fission yields at different fission-product kinetic energies for thermal-neutron-induced fission of...

Nuclear Physics A430 (1984) 21-60

@ North-Holland Publishing Company

FISSION YIELDS AT DIFFERENT FISSION-PRODUCT KINETIC

ENERGIES FOR THERMAL-NEUTRON-INDUCED FISSION OF 239Puf

C. SCHMITT’, A. GUESSOUS’, J.P. BOCQUET’, H.-G. CLERC’,

R. BRISSOT-‘, D. ENGELHARD?, H.R. FAUST’, F. GBNNENWEIN’, M. MUTTERER’, H. NIFENECKER’, J. PANNICKE’,

CH. RISTORI’ and J.P. THEOBALD’

’ Institutfiir Kernphysik, Technische Hochschule Darmstadt, 6100 Darmstadt, Federal Republic of Germany ’ Centre d' Etudes NuclPaires-DRF/ CPN-85X, 38041 Grenoble Cedex, France

3 Institut Laue Langevin, 156X, 38042 Grenoble Cedex, France 4 Technische Universitiit Karlsruhe, WOO Karlsruhe, Federal Republic of Germany

Received 26 March 1984

(Revised 29 May 1984)

Abstract: At the recoil spectrometer “Lohengrin” of the Institut Laue-Langevin in Grenoble, the yields

of the light fission products from the thermal-neutron-induced fission of 239Pu were measured as

a function of A, 2, the kinetic energy E and the ionic charge states 9. The nuclear charge and

mass distributions summed over all ionic charge states were determined for different light fission-

product kinetic energies between 93 and 112 MeV. The proton odd-even effect which was measured

to be (11.6 f. 0.6)% causes considerable fine structure in the yields. The average kinetic energy of even-Z elements in the light fission-product group is 0.3 f 0.1 MeV larger than for odd-Z elements.

The neutron odd-even effect is (6.5 f 0.7) %. The comparison with previously ‘published data ‘) for

thermal-neutron-induced fission of 23sU reveals a correlation between the proton odd-even effect

in the yield and in the kinetic energy of the elements. The dependence of the proton odd-even

effect on the fragmentation is very similar for 235U and 239Pu when it is considered as a function

of the nuclear charge of the heavy fission products. The isobaric variances a$ for thermal-neutron

fission of 235U and 239Pu coincide at all kinetic energies if the influence of the proton odd-even

effect is averaged out. This supports the hypothesis that the magnitude of a$ is determined only

by quantum-mechanical zero-point fluctuations. The influence of the spherical shells Z = 50 and N = 82 on the fragmentation is discussed.

NUCLEAR FISSION 239Pu(n, f), E = thermal; measured mass and nuclear charge distribu-

E tions of light fission products at different kinetic energies: deduced fractional independent

yields, odd-even effects, average kinetic energies of the elements and isobars. 1

1. Introduction

In nuclear fission a compact mononuclear system transforms into a dinuclear system. In thermal-neutron-induced fission, this large-scale rearrangement of nuclear matter starts from a system with an excitation energy below the proton pairing energy at the saddle point, and nuclear shell and pairing effects play an important role. At present we do not have a comprehensive theory which describes this

’ This work forms part of the Ph.D. thesis of C. Schmitt and A. Guessous.

21

22 C. Schmitt et al. 1 Fission yields

interesting process in any detail. However, the distribution of nuclear mass and charge as well as the kinetic energy of fragments belong to the most important clues. In particular the difference between the yields of fission products with even and with odd Z-values, which was observed for the first time by Wahl et al. ‘) for the system 235U(n,,,, f), is connected to the pair-breaking probability. The difference between the average kinetic energy of the elements with even and odd Z, which was observed in the spontaneous fission of 252Cf [ref. 3)], and in thermal-neutron fission of 235U [ref. “)I and 22gTh [ref. 5)], may indicate the conversion of collective kinetic energy into single-particle excitation energy. Thus both the proton odd-even effects in the yield and in the kinetic energy are connected to the viscosity of the flow of nuclear matter in low-energy fission.

Up to now, the fragmentation for 23sU(n,h, f) has been known in much more detail than that for any other fissioning system. The fission-product yields for 235U(n,i,, f) were determined as a function of nuclear mass, charge and kinetic energy lV4) at the recoil spectrometer “Lohengrin” “) of the ILL in Grenoble. By comparison, the fission-product yield data which were available for thermal-neutron fission of 23gEu are limited. Energy-dependent charge yields have not been measured previously. Energy-integrated yields as determined by radiochemical methods were reported ‘) for a total number of about 50 nuclides, about half of which belong to the light fission-product group. From an analysis of radiochemical yield data for 23gEu(n,,,, f), Amiel et al. *) found a proton odd-even effect of ( 11 f 9)%. Similarly, from fission- product yields for isotopes of krypton, xenon, bromine and iodine as obtained by on-line mass separation ‘), a proton odd-even effect of only (3.4 f 5.0)% was deduced for 239Pu(nth, f).

In the present work, the yields for more than 100 nuclides in the light fission- product group of 239Pu(n,,,, f) were measured as a function of the kinetic energy at the recoil spectrometer “Lohengrin”. The precision of the present data is similar to that for 235U(n,,,, f) [refs. ‘*4)], and a detailed comparison of the two systems will be possible. It is hoped that features in the fragmentation, which are specific for the particular system under study, may be distinguished from those features which reflect a more general trend in low-energy fission.

2. Experiment

2.1. EXPERIMENTAL SET-UP

The measurements were performed at the recoil mass spectrometer “Lohen- grin” lo). Fig. 1 shows a schematic view of the experimental set-up. In order to obtain a sufficiently good mass resolution of A/AA = 400 (full-width & maximum), the size of the source was limited to 40 x 3 mm*. The exit slit of “Lohengrin” was chosen to be 35 x 3 mm* for the mass-yield measurements, and 20 x 3 mm* for the measurements of the nuclear charge yields. The sources consisted of about 50 pg/ cm2

C. Schmitt et al. / Fission yields 23

SOURCE

,x

Fig. 1. Schematic view of the experimental set-up. The source, the horizontal magnetic deflector, the

vertical electric deflector and the exit slit of the recoil mass spectrometer “Lohengrin” are indicated. The ionization chamber and the removable absorber are mounted behind the exit slit.

of 23yPu02 on a titanium backing. In order to reduce the sputtering of 239Pu from the source, the 239Pu02 layer was covered by 125 f 50 pg/cm* of tantalum.

The mass yields at fixed ionic charge states q were determined by the method described previously I’): “Lohengrin” separates the fission products according to their A/q and E/q values, with A being the mass number, and E the kinetic energy of the fission products. The measurements were performed at a constant high voltage setting at the condenser (corresponding to fixed E/q values) by scanning the magnetic field with a constant velocity. The different masses contributing to one A/q line and the masses of different, but not well resolved, A/q lines could be separated by their different kinetic energies (related to their q-values) with a high-resolution ionization chamber 12). The nuclear charge distribution for a given mass number A and ionic charge state q was obtained by measuring the residual energy behind a homogeneous parylene C absorber (8 foils with 0.1 mg/cm2 each) which was mounted in front of the ionization chamber. The nuclear charge resolution of this set-up [Z/AZ = 58 for 2 = 39, see Quade et al. “)] is considerably improved as compared to the resolution of Z/AZ = 45 obtained with our previous set-up used for the investigation of 235U(nt,,, f) [refs. ‘*‘3)]. This was of particular importance for

separating the higher nuclear charges above Z = 42 in the light fission-product group of 239Pu(n,h, f).

2.2. CHOICE OF THE KINETIC ENERGIES, MASS NUMBERS AND IONIC CHARGE

STATES

Mass yields for the mass numbers 80 s A G 113 were determined at seven fission- product kinetic energies between 93.2 MeV and 112 MeV for ionic charge states in the interval 16 s q s 27. Isobaric nuclear charge distributions were measured for the mass numbers 86 s A s 109 at five kinetic energies between 95.5 MeV and 109.9 MeV

24 C. Schmitt et al. / Fission yields

for selected ionic charge states. A combination of the measured data allowed the mass yields and the nuclear charge yields summed over the ionic charge distributions to be determined.

3. Data analysis and results

3.1. PROPERTIES OF THE 239Pu SOURCE AND THE ENERGY CALIBRATION

For the fission fragment source of 50 pg/cm’ of 239Pu, the thermal neutron flux of 5 X 1014 cm-* - s-’ at the position of the source results in 5 x 10” fission events per cm* per second. On the basis of the large capture cross section for thermal neutrons (about 1000 b), the calculated reduction of the source strength amounts to 17% in 100 hours. The measured reduction of the source strength, however, is found to be appreciably larger, see fig. 2a. This may be due to sputtering processes in the source caused by the very high fission rate. In order to determine absolute mass yields as a function of the fission-product kinetic energy, the change of the source strength with time as well as the time-dependent kinetic energy loss in the

0 100 200

Time/h

Fig. 2. Change of source properties with time. (a) Counting rate at different kinetic energies in the

spectrometer as a function of the time after installation of the source. The counting rates are normalized

to one at the time 190 h after source installation. Symbols: measured counting rates; lines: calculated

from folding the primary distribution with the source function I(AE, t). (b) Most probable fission-product

kinetic energy E, in the spectrometer as a function of time. Vertical bars: measured values; dashed line: calculated from folding the primary energy distribution with the source function I(AE, t).


source have to be taken into account. For this purpose, a measurement of the counting rate for A/q = 4 at a spectrometer high voltage of 460 kV was repeated daily during the 9 days of absolute mass yield measurements. The different combinations of A and q contributing to A/q =4 allowed to follow the change of the counting rates at kinetic energies between 85 and 114 MeV in the spectrometer (i.e. after traversing the source). Fig. 2a shows examples of these “burn-up” measurements for three selected kinetic energies.

In addition to these measurements which were performed at a fixed high voltage, the energy distribution of the fission products with A/q = 4 was determined three times during the nine day measuring period. For this purpose the spectrometer high voltage was varied between 440 kV and 520 kV, corresponding to a change in the kinetic energy of about 15 MeV. This allowed a determination of the most probable kinetic energy as a function of time for the A/q combinations 84/21, 88/22 and 92/23. The most probable kinetic energies for these three masses differ by less than 1 MeV from each other; their time dependence is shown in fig. 2b.

Fig. 2a shows that the “burn-up” at low and high kinetic energies is quite different. This may be explained by the change of the kinetic energy distribution with time (shift to higher kinetic energies, see fig. 2b), and by the decrease of the source strength. The energy distribution behind the source, summed over all light fission- product masses, may be described by folding the primary energy distribution with the time-dependent intensity distribution Z(AE, t) of fission products as a function of the kinetic energy loss AE in the source. The term primary energy distribution is used here for the post-neutron emission energy distribution of the fission products before traversing the source; it is taken to be of gaussian shape with an average value of 102 MeV and a width parameter u E of 5.8 MeV [ref. ‘“)I. The intensity distribution Z(AE, t) reflects the distribution of fissile material in the source layer, in the source backing, and in the covering tantalum layer. It is assumed to be a S-function at the time of the installation of the source in the reactor (t = 0); with increasing irradiation time, the energy-loss distribution is smeared out due to diffusion and sputtering processes in the source. The function Z(AE, t) was chosen in such a way that it reproduces the “burn-up” measurements shown in fig. 2a. The calculated “burn-up” curves were used to perform an energy-dependent normalization of all measured counting rates to the time at the end of the measurements (190 h after installation of the source).

Fig. 2b shows that the function Z(AE, t), which was chosen to fit the “burn-up” measurements only, also provides a satisfactory description of the most probable kinetic energy as a function of time. Another important check of our description of the energy loss in the source is provided by the energy distribution of the light fission products (summed over 85 s A s 108) behind the source at a fixed time after installing the source. Fig. 3a shows that the agreement between the measured and calculated energy distribution is good. An exception are the two points at very high kinetic energy, which are found experimentally to be below the calculated curve.


80 90 100 110 120 80 90 100 110 120

E spectrometer/MeV E/MeV

Fig. 3. (a) Energy distribution of the fission products summed over the masses in the light group (85 G As 108). Abscissa: kinetic energy in the spectrometer EEpcctrometer (behind the source), 190 h after installation of the 239Pu source in the reactor; furi circles: measured values; line: calculated by folding the primary energy distribution with the distribution of energy losses in the source. (b) Calculated primary intensity distributions which contribute to the yield at fixed energies in the spectrometer (the values for the spectrometer energies are the abscissa values of the measured points in (a)). The arrows mark the

adopted average primary energies (see also table 1).

This deviation is caused most probably by our assumption of a gaussian shape for the primary energy distribution: due to Q-value limitations at very high kinetic energies, the primary energy distribution has to decrease faster with increasing kinetic energy than a gaussian.

Fig. 3b shows the primary intensity distributions as a function of the primary kinetic energy, which according to the calculation contribute to each one of the measured points shown in fig. 3a. The average primary energies corresponding to the measured points were obtained as the centers of gravity of the intensity distributions of fig. 3b. Fig. 3b shows that in particular the measurements at low kinetic energies represent averages over a relatively large primary energy interval. In order to account for the shortcomings of the calculation for the highest kinetic energies, the calculated average primary energy of 110.7 MeV was reduced by 0.8 MeV, and that of 112.9 MeV by 0.9 MeV. The finally adopted average primary energies are listed in table 1 together with the corresponding energies in the spectrometer.

3.2. IONIC CHARGE DISTRIBUTIONS OF THE ISOBARS Y(q)!,,,

Ionic charge distributions are shown in fig. 4 for the examples A=98 and 99. Since the ionic charge distribution was not measured in the tails of the distribution, the missing values were estimated by extrapolating the low-q and high-q sides of the distribution. For this purpose one gaussian was fitted to the lowest four measured


TABLE 1

Average primary kinetic energies E and the corresponding kinetic energies in the spectrometer E rpccrr,,merer (i.e. after traversing the source) according to the calculations (see subsect. 3.1)

E rpccrrometer [Meal E [M-W

83.0 93.2 * 1.5 88.0 95.5 * 1.0

93.0 98.4kO.5

98.0 101.8*0.5

103.0 105.8 ho.3 108.6 109.9 f 0.5

111.0 112.0*0.5

values, and another gaussian was fitted to the highest four measured values. As can be seen, the distribution for A = 99 extends to larger q-values than that for A = 98.

This is due to the internal electron conversion process, which appears to be much stronger for A = 99 than for A = 98. The average values q and the variance m’, were calculated as the first and second moments, respectively, of these distributions. The

Fig. 4. Examples

10 20 30 9

of ionic charge distributions for A = 98 and A = 99 at ESpeetrOmetcr measured values; open circles: extrapolated values.

= 98 MeV. Full circles :

results are shown in figs. 5 and 6. Both q and a4 show a fine structure which is similar at the three different kinetic energies. This fine structure is due to the internal electron conversion process which depends on the details of the nuclear structure of each nuclide and consequently influences different isobars to a different extent. A detailed discussion of this effect in the ionic charge distribution of the fission products from 235U(n,r,, f) was given previously 15). Those isobars which showed a

C. Schmitt et al. J Fission yields

I ’ I ’ I 1 I ‘ 25 _ 109.9 MeV

20 -

I' I I I I I ' 11 I ’ 101.8 MeV

'O- 20

$yyy@yy;

- 955 MeV

20 -

-ppyy@,;

80 90 100 110

A Fig. 5. Average ionic charge state (5 of the isobaric ionic charge state distributions as a function of the

fission-product mass number A, for three different kinetic energies.

4-"I""L 109.9 MeV

2 -'

I I I I,, I- n"""

101.8 MeV

I I I I I I I I

4-"""" 95.5 MeV

2-

I I I I,,,,

80 90 100 110

A Fig. 6. Width parameter o4 (square root of the second moment) of the ionic charge state distributions

as a function of the mass number A, for three different kinetic energies.


particularly strong influence of internal conversion in the fission of 236U(A = 8689,

99) are seen to have above-average values of 4 and a4 also for the z40pU case, see figs. 5 and 6. More details on the nuclides (as specified by their mass number A

and their nuclear charge 2) which show the influence of internal electron conversion are given in subsect. 3.7.2.

For the procedure to determine nuclide yields Y( A, Z)l E from the yields measured at a few selected ionic charge states q only, which will be described in subsect. 3.7, it is necessary to know the dependence of q and crq on the nuclear charge Z in the “regular” case, where the influence of the internal conversion process is small and may be neglected. For this purpose the mass numbers A = 85, 87, 88,91,93 and 95 were selected, where the influence of the internal conversion seems to be weak. The average nuclear charge 2 of these isobars at each given kinetic energy was obtained from a preliminary analysis of the nuclear charge yields. The resulting q/z and a4 values are shown in figs. 7 and 8, respectively. It can be seen in fig. 7 that the Q/z values from ref. 15) for 236U are distinctly larger than the present values for 240Pu. This may be due to the fact that the 239Pu sources were covered by 150 pg/cm* of tantalum, while the 235U sources were uncovered. The formula of Nicolaev and Dmitriev 16) (see caption to fig. 7) predicts even larger q/z values. In order to empirically describe the relationship between q/z and the reduced velocity u, [ref. ‘“)I (for the definition of u, see caption to fig. 7), a straight line was fitted to the data:

q/z = 0.548u,+O.O88 .

The width parameter oq seems to be almost independent of Z and can be represented by its average value (see fig. 8):

(a,)=2.31 kO.15.

Nikolaev ,-* ‘.:.I

0.7 0.8 0.9

v ‘VAV, z o.45 1 r

Fig. 7. Relative value of the average ionic charge q/z of selected isobars (A = 85, 87, 88, 91, 93, 95)

with average nuclear charge 2 as a function of the reduced velocity u, = u/( L+.?‘~~), with u, = 0.36 cm/ns.

Dashed curve: estimation according to the expression of Nikolaev and Dmitriev 16), g/z= (1 +,;l/o.6)-06; d otted cuwe: experimental result from 235U(n,,,, f) from ref. 15); solid curve: linear fit

through the data points for 239Pu(n,,,, f).


Cl I I I I 1 I-I 34 36 38 40

z

Fig. 8. The width parameter o4 (square root of the second moment) of the ionic charge distributions of selected isobars (A = 85,87, 88,91,93,95) as a function of the average nuclear charge .?. The solid line

represents the average value.

3.3. MASS DISTRIBUTIONS Y(A)],, Y(A)

The mass yields Y(A)J, at fixed kinetic energies were obtained by summing the isobaric ionic charge distributions over all ionic charge states q:

YWI, =C Y(q)L,E. 9

The results are given in table 2 and in fig. 9. The yields are normalized to 100% for each energy. The mass distribution summed over the yields measured at the different kinetic energies is given in the last column of table 2 and in fig. 10. Before summing up the mass yields for the different energies, they were weighted by the energy distribution summed over all masses as listed in table 3.

3.4. COMPARISON OF THE ENERGY-SUMMED MASS DISTRIBUTION WITH RADIO-

CHEMICAL RESULTS

The mass distribution obtained by summing over the yields measured at different kinetic energies may be compared with radiochemical mass yields as compiled in ref. i7). As can be seen in fig. 10, the agreement is good. A similarly good agreement was found in the case of 235U(n,,.,, f) between the energy-summed mass yields obtained with “Lohengrin” ‘) as well as with the recoil spectrometer “Hiawatha” ‘8S’9) and radiochemical mass yields. Thus it is confirmed that recoil spectrometers are valuable sources also for energy-integrated mass yields.

In some cases there are small, but significant deviations in the yields. The yields for A=83, 84, 85, 101, 102 and 109 differ by more than two standard deviations from the radiochemical yields 17). More recently, the yield for A = 101 was determined radiochemically by Dickens and McConnell 20) to be (6.57*0.37)%. This value is in good agreement with our result of (6.34 f O.OS)% . It is interesting to note that for those mass numbers, where the mass yields of 235U(nm, f) obtained at “Lohengrin” ‘) d’ff f 1 er rom the radiochemical results, namely A = 83, 85 and 102,


0

10

Fig. 9. Mass distributions for different kinetic energies of the fission products. Tbe distributions are normalized to 100% for each energy.

the mass yields for 239Pu(n,,,, f) differ significantly, too. At present, the reason for these deviations is not known.

3.5. ENERGY DISTRIBUTIONS OF THE ISOBARS Y(E)],

The first and second central moments E(A) and &(A) of the primary energy dist~butions Y(E)], of the isobars can be determined from the measured energy distribution without any assumption about the shape of the primary energy distribution. If the measured energy distribution is considered as resulting from folding the

Fig. 10. Mass yields summed

80 90 100 110

A over the kinetic energy of the fission products. The

the yields given in ref 17) . . solid line represents

TA

BLE

2

Relative mass yields fo

r th

e thermal-neutron induced fission of *?'u as a function o

f th

e kinetic energy

of t

he

fission products (the yields arc normalized

to 100%

for each energy)

A

E =93.2MeV

95.5 MeV

98.4 MeV

101.8 MeV

105.8 MeV

80

0.22*0.16

81

0.17*0.13

82

0.11*0.11

83

0.47io.22

84

0.42*0.17

85

0.91 f 0.31

86

0.50*0.10

87

0.92iO.16

88

1.32iO.18

89

1.25*0.14

90

2.02iO.24

91

2.03*0.22

92

2.74i0.23

93

4.54ztO.42

94

4.06*0.35

95

4.50*0.28

96

4.57*0.29

97

5.38+0.32

98

5.70*0.31

99

6.18*0.33

100

101

102

103

I04

I05

I06

107

I08

I09

II0

III

II2

II3

5.27kO.29

5.78+0.30

7.03*0.33

6.76-tO.34

6.21*0.31

5.47kO.30

4.77+0.29

3.2OkO.23

2.72*0.21

1.78;tO.l7

1.31*0.16

0.77iO.12

0.58iO.13

0.34*0.10

0.0?8*0.023

0.107*0.030

0.146*0.025

0.305*0.060

0.490*0.084

0.79*0.10

O&66*0.035

I.01 *0.07

1.24+0.05

1.60*0.06

2.04kO.08

2.7O*O.ll

3.08*0.10

4.OO*O.I2

4.34io.14

4.71 io.13

4.70*0.13

5.69iO.17

5.91 r0.18

6.10*0.17

6.07*0.17

6.34kO.18

6.65r0.19

6.69kO.19

6.27k.018

5.17*0.14

4.4oio.13

3.29iO.13

2.34kO.07

1.36iO.05

0.859kO.037

0.489*0.029

0.230*0.019

0.121*0.012

0.089*0.009

0.111*0.010

0.192*0.013

0.305*0.017

0.463*0.025

0.673kO.027

0.785i0.040

0.939*0.032

1.50*0.04

1.90*0.08

241*0.06

3.01 kO.08

3.50*0.10

4.37*0.11

5.13*0 I9

5.24iO.15

5.56*0.14

6.09*0.19

5.94kO.16

5.86*0.24

6.18*0.20

5.98*0.22

6.45iO.25

6.39i0.29

607*0.31

4.60*0.22

3.80*0.21

2.46io.25

1.79*0.10

1.03*0.10

0.75*0.14

0.246*0.029

0.111 *0.019

0.074*0.045

0.086*0.010

0.155*0.013

0.2?4iO.O20

0.422iO.031

0.592*0.049

0.675ztO.036

0.813*0.025

1.09io.03

1.67*0.07

1.87+0.04

2.55*0.07

2.64-tO.05

3.28 iO.06

4.09*0.06

4.78*0.07

4.99io.07

5.03*0.07

5.44iO.08

5.71 io.10

6.lOztO.12

6.36*O.ll

6.32iO.12

6.42kO.13

6.55kO.14

6.30*0.14

5.28*0.13

4.12iO.10

2.75rtO.08

1.87+0.05

1.05*0.03

0.519*0.020

0.179*0.010

0.066*0.005

0.027iO.004

0.129~0.022

0.162*0.023

0.210*0.025

0.355*0.037

0.597*0.051

0.605+0.049

0.723*0.052

1.00*0.06

1.38ztO.09

I.71 *o.os

1.94*0&J

2.41 *O.lO

3.00*0.11

3.57*0.11

4.27iO.13

4.9oio.14

4.96*0.14

5.17io.14

4.90*0.14

6.37* 0.17

6.97iO.17

6.56*0.15

6.99kO.16

6.89kO.16

7.46*0.17

6.03+0.15

4.78*0.13

2.85iO.12

1.77*0.09

0.885*0.062

0.347*0.033

O.O96=0.019

0.021 *0.009

0.016x0.019

109.9MeV

0.252*0.056

0.265*0.041

0.341 *0.035

0.476+0.047

0.706*0.057

0.903*0.065

0.838*0.058

1.04io.09

1.26*0.12

1.39*0.06

1.65*0.07

1.57 io.07

1.98*0.08

2.74-tO.10

3.60*0.11

3.95*0.11

4.24iO.13

3.99*0.10

4.22*0.11

5 34iO.12

6.95kO.14

7.16*0.14

7.59*0.15

8.08*0.15

8.63iO.16

8.02*0.12

6.52*0.13

3.26*0.09

1.60*0.07

0.906*0.051

0.290*0.028

0.061*0.013

0.045*0.013

112.0 MeV

ZE

0.41*0.17

0.46*0.17

0.46*0.15

0.85*0.24

1.09*0.29

l.l4*0.24

1.27kO.31

0.82*0.18

2.25-to.52

1.36-tO.24

1.69kO.29

1.62*0.26

1.66*0.26

l.75i0.23

2.74*0.33

2.99iO.34

3.54io.39

2.9l~tO.32

3.03 io.34

5.50*0.55

6.65kO.53

5.86i0.48

7.8liO.61

7.93 iO.60

8 52*0.65

9.53 f 0.71

7.77*0.65

3.89kO.53

2.64io.44

1.55*0.38

0.31 *0.10

0.113*0.010

0.153*0.010

0.211*0.011

0.377*0.018

0.563ztO.024

0.687iO.023

0.765~0.020

1.02*0.02

1.49*0.04

1.76ztO.03

2.23*0&I

2.58ztO.04

3.13*0.04

3.91*0.05

4.56*0.06

4.90*0.06

5.02*0.06

5.42+0.06

5.44* 0.06

6.08*0.08

6.47*0.08

6.34*0.08

6.69ztO.08

6.71 f 0.09

6.71 iO.09

5.53*0.08

4.44*0.07

2.82ztO.07

1.88*004

1.04*0.03

0.573*0.031

0.224+0.010

0.111 +0.008

0.075*0.024


TABLE 3

Energy distribution of the light fission

products summed over A (the yields

are normalized to 100%)

E [Meal Y(E) PI

93.2 2.843 f 0.041

95.5 8.973 ztO.060

98.4 20.447 f 0. I79

101.8 33.309*0.147

105.8 28.498 * 0.179

109.9 4.870 + 0.027

112.0 I .060 f 0.024

104

103

2

P 102 IW

101

7

?z

56

GY

5

t

I I I I I 8 I

I

, )

I I I I I I 1

0

I I I I I I I

80 85 90 95 100 105 110

A Fig. I I. Moments of the isobaric energy distributions of the light fission products (corrected for the

energy loss in the source) as a function of the mass number A. Upper part: average kinetic energy 8; lower part: standard deviation CT~

C. Schmitt et al. / Fission yields

0

-

Y

-0 20-

3! >

0 1; A=106 ((.!;I

- A=108 .

‘“-, fi + ,I 0 90 95 100 105 110 115

E/MeV

Fig. 12. Energy distributions (corrected for the energy loss in the source) for the isobars A = 98, 106 and 108.

primary energy distribution with the distribution of energy losses I(AE, t = 190 h) in the source (see subsect. 3.1), the moments of the primary energy distribution can simply be obtained by subtracting from the measured moments the moments of I(AE, t = 190 h). The results are shown in fig. 11. Fig. 12 shows as examples the energy distributions of the isobars A = 98, 106 and 108.

3.6. NUCLEAR CHARGE YIELDS AT SELECTED IONIC CHARGES Y,,,(Z)(,,,

3.6.1. Unfolding procedure of the residual energy spectra. The relative nuclear charge yields for a given mass, energy and ionic charge state were determined by a least-square analysis of the residual energy spectra. This routine minimizes the weighted non-linear least-square expression:

x2= E (%-A)*

i=l ni ’

where i represents the channel number, ni the counts per channel, and

G J = c Ak e[-(i-Pk)2/*d .

k=l

A given spectrum is thus analysed into G nuclear charge components, each of them being characterized by its individual amplitude Ak, position pk, and a common width parameter cr. The position pk is a smooth function of the nuclear charge and energy


88.0MeV 93.0MeV 98.0MeV 103.0MeV 108.6 MeV

200 300 400 500

residual energy (channel no.) Fig. 13. FHWM of the Z-lines in the residual energy spectra as a function of the residual energy. Each measured point corresponds to the most prominent Z-line in a residual energy spectrum measured for

a certain incoming energy (as indicated on the figure) and a certain mass number A.

(and also of the mass to a small extent), and has been used to unambiguously assign the different nuclear charges. The width parameter u depends on the nuclear charge and the kinetic energy, see fig. 13. The influence of this effect on a given spectrum is small and has been neglected. A typical analysis is shown in fig. 14. The use of more sophisticated line shapes (exponential tails for instance) does not significantly improve the fit.

3.6.2. Contamination by neighbouring A/q lines. The spectrometer separates the fission fragments according to their A/q value. Therefore several combinations of A and q leading to the same A/q result in mixtures of masses at different energies (e.g. A/q = 4 or A/q = 5). We have limited our measurements to the cases where the relative intensities of the parasitic lines do not exceed 5% of the total intensity. The intensity and nature of the contaminants were measured by recording an energy spectrum without absorber, thus permitting the evaluation of the positions and

260 280 300 320 340 360

residual energy (channel no.) Fig. 14. Example of a residual energy spectrum fitted with four gaussians; A/q =98/ 19, E = 101.8 MeV.


amplitudes of the contaminants to be subtracted from the residual energy spectrum. The subtraction of contaminants has been of importance for the low-yield experimental points, i.e. kinetic energies or masses far from their most probable values.

3.6.3. Correction for multiple scattering in the absorber. Due to the scattering in the plastic absorber the efficiency of the ionization chamber (located about 40 cm behind the absorber) depends on the nuclear charge and on the energy of the fission products. In order to correct the nuclear charge distributions, the ratios of the counting rates with absorber Nabs and without absorber N were measured for all the experimental settings.

The ratios Nabs/N depend on (Z/E,), with .? being the average nuclear charge in a mass chain and Ei the energy at the entry of the absorber ‘). This dependence can be used to determine that the detection efficiencies of two neighbouring Z- components differ by a factor which ranges between 1.035 at 95.5 MeV and 1.029 at 109.9 MeV. All the nuclear charge distributions have been corrected for this effect.

3.7. DETERMINATION OF NUCLIDE YIELDS Y(A,Z)(,

3.7.1. Introduction. The measured relative nuclear charge yields at fixed ionic

charge K,i(z)l qE,q (see subsect. 3.6) are normalized by the condition

By multiplying these relative nuclear charge yields with the ionic charge yields at fixed mass number and fixed energy Y(q)lA,E (see subsect. 3.2), the ionic charge

yields for the nuclides are obtained:

Y(q)1 A,Z,E = ~ed~ki,E,qY(d~A,E*

In order to finally obtain the nuclide yields, the ionic charge distributions of the nuclides have to be summed over q:

Y(A z)l, =c Y(q)iA,Z,E * 9

3.7.2. Ionic charge distribution of the r&ides. Since the yields Y(q)lA,z$ are known only at a few selected q-values, the yields at the other ionic charges have to be obtained by extrapolation. For this purpose the ionic charge distributions of the nuclides are described as the sum of two gaussians ‘):

mA4,Z*E =I{(1 - yi.c,lA,Z,E) &(q-@*‘2~1 c, Y(q)iA,Z,E a,&

+ &.lA,Z,E e 1-(q-4-&)2/*~ql} (1)

Here Q and uq are the parameters of the “regular” ionic charge distributions as

determined in subsect. 3.2. yi .=.(A,z,E is the fraction of the converted part which is


assumed to have the same width parameter us as the “regular” part. The shift Aq of the converted part to higher ionic charge states is assumed to be the same as was determined 15) for the light fission products in 235U(nth, f), namely Aq = 3.0*0.3.

The quantity Y.&,z~ is zero for nuclides which show no influence of the internal

electron conversion. The decision whether or not a nuclide has a converted component in its ionic

charge distribution was made on the basis of the relative nuclear charge yields

Yrel(Z)IA,E,g measured for two or more different ionic charge states. For this purpose the “regular” dependence of Yre,(Z)IA,E,S on q was calculated by using the “regular”

q and a4 values, and by setting yi c.lA,Z,E = 0. If the yields Yrel(Z)IA,E,q measured at the high q-values are larger than the calculated yields by more than one standard deviation, the nuclide is considered as having a converted fraction ( Y.c.(A,Z,E # 0).

The ionic charge distribution for nonconverted nuclides is obtained by fitting expression (1) with Yi,c.lA,=,E = 0 to the measured yields. Here the normalization

factor C, Y(q)l a,z,E is the only free parameter. For nuclides with a converted fraction, the procedure to determine the ionic

charge distribution is somewhat different depending on whether a given isobar contains only one, or whether it contains several converted nuclides. Fig. 15 shows as an example the isobar A = 98 which contains only one converted nuclide, namely z:Y. In addition to the yields measured for z:Y, some ionic charge state yields for this nuclide can be obtained by subtracting the sum of the fitted yields of all other nuclides contributing to this isobar ($Sr , z:Zr and ZyNb) from the measured isobaric

ionic charge state yields. The ionic charge yields completed in this way were then fitted by expression (1).

In the case with several converted nuclides contributing to the yield of an isobar, the ionic charge state yields measured for each nuclide are fitted separately by

Fig. 15. Determination of nuclide yields Y(q)1 ,_,&e as a function of q for A = 98 at E = 101.8 MeV (one converted nuchde only: p: Y). Open squares: measured isobaric ionic charge state yields for A = 98; full

circles: measured yields of z;Y; dotted line: summed yields of 98Sr 38 , :iY and ~:Mo as measured (extended

to full ionic charge range by using the “regular” ionic charge distributions); open circles: difference between open squares and dotted line; dashed line: fit curve through the open and full circles (yield for

;;Y); full line: sum of dotted and dashed lines.


Fig. 16. Determination of nuclide yields as a function of q for A = 99 at E = 101.8 MeV (two converted nuclides: ZZr, ZTNb). Open squa es. r measured isobaric ionic charge state yields for A = 99; full circles: sum of measured yields for ZZr and ZNb; dotted line: summed yields of $r, z;Y and z;Mo as measured (extended to full ionic charge range by using the “regular” ionic charge distributions); dashed line: sum

of the fitted yield curves for ZZr and ZyNb; full line: sum of dotted and dashed lines.

expression (1). In this case a comparison of the sum of all fitted nuclide yields (converted and nonconverted) with the measured isobaric charge distribution provides a check whether the fit is reasonable. Fig. 16 shows the case of A = 99 as an illustration.

As a result of the fits, the fractions Y.c.]A,Z,E were obtained for different kinetic energies E. Within the uncertainties of the fits, a systematic trend in the dependence

of Yi.c.lA,z,E on E could not be observed. In a last iteration step, the ionic charge distributions were therefore calculated with energy-averaged values Yi.c,(A,Z.

3.7.3. Occurrence of internal electron conversion in the light @ion-product group. The converted fractions Y,.c.(A,Z which were used to calculate the ionic charge distributions of the nuclides are displayed in fig. 17. Most of the nuclides which show isomerism in 235U(n,,,, f) [ref. “)I appear to have converted fractions in 239Ru(n,h, f), too, namely: 86Br, 89Kr, 90Br, 92Rb, 94Rb, 97Sr, 98Y, 99Zr, “‘Nb. A few other nuclides which appear to be converted in 235U(n,i,, f), but not in 239Pu(n,,,, f), have only small yields in 239Pu(n,h, f). A large number of nuclides with Aa 104, which have only small yields in 235U(n,,,, f), were found in 239Pu(n,,,, f) to have fairly large converted fractions. As was already discussed in ref. “), nuclei with an odd neutron number are preferentially converted. In addition, nuclides with N 3 60 show strong conversion. This does not seem unreasonable, since these nuclei are permanently deformed and have, therefore, rotational levels with small transition energies.

3.7.4. Results. The nuclide yields Y( A, Z)l E were determined by summation over the ionic charge distributions for each nuclide. From these the fractional independent yields Yre,(Z)JA,E were obtained by normalizing the nuclide yields to 100% for each fixed value of A and E. The resulting fractional independent yields are listed for


100% 80% 60% 40% 20%

0%

N- Fig. 17. Converted fraction Y, E IA,= of the ionic charge distributions for the different nuclides. Y, c IA,=

are obtained as averages over the values determined at different kinetic energies.

each energy in tables 4 to 8, and for the energy-summed yields in table 9. Also given in tables 4 to 9 are the average nuclear charges _?? and the standard deviations a, (square root of the second moment) of the isobaric nuclear charge distributions. The parameters 2 and oz of the isobaric nuclear charge distributions summed over the energy are shown in figs. 18 and 19. Fig. 20 displays the isotopic yields at the different kinetic energies as well as the isotopic yields summed over the kinetic energy. Element yields were obtained by summing over the yields for the isotopes of each element, see fig. 21. The summed yields for fixed neutron numbers (isotonic yields) are displayed in fig. 22.

4. Discussion

4.1. PROTON ODD-EVEN EFFECT IN THE YIELDS AND IN THE KINETIC ENERGIES

The strong influence of the proton odd-even effect on the yields can be seen in the element yields at all kinetic energies, see fig. 21. Also, the modulation of the deviation AZ of the average nuclear charge from Z,,,, (fig. 18), as well as the modulation of the width a, of the isobaric nuclear charge distributions (fig. 19), is a consequence of the proton odd-even effect. From the yields summed over the kinetic energy (see table 2) one obtains

A,= 1 (Ye,- Y,,)=(11.6*0.6)%. (2) 36SZS43

This value is in contradiction to the value of (7+3)% according to ref. 2’) and

TA

BLE

4

Frac

tion

al

ind

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d

a,

at

a k

inet

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ener

gy

of

95.5

M

eV

A

2=33

34

35

36

37

38

39

40

41

42

43

44

45

z

0,

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

0.6+

0.1

12.3

ztO

.7

53.S

k2.

9 32

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3.

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61

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3.0*0.2 34.8i2.2

1.3kO.I 12.4k2.0

4.6ztO.2

2.2zkO.l

1.3*0.1

37.213*0.104 0.692*O.OlX

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37.425kO.023 0.719*0.011

11.6ZtO.S

37.814*0.010 0.671*0.009

28.2~~~4.9

38.183+0.046 0.608*0.022

53.Si3.6 8.7~0.8

57.7zk3.1 28.5* 1.1

37.212.2 53.8*2.7

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38.680*0.047 O&72*0.036

39.13S*o.o25 0.666+0.016

39.580*0.023 0.650*0.014

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17.lzk4.9

4.4* 1.0

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38.9*4.1 8.8iO.S

79.iiO.6 3.8kO.2

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21.5* 1.2 68.3zt3.6

6.52 1.0 60.2rt6.3

40.554*0.035

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41.600+0.024

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30.2k2.8 3.1 *to.3

42.299kO.030

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42.666~0.032

56.9*3.9 20.41t2.0

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0.668*0.011

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0.634+0.019

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22.lLt6.6

5.4ttl.O

2.4zkO.6

0.593*0.014

0.656*0.031

0.652kO.022

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A

z=33

TA

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5

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M

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34

35

36

37

38

39

40

41

42

43

44

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z u.

z

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

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107

108

109

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35

36

37

38

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44

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86

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88

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91

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92

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93

2.2ztO.l 33.lk1.8 59.8k2.3

94

0.5*0.1 13.1 zkO.8 70.6e2.2

95

96

97

98

99

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0.9*0.1

0.2*0.1

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12.6ztO.6 57.0*2.1 28.4* 1.4

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100

101

102

103

104

105

106

107

108

109

1.6i0.2

4.9*0.2

14.4Ykl.l

5.3 *0.3

1.4iO.l

1.4*0.1

1.7*0.3

3.8*0.4

12.6kO.8

72.4k2.7 21.111.0 1.2iO.l

38.1k5.9 58.6*9.0 1.9*0.1

17.8*2.8 52.7*8.0 28.7i4.5

3.OkO.2 38.9k3.2 56.0*2.4

1.0*0.1 17.6-tl.O 70.7*3.0

8.2*0.7

0.6kO.l 60.5i3.0

48.4k3.5

16.1k4.4

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o.s*

o.1

2.liO.4

10.6*0.8

40.184*0.011 0.529+0.009

40.611 kO.050

0.551*0.013

41.126*0.051 0.694*0.033

41.572*0.022 0.589*0.008

41.909*0.013 0.561*0.011

30.5* 1.8 0.9*0.1

42.241iO.018 0.604+0.011

44.3*3.3 6.6k0.6

42.57010.026 0.625iO.010

57.3*9.8 23.4+7.6 3.211.0 43.136*0.086 0.710*0.048

25.5*2.0 63.9+4.5 1.4zto.3 43.577kO.025 0.674*0.015

27.5k4.8 67.8k7.8 4.7i2.8 43.771*0.054 0.519*0.040

34.724*0.050 0.698*0.048

35.189kO.022 0.674*0.013

35.603iO.026 0.594*0.010

35.970*0.007 0.623*0.012

36.398*0.022 0.629*0.017

36.829*0.016 0.643kO.012

37.259iO.014 0.671*0.008

37.674kO.015 0.601 *0.006

38.029*0.014 0.592ztO.010

38.386kO.016 0.623+0.007

38.710*0.017 0.650*0.008

39.188*0.016 0.672*0.011

39.493io.030 0.663*0.011

39.867+0.019 O.621;tO.Oll

TA

BL

E 7

Frac

tiona

l in

depe

nden

t yi

elds

and

the

nuc

lear

ch

arge

di

stri

butio

n pa

ram

eter

s 2

and

pz

at a

kin

etic

en

ergy

of

105.

8 M

eV

A

2=33

34

35

36

37

38

39

40

41

42

43

44

45

2

cr,

86

0.8i

O.l

46.5

*2.6

47

.4k3

.2

5.3~

1~0.

5 87

0.

4*0.

1 17

.9*2

.1

57.4

k3.4

22

.8kl

1.1

1.6&

0.1

34.5

72 *

0.05

9 0.

605

* 0.

021

88

3.6k

O.2

39

.9rt

2.3

52.9

k2.9

3.

6kO

.2

35.0

72 ~

t0.0

25

0.69

3 rt

0.0

16

89

O.ti

*O.t

17.4

+ I

.0

71,3

*5.4

9.

6;to

.4

1.fr

tO.2

35

.566

ztO

.018

0.

624&

0.00

6 35

.933

*o.o

t2

os77

~o.O

fg

90

4.3i

l.l

62.O

k3.9

30

.2e2

.3

3.5z

tO.8

91

1.

2kO

.l 33

.5A

1.9

55.8

zt2.

9 9.

6hO

.9

36.3

29-4

0.0

28

0.61

3 *

0.02

2

92

12.0

*0.7

60

.3b3

.4

27.6

i1.3

36

.737

zt 0

.020

0.

639

rt: 0

.012

93

2.O

kO.l

39.8

12.1

56

.3zt

2.4

1.8z

tO.2

37

.156

rtO

.015

0.

610~

0.01

2

94

0.5r

tO.l

lS.O

*t1.

1 76

.Ort

4.4

8.51

0.8

37.5

8Ort

O.0

16

0.56

6rtO

.005

37

‘925

LtO

.014

O

A98

iO.O

fS

95

6.O

kO.3

66.

5rt3

.7

27.5

+ 1

.9

96

38.2

16L

t:O

.O17

0.5

37~0

.011

0.

8*0.

1 46

.8rt

2.2

47.5

k2.8

5.

Ort

O.4

38

.567

~J~O

.019

0.6

01 z

kO.0

07

97

19.4

rt0.

7 63

.1~1

~2.2

17.6

tt; 1

.7

98

38.9

82zt

O.0

18

0.60

840.

012

6.9r

tO.4

51

.7~k

3.2

38.5

rt2.

6 2.

9kO

.4

39.3

742t

O.0

22

0.65

6rtO

.011

99

0.

7rtO

.l 30

.6&

tf,5

61

.1~3

,0

7.5i

tO.7

39

.754

*O.O

f6

0,59

2*0.

~~0

100

6.3k

O.3

78

.5~~

~3.3

15.2

* 1.

4 10

1 40

.089

iO.0

13

0.45

5 jz

0.0

12

1.8’

icO

.l 48

.1k2

.6

47.6

1k2.

6 2.

5hO

.2

40.5

09zt

O.0

19

0.58

Ort

:O.O

OS

10

2 27

.5rt

l.6

56.1

*3.2

15

.8~t

l.O

0.7r

tO.1

40

.896

rtO

.019

0.

669r

tO.0

13

103

4.41

0.4

45.8

k4.6

47

.St3

.2

2.4~

kO.6

4t

.479

kO

.029

0.

620r

tO.O

f2

104

1.2*

0.1

22.1

Lti

.9

67.7

rt5.

0 9.

1~1.

0 41

.s46

*0.0

21

0.57

9io.

017

105

11.4

jzO

.9 6

3.31

3.8

25.3

rt1.

8 10

6 42

.139

~0.0

19

O.S

90&

0.01

4 1.

Ort

O.l

61.1

k3.

5 35

.0rt

2.4

2.9r

tO.3

10

7 42

.397

f 0.

021

0.56

4 $:

0.00

8

108

O.S

*O.l

24.2

k4.4

59

.316

.1

14.4

k3.2

1.

6zt1

.7

42.9

24*0

&X

4 0.

679~

kO.0

56

f6,fi

* I.

8 31

.0*3

,0

52.2

~~~S

.1

109

43.3

53 f

0.04

2 0.

752

+O

.Of g

1.

6*0,

.5

34.1

iS.6

63

.6*1

1 0.

7h6.

9 43

.635

ztO

.108

0.

527z

tO.1

06

TA

BL

E

8

Fra

ctio

na

l in

dep

end

ent

yie

ids

an

d t

he

nu

clea

r ch

arg

e d

istr

ibu

tio

n

pa

ram

eter

s 2

an

d r

r,

at

a k

inet

ic e

ner

gy

of

109.

9 M

eV

A

2=33

34

3.

5 36

31

38

39

40

41

42

43

44

45

P

*z

86

1.4k

O.l

87

88

89

90

91

92

93

94

9s

96

97

98

99

1GfJ

10

1 10

2 10

3 10

4

10s

106

58.3

zt3.

9 36

.4A

z9.6

3.

8 f

0.4

22.1

k4.

9 58

.914

.3

17.2

* 1.

6 4.

Oh

O.2

42

.5zk

I.9

51.S

r2.5

0.

71~

~0.

1 19

.510

.9

72.5

k5.

2

2.9k

O.7

73

.5k

3.2

1.02tO.l 41

.4;t

l.B

15.0*0.7

1.6*0.1

0.610.1

1.8rtO.l

2.frtO.f

s.sio.4 1.4zko.3

21.1rt1.9 2.6kO.8

51.4zt2.5 6.21 1.6

61.Srt9.7 22.1* 1.4

42.6z!z2.8

52.8a2.7

13.6zk

1.6 79.Szk8.6

6.9iO.5

0.8zkO.l 75.8k7.4 16.2~!=1,9

S9.2&2.0 37.5i4.0

24.911.4 61.6A2.6

10.4* 1.t 60.816.S

l.OiO.1 38.Oil.S

0.2;tO.l 1.3*0.1

3.1 rt0.t

6.2kO.9

1.3ztO.8

2.6kO.2

0.3*0.1

1.1 io.l

2.5*0.4

11.011.5 2.6iO.8

27.514.1 1.3cto.2

56.izk3.S 4.9* 1.4

82.9-166.4 9.5* 1.1

62.7kS.0 33.8zt3.1

42.8i3.4 49.1k4.0

7.2&0,9 58.4ct7.6

1.9i0.2 21.3i3.9

34.426r0.058 0.591 *0.0

09

34.987*0.051 0.681 *0.02s

3S.S16*0.016 0.610~0.005

3S.87110.022 0.569*o.o43

36.233*0.023 0.537iO.023

36.629*0.026 0.614~0.020

37.O98+0.018 0.64410.031

37.574*0.020 0.581 +O.O04

37.914*0.019 0.464ztO.024

38.115*0.020 0.512ct0.021

38.417ztOo.026 0.556a0.008

38.913kO.027 0.674iO.026

39*197*0.03i? 0.626+0.023

39.648rtO.025 0.58910.019

40.017*0.014 0.421*0.019

0.9io.z

40.330*0.027 0.539*0.011

7.8~1~0.9

40.643*0.029 0.626ztO.014

33.0i33.2 1.31to.4

41.284*0.534 0.612*0.022

66.7rt9.5 4.111.2

41.730*0.041 0.564*0.026

13.Oztl.l 69.4k4.7 17.61-1.4

42.04SiO.018 0.551*0.017

1.3kO.l 67.7k6.3 31.Ok5.4

42.297*00.042 0.48S*O.O17

TABLE

9

Frac

tiona

l in

depe

nden

t yi

elds

an

d th

e nu

clea

r ch

arge

di

stri

butio

n pa

ram

eter

s ,f

and

a,

sum

med

ov

er

the

kine

tic

ener

gy

A

z=33

34

3s

36

37

38

39

40

41

42

43

86*

O.S

*O.l

39.1

f

1.7

50.4

+8.

6 9.

4 f

0.6

0.3*

0.1

87*

0.1*

0.1

14.O

il.O

55

.9k2

.3

28.5

kl.3

1.

5*0.

1 ss

* 3.

3kO

.l 35

.4*

1.3

56.8

*2.6

4.

5 *

0.2

89*

0.3*

0.1

15.3

kO.4

68

.3k2

.6

15.1

*0.5

0.

9*0.

1

90*

2.8-

t0.4

55

.5*1

.5

36.9

+

1.3

4.8

+ 0

.4

91

0.8i

O.l

27.9

kO.7

55

.6*

1.4

15.6

k2.1

92

O

.l*O

.l 10

.8zt

O.3

53

.3*1

.5

34.4

* 0.

9 93

2.

2*0.

1 34

.2 z

t 0.9

s8

.6*

1.2

94

0.5*

0.1

12.8

*to

.5

71.2

zt

1.7

95

96

97

98

99

5.0

f 0.

2 0.

8*0.

1 0.

1 *t

o.1

56.2

* 1.

5 36

.1 f

1.

6 2.

7+0.

1 37

.3 *

1 .o

so

.9*

1.3

11.0

*0.3

13

.5 *

0.3

55.2

* 1.

1 29

.7 +

0.8

5.

5 *

0.2

39.9

f

1.2

49.1

*2.1

0.

6ztO

.l 23

.4zt

O.8

60

.2 *

1.4

100

101

102

103

104

0.1*

0.1

10s

106

107*

10

8*

109*

O.li

O.1

1.

5*0.

1 5.

OiO

.l 14

.9*0

.7

5.lz

tO.l

1.4i

O.l

0.1*

0.1

0.7*

0.1

1.5k

O.2

5.

5 *

0.2

15.3

zto.

7 0.

6*0.

1

70.6

* 1.

6 22

.2 f

0.8

2.

1 zt

o.1

38.8

f

2.4

57.4

*3.s

2.

3*0.

1 19

.9*

I.1

50.3

*3.1

28

.1*

2.0

1.1*

0.1

3.2

f 0.

2 38

.7 f

I .

8 54

.6 *

2.3

3.

5*0.

3 1.

0*0.

1 17

.6*0

.8

68.1

k2.2

12

.8iO

.5

8.7k

O.4

0.

8iO

.l 0.

1*0.

1

57.7

+

1.7

32.7

* 1.

0 49

.7*

1.8

42.1

* 1.

5 17

.7*2

.0

54.5

*3.9

10

.3~t

O.6

25

.9*1

.2

0.4k

O.l

27.3

*2.

7

44

45

z oi

34.6

92 f

0.

030

0.65

7 f

0.02

3 35

.173

*0.0

16

0.67

8 f

0.01

0 35

.626

iO.0

13

0.62

4 *

0.00

6 36

.008

f

0.00

6 0.

594

f 0.

009

36.4

37*0

.013

0.

632

+ 0

.009

36

.863

+ 0

.025

0.

674*

0.01

4 37

.266

f 0

.009

0.

665

* 0.

005

37.6

65 f

0.

007

0.60

5 f

0.00

3 38

.026

* 0

.008

0.

568

f 0.

007

38.3

64*0

.012

0.

621

+ 0

.004

38

.720

f 0

.009

0.

662

* 0.

004

39.1

92 f

0.0

09

0.67

8 *0

.006

39

.547

f

0.01

3 0.

685

zt 0

.006

39

.918

*0.0

11

0.65

3 f.

0.0

07

40.2

13iO

.007

40

.607

f 0

.020

41

.109

*0.0

22

41.5

83*0

.015

0.

4*0.

1 41

.940

* 0

.009

0.8*

0.1

42.2

56iO

.010

7.

2 f

0.3

0.1

zto.

1 42

.562

f

0.01

3 25

.3 *

2.8

2.3

f 0.

6 43

.118

*0.0

36

61.9

k2.5

1.

910.

2 43

.553

*0.

016

67.4

~~4.

6 4.

912.

2 43

.769

f 0

.036

0.55

8 +

z 0.0

05

0.55

9 *

0.00

5 0.

720*

0.01

3 0.

614

f 0.

006

0.59

7 f

0.00

8

0.61

8 f

0.00

6 0.

644

f 0.

005

0.71

6+0.

022

0.70

1 *0

.010

0.

533

+ 0

.029

* T

he

nucl

ear

char

ge

dist

ribu

tions

of

the

m

asse

s A

=86

, 87

, 88

, 89

, 90

, 10

7,

108

and

109

have

no

t bee

n m

easu

red

at a

ll ki

netic

en

ergi

es.

To

obta

in

the

frac

tiona

l in

depe

nden

t yi

elds

su

mm

ed

over

E

th

e m

issi

ng

char

ge

dist

ribu

tions

ha

ve

been

es

timat

ed.

_ _

0.5

0.0

IN I

-0.5

8

I3 II

-1.0

F1 0.0

-0.5

-1.0

C. Schmitt et al. 1 Fission yields

236~

I I I I I I I I I I I I I I I I III II

1 I I I I I I I i%l III I nl I I I I

I I I I

110 100

ALI 90 80

Fig. 18. Deviation of .?! from the unchanged charge density value Z,,,=$$A~ as a function of

At = A, + C(AL). The quantity 2 is the average value of the isobaric nuclear charge distributions summed

over the kinetic energy. The quantity A, is the light fission-product mass number after neutron emission,

and s(AL) is the average number of neutrons emitted from the fission fragment as a function of the

pre-neutron emission mass number”). Upper part: 23sU(n,,, f) according to ref. ‘); lower part: Vu(nth, f).

Fig. 19. Standard deviations cz of the isobaric nuclear charge distributions summed over the kinetic energy as a function of the average isobaric nuclear charge .?.

35B

r 36

Kr

37R

b 3&

r 39

y 40

Zr

4W

42M

o 43

TC

50

60 50

60 50

60

50

60 50

60

60

60

60

60

70

N

Fig.

20

. N

uclid

e yi

elds

fo

r th

e lig

ht

fiss

ion

prod

ucts

at

di

ffer

ent

kine

tic

ener

gies

an

d su

mm

ed

over

th

e ki

netic

en

ergy

. T

he

yiel

ds

are

norm

aliz

ed

to

100%

fo

r ea

ch

ener

gy

sepa

rate

ly.

The

nu

clid

e di

stri

butio

ns

sum

med

ov

er

the

kine

tic

ener

gy

are

also

no

rmal

ized

to

10

0%.


25r.,.,.,.,.,,,.

2. _ 109.9 MeV 1

32 34 36 36 40 42 44 46

2

Fig. 21. Element yields for the light fission products at different kinetic energies. Since the isotopic yields of the elements Se (2 = 34) and Ru (Z = 44) were not measured completely, the missing values have been estimated by using the corresponding measured mass yields. The distributions are normalized to

100% for each energy.

(3.4*5.0)% according to ref. 9), which were determined from radiochemical measurements. Fig. 23 shows the dependence of the proton odd-even effect in the yield on the kinetic energy. The increase with energy is similar as found for 236U [ref. ‘)I, but the magnitude of the effect is about a factor of two smaller than in 236U.

The dependence of the proton odd-even effect on the nuclear charge Z of the fragments is shown in fig. 24. Here the odd-even effect was calculated by a method of differences as proposed by Tracy et al. **):

dP=$(-l)=+‘[(&-&)-3(&-L,)]. (3)


1 1 I 1 1 1 I - I ’ I ’ 1 c

*’ 109.9 MeV 1

ok:::: I:::::;: 1:

20 -

95.5 MeV 15 -

10 -

5-A

49

_A 52 54 56 56 60 62 64 66

N

Fig. 22. Isotonic yields for the light fission products at different kinetic energies.The distributions are normalized to 100% for each energy.

L,, L,, Lz, L3 are the natural logarithms of the energy-summed element yields for 2, Z-t 1, Z +2 and Z + 3, respectively. A, is the average odd-even effect in the Z-interval centred at (Z+$). The magnitude of A, for the elements near Z,= 40 (corresponding to Zu = 54), which have the largest fission yields in 239Pu(n,,, f) is found to be in good agreement with the overall odd-even effect A, = 11.6% as calculated by the formula (2). Clearly, the odd-even effect changes with the fragment nuclear charge. It is very interesting to note the similarity in the structure of the odd-even effect for 236U and 240Pu. If in fig. 24 the curve for 236U is shifted by two units of nuclear charge to the right, the observed oscillations in the odd-even effect for the two systems are in phase. Thus it seems that the observed structure is essentially determined by the heavy fragment: particularly large values of A, are observed when approaching Z,= 50, a minimum occurs near Z,=54, and a


oh n ’ ’ ’ ’ ’ a il 80 90 100 110 120

E/MeV

Fig. 23. Proton odd-even effect in the light fission-product yields of 236U [ref. ‘)I and ?+ as a function

of the fission-product kinetic energy. The proton odd-even effect is defined as the difference between

the yields of even-Z and odd-Z elements in percent. The full curves are calculated from the measured energy shift between even-Z and odd-Z elements by using for the energy distributions of the even-Z

and odd-Z elements the functional shapes as implied by the model of ref. 4).

maximum near ZH = 56. Certainly, the large odd-even effect near Zn = 50 is influenced by the spherical proton shell which is known to play a role in fission from the extremely low technetium yield in the fission of 236U (see the discussion in subsect.

01 ’ 1 ’ a ’ ’ 8 ’ 0 ’ 0 ’ 1 32 34 36 38 40 42 44

Z Fig. 24. Proton odd-even effect in the element yields summed over the kinetic energy as a function of

the proton number Z of the light fragment for 236U [ref. ‘)I and 240Pu. The proton odd-even effect was

calculated from the measured element yields by using the method of differences as proposed by Tracy et al. “).

4.5.1). The strong dependence of the odd-even effect on the fragmentation may indicate that pair-breaking occurs in a rather late stage in fission when the structure of the two nascent fragments is already important. The same conclusion was drawn by Mariolopoulos et al. 5, from the dependence of the odd-even effect on the fragmentation in the thermal-neutron-induced fission of 229Th and in the spontaneous fission of 252Cf.

Fig. 25 shows that the average kinetic energy of the even-Z elements is larger than that of their odd-Z neighbours. The average odd-even effect was calculated


2 f IW

102.2 - 24OP”

1018

: w;

988

981

990

30 32 3b 36 38 40 b2 Lb

Z Fig. 25. Average kinetic energy of the elements in the fission of *?J [ref. ‘11 and 240Pu.

by fitting a gaussian through the E-values of the odd-Z elements with Z = 37, 39,

41 and 43. The difference of the measured values for the even-Z elements with

Z = 36, 38, 40 and 42 and the values calculated from the fitted gaussian was then

averaged to obtain

SE’;“. = 0.3 f 0.1 MeV .

The corresponding difference in the total kinetic energy is

S&W = 0.50*0,17 MeV.

A closer inspection of fig. 25 reveals that the odd-even effect in the kinetic energy

is relatively small near Z, = 40, while it seems to become larger for lower and higher

Z-values. This observation correlates nicely with the minimum in the odd-even

effect in the yields at Z,=40 shown in fig. 24. A weak indication of a correlation

between the Z-dependence of the odd-even effect in the kinetic energies and in the

yields can also be observed for 236U. Furthermore, when comparing the fissioning

systems 230Th, 236U and 240Pu, the reduction in the odd-even effect in the yield is

accompanied by a reduction of the odd-even effect in the kinetic energy, see table

10.

In ref. “) a simple model was proposed which provides a correlation between the

odd-even effect in the yield and in the kinetic energy of the elements. It was assumed

that at most one proton pair is broken, and that the energy AE needed to break a


TABLE 10

Measured proton odd-even effects in the energy-summed yields (A,) and in the average total kinetic energy of the elements (SE rKE) for thermal neutron fission

of 229Th [ref. ‘;)I, 235U [ref. ‘)I, and 239Pu

System *3cETh 236U =%I

A, lohI 35 23.1* 0.7 11.6LtO.6 SE;kE [Mevl 1.3rto.3 0.7 f 0.2 0.50+:0.15

SE,,, [relation (4)] 1.04 0.70* 0.38 6Erka [relation (5)] 1.33 0.70* 0.33

The last two rows list the %&n values as calculated from the measured A, values by means of relations (4) and (5), respectively. The calculated SE&, values are normalized to the value of 0.7 MeV measured for 236U. This normalization corresponds to a pair-breaking energy of AE = 1.83 MeV in relation (4), and to K = 2.79 MeV in relation (5).

pair is taken from the prescission kinetic energy. This leads to the relation “>

24 rSETKE = AEL

1 +A,’

The 6ETK, values which were calculated from the measured odd-even effect A, in the yields by using relation (4), are listed in the 4th row of table 10. They are seen to be in agreement with the measured odd-even effect in the kinetic energy. The assumptions underlying the model used here are probably oversimplified. However, since the model contains only one free parameter, namely the energy AE necessary to break a pair, the explanation of the correlation of the proton odd-even effects in 230Th, 236U and 240Pu may be considered to be satisfactory.

A more comprehensive combinatorical treatment of pair-breaking in fission was given recently by Nifenecker et al. 23) and by Montoya 24). They assume that pairs can be broken close to the saddle point and close to the scission point. Only the energy necessary to break pairs at the scission point is taken from the prescission kinetic energy, while pairs broken at the saddle point do not influence the kinetic energy of the fragments. Furthermore, proton and neutron pair-braking are simul- taneously taken into account, and the number of broken pairs is not restricted to one unit but is only limited by the available energy. It turns out that the dependence of the odd-even effect in the kinetic energy of the elements on the proton odd-even effect in the yields is then given by the expression

SETKE = KA. P

The constant K can be chosen to fit the data. The SETKE values calculated from this relation are listed in the last row of table 10. With the limited accuracy of the experimental data, the two different relations (4) and (5) give an equally good agreement with the data.


4.2. ORIGIN OF THE FINE STRUCTURE IN THE AVERAGE ISOBARIC KINETIC ENERGY

The average kinetic energy of the isobars I? (A) shows a pronounced fine structure, see fig. 11. Similar fine structures were observed, e.g. for 235U(nt,,, f) [ref. ‘)] and 229Th(n,r,, f) [ref. “)I. The correct interpretation of these fine structures is important, since in some cases the isobaric energy distributions may be more easily experimentally accessible than, for example, the energy distributions of the elements. Mariolopoulos et al. ‘) have tried to explain these structures in the case of 23’?h by the odd-even effect in the element yields and in the average kinetic energy of the elements. However, the amplitude of the oscillation of E(A) (fig. 11) is considerably larger than the amplitude in the oscillation of I?(Z) (fig. 25). We have therefore calculated the average kinetic energy of the isobars from the energy distributions which were measured for each nuclide separately.

Fig. 26. Average kinetic energy of the isotopes of different elements as a function of the neutron number.

Fig. 26 shows the average kinetic energy for the isotopes of different elements as a function of the neutron number. The average kinetic energy is seen to increase strongly with neutron number by about 1 MeV/neutron. The neutron evaporation process in conjunction with the different Q-values for the different nuclides is probably mainly responsible for this behaviour. Due to the preferential abundance of even-Z elements, a given isobar A may contain neutron-poor isotopes of a given even-Z element (corresponding to low kinetic energies): if one now moves on to the next isobar (A + l), the isotopes of the elements get more neutron-rich and consequently more energetic. This trend continues, until finally the elements (Z + 1) and (Z +2) take over, which have a smaller N/Z ratio, and consequently a lower kinetic energy. This effect is the main reason for the large amplitude in the oscillation of l?(A).

54

1026

102.4

102.2

102.0

2

1018

B Iw 101.6

1OlL

1012

1010

1008

P-


‘t

Ii 4, I, I I I, I, I, I, I, I,,

99 90 92 94 96 98 100 102 106 106 108

A

Fig. 27. Measured and calculated average isobaric kinetic energies .!?(A). Full circles: measured values; open circles: calculated from the measured energy distributions of the different nuclides contributing to the given isobar,

B(A) = Cz,,v.z+,v=a Y(z, N) x-&T N);

I: z,,w,z+N=A Y(Z N)

stars: calculated from the fractional independent Z-yields (summed over the kinetic energy) Y_,(Z)!,+ and the average kinetic energy of the elements I?(Z),

B(A) =; Yrc,(=)l~~(=) .

The average kinetic energy of the isobars was calculated from the average kinetic energies of the nuclides (see fig. 26) by using the approximate relation

&A)= 1 Y(5 m;(z N) Z,N:Z+N=A /

c Y(3 N) * Z,N;Z+N=A

Fig. 27 shows the comparison of the measured and calculated average kinetic energy of the isobars. The positions of the extrema as well as the amplitude of the oscillations are seen to be reproduced well. For comparison, the procedure used in ref. ‘) to calculate l?;(A) for 229Th(n,h, f) was applied to 239Pu(n,h, f); for this purpose the


average isobaric kinetic energy was calculated from the relation

B(A) =; r,,(-%~(z) .

55

It is obvious from fig. 27 that the large amplitude in the oscillation of l?(A) cannot be explained by this calculation.

The following conclusion can be drawn: The oscillation in l?(A) is mainly the result of the proton odd-even effect in the yield in conjunction with the dependence of the kinetic energy on the neutron number of the isotopes. Even with no odd-even effect in the kinetic energy of the elements, an oscillation in E(A) can be expected, if the even-2 elements are more abundant than the odd-2 elements.

4.3. NEUTRON ODD-EVEN EFFECT IN THE YIELDS

The neutron odd-even effect in the yields summed over the kinetic energy was measured to be

A,,= C (YeN- Y,,)=(6.5*0.7)%. (6) 53sNs64

This value is very close to the value of (5.4*0.7)% found for 235U(nu,, f) [ref. ‘)I. Figs. 28 and 29 show the dependence of the neutron odd-even effect on the kinetic energy and on the neutron number for 239Pu(n,r,, f) together with the results for 235U(nt,,, f) [ref. ‘)I. As can be seen, the 239Pu results and the 235U results fit together nicely. This surprisingly similar behaviour of the two systems supports the conclusion that a possible primary odd-even effect is masked completely by neutron evaporation. However, one difference between the two systems with regard to the isotonic yield should be noted: the isotonic yields shown in fig. 22 exhibit a strong suppression of nuclides with N = 59 at low kinetic energies. Such a depression of the N = 59 yield was not observed for 235U(n,,, f), see fig. 8 of ref. ‘). In order to understand

Fig. 28.

80 90 100 110 120

E/MeV Neutron odd-even effect in the light fission-product yields as a function of the fission-product

kinetic energy. FUN circles: ‘%J(n,,, fJ [ref. ‘)I; open circles: 239Pu(n,,, f).


0 50 55 60 65

N Fig. 29. Neutron odd-even effect as a function of the neutron number N. The odd-even effect was

calculated from the isotonic yield distribution summed over the kinetic energy by using the method of

differences 22). Full circles: 235U(n,,, f) [ref. ‘)I; open circles: 239Ru(n,,, f).

the origin of this interesting difference between the two systems, neutron-evaporation calculations would be useful.

4.4. VARIANCE OF THE ISOBARIC NUCLEAR CHARGE DISTRIBUTIONS

Fig. 19 shows that the width of the isobaric nuclear charge distributions is strongly influenced by the proton odd-even effect. This influence can be eliminated, if the variance a% is averaged over the whole mass region investigated. For the system 235U(nu,, f) it was shown ‘) that the observed energy dependence of the post-neutron- emission variance averaged over all masses in the light fission-product group can be explained by an energy-independent pre-neutron emission variance of 0% = 0.40 f 0.05. This large variance even at high kinetic energies was interpreted as being due to quantum-mechanical zero-point fluctuations. If this interpretation is to be correct, the large and energy-independent value of the pre-neutron-emission variance should be a general phenomenon in fission. Fig. 30 shows the mass-averaged post-neutron-

0.6 -

A 0 hl N 0.4 -

s l oe %ooo

0.2 -

00.'~'~"" ‘s’m 85 90 95 100 105 110

E/MeV Fig. 30. Variance of the post-neutron-emission isobaric distributions, averaged over the mass region

86~ A s 109, as a function of the kinetic energy of the fission products. Full circles: 23sU(n,h, f) [ref. ‘)I; open circles: 239Pu(nth, f).


emission variance (c&) as a function of the kinetic energy for 235U(ntr,, f) and 239Pu(n,,,, f). Both systems are indeed almost indistinguishable in fig. 30. It may be concluded that the pre-neutron-emission variance will be the same for both systems. Thus it seems that an energy-independent pre-neutron-emission value of us = 0.40 is a more general feature of fission, which does not change drastically from system to system as does the proton odd-even effect. Such a behaviour would be expected, if a$ is not determined by the internal excitation of the nucleus at the scission point, which may vary from system to system, but rather by the general phenomenon of quantum-mechanical fluctuations.

4.5. INFLUENCE OF SPHERICAL SHELLS ON THE FRAGMENTATION

4.5.1. 2 = 50. The impressive success of the scission-point model in the version of Wilkins et al. 26) has made apparent that deformed nucleon shells, in particular

the neutron shell near N = 88, are most important for understanding the asymmetric mass distributions in actinide fission. However, the influence of spherical fragment shells can also be detected in low-energy fission. In the discussion given in ref. 27) it was tentatively assumed that the extremely low 43T~ yield is caused by the stability of the 2 = 50 shell in the heavy fragment. This can now be proven by comparing the 43T~ yield from 235U(n,r,, f) with those from 239Pu(n,,,, f), see fig. 31. When displayed as a function of the fission-product mass number A, the relative Z-yields of 39Y and 41Nb are quite similar for the two systems. In particular, the maxima in

60

LO

CO

Fig. 31. Fractional independent Z-yields Yrcl(Z)IA for Y, Nb and Tc as a function of the light fission-

product mass number A for 235U(n,,, f) [ref. ‘)I and 239Pu(n,,, f). Open symbols: ref. 28).

58 c. Schmitt et al. / Fission yields

the relative yields for a given element are reached at approximately the same mass number. For 239Pu(nth, f), the 43T~ yield shows the same behaviour as the 39Y and 41Nb yields, and it reaches a maximum value of more than 50% for A = 107. In contrast, the 43T~ yield for A= 107 in 235U(n,,, f) is only (15.4*4.9)% [ref. I)]. This comparison shows clearly that the low 43T~ yield in 235U(nt,,, f) is connected to the properties of the complementary heavy fragment, most probably to the 2 = 50 shell. A similar conclusion was drawn by Vine and Wahl 28) in their radiochemical study of the yields of ro4Tc and ro5Tc in 235U(n,i,, f) and 239Pu(n,h, f). In analogy to the 43T~ yield in 235U(n,,,, f), the &h yield in 239Pu(n,i,, f) is expected to be very small. However, due to difficulties in separating the elements with 2245 by their different energy loss, there are presently no data available to check this prediction.

4.5.2. N = 82. For the thermal-neutron fission of 235U and 233U it has been shown “*29*30) that fragmentations with 82 neutrons in the heavy fragment have particularly large yields at high kinetic energies. For 239Pu(n,,,, f), Thierens et al. 31) observed strongly asymmetric total kinetic energy distributions for the mass splits withA,=130... 135, and they attributed this asymmetry to the spherical neutron shell NH = 82. In the present measurements of thermal-neutron fission of 239Pu, mass yields were determined for the light fission-product kinetic energies up to 112.0 MeV, see fig. 9. Examples of energy distributions are shown in fig. 12. The distributions of A = 106 as well as that of A = 105 (not shown in fig. 12) are shifted to higher kinetic energies when compared, e.g. to A = 98 and A = 108. At 112.0 MeV, the largest mass yield is observed for AL = 105 ; this isobar contains essentially ‘~:Mo~~ (69.4% at 109.9 MeV, see table 8); the total excitation energy corresponding to 112.0 MeV is E* z 12 MeV. If neutron evaporation is neglected, we obtain for the complementary fragment N,., = 83. In ref. 14) 2, = 43 was tentatively assigned to A,_= 105, which lead to the erroneous conclusion that NH = 84 dominates the high-energy yield. Recent measurements of Montoya 32) for 239Pu(n,i,, f) at even higher kinetic energy (E L 2 119 MeV) show A,_ = 106 to have the largest yield; this isobar contains essentially ‘~:Mo~~ (67.7% at 109.9 MeV, see table 8), and the complementary fragment has NH = 82. Thus the high kinetic energy yield seems to be dominated by NH = 82 in a similar way as it was found for the thermal-neutron fission of 233U and 235U.

5. Conclusion

The detailed knowledge of the yields in thermal-neutron fission of 239Pu and their comparison with the yields in thermal-neutron fission of 235U has revealed interesting

features of the proton odd-even effect: the magnitude of the proton odd-even effect in the yield, which is reduced from 24% (236U) to 12% (‘“Pu), is associated with a reduction in the odd-even effect in the total kinetic energy of the elements from 0.7 MeV (236U) to 0.5 MeV (240Pu). There are some indications that also the dependence on the fragmentation is similar for the odd-even effect in the yield and in


the kinetic energy. This correlation supports the view that the magnitude of proton odd-even effect can be used as an indicator for the intrinsic excitation of the system during its descent from saddle to scission. In a very simple model “) which is based on the assumption that the energy necessary to break a pair is taken from the prescission kinetic energy, the fraction of fission events in which all protons stay in a paired state was estimated to be 24% for 236U. With the same reasoning, one

arrives at 12% as the fraction of events with all protons in paired states for 240Pu. Thus it seems that the damping of the fission mode into intrinsic excitations is weak in both cases, but it is stronger for ‘?u than for 236U. In order to exclude the possibility that the observed correlation between the odd-even effect in the yield and in the kinetic energy is accidental, it is highly desirable to determine the energy dependence of the yields for other fissioning systems with the same accuracy as for the thermal-neutron fission of 235U and 239Pu.

The characteristic dependence of the proton odd-even effect in the yield on the nuclear charge of the heavy fragment, which is very similar for 236U and 240Pu, may serve as a critical test for future theoretical calculations of pair-breaking in fission.

In contrast to the proton odd-even effect, the isobaric variance (a:), averaged over all light fission-product mass numbers, is the same for thermal-neutron fission of 235U and 239 Pu. In particular the large value of us at high kinetic energies is a common feature of both systems. This result is in accordance with the interpretation that the magnitude of a$ is caused by the general phenomenon of quantum- mechanical zero-point fluctuations.

Although the main feature in actinide fission, namely the asymmetric fragmentation, may be interpreted by deformed fragment shells 26), spherical shells seem to be responsible for some special phenomena: the comparison between the thermal- neutron fission of 235U and 239Pu reveals that breaking of the 2 = 50 shell is unlikely. The N = 82 spherical neutron shell is responsible for compact scission configurations which lead to very high kinetic energies. This phenomenon was found previously for thermal-neutron fission of 233U and 235U [refs. 11*29V30)] and it is observed again in thermal-neutron fission of 239Pu.

The authors wish to thank U. Quade and K. Rudolph for letting us use their high-resolution ionization chamber and for their support during the installation of the experimental set-up.

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fission yields at different fission-product kinetic energies for thermal-neutron-induced fission of...

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