C. Jared, S. G. Thompson and J. B. Wilhelmy, Phys. Rev. Lett. 25 (1970) 38 2) J. B. Wilhelmy, S. G. Thompson, R. C. Jared and E. Cheifetz, Phys. Rev. Lett. 25 (1970) 1122 3) R. L. Watson, J. B. Wilhelmy, R. C. Jared, C. Rugge, H. R. Bowman, S. G. Thompson and J. O. Rasmussen, Nucl. Phys. A141 (1970) 449 4) F. Horsch and W. Michaelis, Proc. 2nd Symp. on the physics and chemistry of fission (IAEA, Vienna, 1969) p. 527 5) F. Horsch, Proc. Conf. on the properties of nuclei far from the region of fl-stability (CERN, Leysin, Switzerland, 1970) vol. 2, p. 917 6) T. A. Khan, D. Hofmann and F. Horsch, Proc. European Conf. on nuclear physics, Aix-enProvence, France, 1972, J. de Phys. 2 (1972) 30 7) F. Horsch and I. Piper, Kernforschungszentrum Karlsruhe report K F K 1003 (1969) 8) A. C. Wahl, A. E. Norris, R. A. Rouse and J. C. Williams, Proc. 2nd Symp. on the physics and chemistry of fission (IAEA, Vienna, 1969) p. 813, and private communication 9) W. John, F. W. Guy and J. J. Wesolowski, Phys. Rev. C2 (1970) 1451 10) A. G. Blair, J. G. Beery and E. R. Flynn, Phys. Rev. Lett. 22 (1969) 470 11) F. F. Hopkins, G. W. Phillips, J. R. White, C. F. Moore and P. Richard, Phys. Rev. CA (1971) 1927 12) F. F. Hopkins, J. R. White, G. W. Philips, C. F. Moore and P. Richard, Phys. Rev. C5 (1972) 1015

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