Fission yield measurements of Rb, Sr, Cs and Ba isotopes far from the center of the isotopic yield distributions in 235U(nth, f)

J. morg nud. Chem V{~la3. pp. 867-875, 1981 Printed in Great Britain

0022M902181/050867-09502.00/0 Pergamon Press Ltd.

FISSION YIELD MEASUREMENTS OF Rb, Sr,, Cs AND Ba ISOTOPES FAR FROM THE CENTER OF THE ISOTOPIC YIELD DISTRIBUTIONS IN 235U(nth, f) M. SHMID, Y. N1R-EL, G. ENGLER* and S. AMIELNuclear Chemistry Department, Soreq Nuclear Research Centre, Yavne, Israel

(Received 30 April 1980: received for publication 10 July 1980) Abstract--Independent fission yields of ,2 ~Rb, ~= "mSr, He ~48Csand 14~ 14~Ba ill the thermal neutron fission of ?3SU were determined at the SOLIS on-line mass separator. The independent fission yields of UgRb, ~4?.14SCsand ~4s-J4'~Ba were measured for the first time. For all the elements a "wing effect" is apparent, i.e. the experimental independent fission yields in the wings of the isotopic (isobaric) yield distributions are considerably higher and their decline with mass (charge) less steep than predicted by fission yield systematics. To account for this effect a corrected semi-empiricaldistribution function for fission yields is proposed. Comparison of the experimental fission yields with the predictions of theoretical fission models also shows the existence of the "wing effect". Since the theory predicts primary fission yields a correction due to prompt neutron emission was calculated. It is shown that the effect of prompt neutron emission is to broaden the isotopic distributions in the wing of heavy isotopes only slightly, and in the wing of light isotopes more significantly, but it does not explain the "wing effect" which seems to originate in the fission process. INTRODUCTION The currently accepted systematics of the distribution of fission yields is the odd-even systematics in which the charge distribution in an isobaric decay chain is described by a Gaussian function[I,2] modified by a fine structure in the form of an odd-even proton effect and a much smaller odd-even neutron effect[3,4]. The Gaussian curve is characterized by a width parameter c, which is approximately constant for all mass chains and by Zp, the most probable charge for a given mass chain. The fractional independent yield (FLY) is given by: F l Y = f,~

I expl ( Z 7Zt,) 2] --~: \ ~'(' C J

(1)

where f ...... is the odd-even effect factor and Z is the charge of the nuclide. Wahl et al.[1,2] developed their systematics based on 19 mass chains for which in most cases only 2-3 fission yields in the central region of the distribution were measured. The same is also the case for the odd-even effect systematics of Amiel and Feldstein [3, 4] which were tested mainly for nuclides around the center of the distributions, i.e. LZ-Z,, ~ 1.5. The reason for this limited range of measurements of yields for a given chain is that the yields of nuclides which are far from the center of the isobaric distribution are very small and therefore difficult to measure. In addition, nuclides with Z much smaller than Z,, have very short half-lives and are therefore difficult to separate, and nuclides with Z much larger than Z,, have independent fission yields which are a small fraction of their cumulative yield and so even a small error in the correction for the decay of the parent nuclides causes a large uncertainty in the measured independent yield. The application of recoil spectrometers with separa*Author for correspondence. +Deceased.

tion times of the order of microseconds permits the measurement of yields of very short-lived nuclides [5]. However, so far this technique has been limited to nuclides in the light mass peak (A ~< 100). The development of high-efficiency and low-delay-time, surface ionization ion-sources for isotope separators[6,7] permits the extension of measurements to the heavy mass peak and to fission yields which are up to 3 charge units away from the center of the isobaric yield distributions. The purpose of the present work was to reveal features of the distribution of yields of nuclides which lie far from the center of the isobaric distribution. A comparison between the newly available data and the oddeven systematics shows that the experimental yields in the wings of the: distributions are much higher than lhe predicted values and their decline with charge much more moderate. Therefore, a correction to the currently used systematics is proposed. The experimental yields are also compared with the predictions of theoretical fission models. [t is found that the theory also fails to account for the behavior of yields in the wings of the distributions. The effect of prompt neutron emission on the shape of fission yield distributions was studied and it was found that it cannot explain the large discrepancies between theory and experimental results. EXPERIMENTAL The measurements were performed at the SOLIS isotope separator[8,9], which operates on-line with the 4 MW research reactor at Soreq Nuclear Research Centre. A very efficient and selective integrated target-ion source system[6, 7] with 23'U targets enriched to 93% and exposed to a thermal neutron flux of --5×10Sn-cm's ~, was used to separate the elements Rb, St, Cs and Ba. The short delay half-times achieved in these sources, 0.270+0.027sec for Rb and Cs, 1.4+0.3sec for Sr and 1.0 + 0.4 sec for Ba, permitted extension of measurements to isotopes with very short half-lives and low fission yields. The surface ionization process provides a means of selective separation of the isotopes of Rb and Cs by the use of a Ta ionizing surface and of the isotopes of Sr and Rb, or Ba and Cs, by the use of a Re: ionizing surface. Calculated surface ionization 867

868

M. SHMID et al. Table 1. Calculated surface ionization efficiencies on Ta and Re surfaces at 2000°K using the Saha-Langmuir equations with ionization potentials taken from Ref.[27] Elament

Element

Ta surface

Br

6o9xi0-18

Ta s~rface}Ra~ surface 6.0xi0-16

I

1.9x10 -14

2.0x10 -12

Kr

7.9xi0 -23

6.9x10 -21

Xe

4.0xi0-18

3.6xi0 -16

Cs

75

Rb

36

98

Re surface

99.6

$r

3.5xi0-2

3.0

Ba

0.57

33

¥

2olx10 -5

1.8x10 -3

La

7.0x10 -3

0.61

Zr

1.2x10-5

8,2xi0-4

Ce

1.2xi0 -2

1.1

efficiencies of the alkali elements Rb and Cs and alkaline earth elements Sr and Ba on Ta and Re surfaces at 2000°K are given in Table I together with those of possible contaminants. It is clear that for Ta ionizers contamination of Sr in Rb ion beams is less than 0.1% and contamination of Ba in Cs beams is less than 1%. The actual contaminations are even less because the efficiency of the target ion-source for Sr and Ba is reduced due to their longer delay times as compared with those of Rb and Cs[6]. For a Re ionizing surface, both the alkali and the alkaline earth nuclides are ionized with appreciable efficiency. In the case of Rb and Sr, the contaminations are lower than 0.1%. In the case of Cs and Ba the contamination due to the presence of La and Ce is as high as 1-3%. Ce isotopes in the measured mass regions are comparatively long-lived and, therefore, their activity is too low to interfere. The contamination of La isotopes might be higher in the heavy mass wing (A = 146-149) because the expected yields of La isotopes are much higher than the yields of the respective Ba isotopes and this causes a systematic error in the yields measured for Ba isotopes in this region. However, it was found that the actual contamination of La isotopes never exceeded 20% due to the long delay time of La in the target-ion source system. For the determination of fission yields, beta activity scans at the collector were performed over the desired mass region using a 300tzm Si surface barrier detector. With this type of counting

one obtains very low gamma background which prevents contamination of the measured beta activity due to intense gamma emission of neighboring mass chains. Mutual contamination between neighboring masses was tested by scanning the beta activity of the masses and fitting a Gaussian function for each peak by the least squares method. It was determined that the contamination was less than 10 6 for the light masses (A = 92-98) and less than 10 4 for the heavy masses (A = 141-149). Activity scans with Ta and Re ionizers in the mass region 92-98 are shown in Fig. 1 and in the mass region 141-149 in Fig. 2. ANALYSIS Rb and Cs. Fission yields of Rb and Cs isotopes were calculated from activity scans with Ta ionizers in which the ion beams consist solely of the alkali isotopes. The yield of an alkali isotope in each mass chain is related to the measured counting rate for this mass by: A = KYf(TD, T,12, t)

(2)

where A is the beta counting rate, K is a normalizing factor which converts the relative yields measured by this method to absolute yields and Y is the fission yield, f(To, Tn/:, t) is a correction factor which takes into account the delay half-time,

105 94

141

92 143

142

95

Rb'Sr

144

104 rO 3 146

I

"

if)

E

¢~ iO 3

>,

14e

i0z

o Rb

,49 ,

÷

~10 2 rO = i

101

I

0

,

2O

I

40

L

1

6O

,

I

8O

,

I fOO

Mass marker position (ram)

Fig. 1. Beta activity scan at the collector in the mass region 92-98. (O) measurement with a Ta ionizing surface; (*) measurement with a Re ionizing surface.

,oo

3O

I

70 riO Mass marker position (mm)

I

150

Fig. 2. Beta activity scan at the collector in the mass region 141-149. (O) measurement with a Ta ionizing surface; (*) measurement with a Re ionizing surface.

869

Fission yield measurements of Rb, Sr, Cs and Ba isotopes 7)>. and the half-life, T~e, of the nuclide in question and also the irradiation time, t. The derivation of this function is given in Ref. [6]. For the special case in which the parent contribution (Kr or Xe) is negligible and the half-life of the daughter is very long compared with that of the nuclide in question, the function ](TI>, T, :. t) is given by: At)

A

f(T.,T~,:,t)=A:~A,-expt-At)+~exp(

A Ao) (3)

where >, is the decay constant related to the halfqife by ~ In 2/Tj: and At~ is the delay constant related to the delay halftime by A~>-In 2/TD. When the daughter and granddaughter half-lives were comparable to that of the nuclide in question, the ](Tt>, T,,z.t) function was modified to take their activity into account. The half-life values used for the calculation are reported elsewhere {101. Sr and Ba. Yields of Sr and Ba isotopes were calculated using the activity scans with both Re and Ta ionizers (see Fig. 2). In a ~can with a Re ionizer, the activity is due to the presence of both the alkali and the alkaline earth isotopes in the ion beam reaching the collector. In order to obtain the net contribution of the alkaline earth isotopes, the contribution of the alkali isotopes was subtracted after normalization. This was done in the following way. In the case of Cs and Ba, the activity scan curves taken with Re and Ta ionizers were normalized so as to coincide at mass 142. This is because in mass 142 the activity should be attributed only to ~2Cs. The contribution of Ba can be neglected for the following reasons. The activity measurements were made a short time (~- 10 sec) after the beginning of the irradiation of the target and since the half-life of 142Ba(TI/2- 10.7 m) is very long compared with both the irradiation time and the halfqife of ~42Cs (T~,z = 1.78 sec). the activity build-up of 142Bais tOO lOWto be of ~tny significance. In the case of Rb and Sr, similar arguments apply to mass 92 where the activity of 92Rb dominates. Therefore, the activity scans of Sr and Rb taken with Re and Ta ionizers were normalized so as to coincide for mass 92. In Figs. 1 zmd 2 the activity scan curves taken with Re ionizers are the experimental ones and those with Ta are normalized as explained

RESULTS Independent yields in 23"U(nth, f) of isotopes of Rb, Sr. Cs and Ba measured in the present work are given in Table 2. For comparison values from the literature, whenever available, are given as well. The yields measured in the present work cover the center of the isotopic distributions and the heavy mass wing. In the low mass wing, yields could not be measured for the following reasons. It was found that in the present target, delay times of Kr and Xe isotopes, which are the parent nuclides of the respective Rb and Cs isotopes, are very long (To > 1000sec). This was also reported by Wfinsch[l I] for the target of the OSTIS mass separator, which is also a matrix of uranium oxide and graphite. In addition, Kr and Xe isotopes have shorter half-lives than the respective alkali isotopes. Therefore they decay within the target and the yield measured for the isotopes of Rb and Cs is a cumulative yield. Since independent yields of isotopes in the light mass wing are a small fraction of their cumulative yield, it is not possible to calculate them with reasonable accuracy. Yields of Sr and Ba isotopes in the light mass wing could not be measured because in these mass regions, i.e. A = 89-93 and A = 138-142, the isotopes of Sr and Ba are much longer lived than their respective parent nuclides, the isotopes of Rb and Cs, and therefore their contribution to the activity in these regions is very small. JINC Vol 4L No. ~--B

Yields of Rb, Sr, Cs and Ba isotopes Rb. The relative yield of Rb isotopes measured in the present work were normalized to absolute values for 95Rb. The absolute value used was the fractional independent yield given by Siegert et a/.[12] multiplied by the chain yield of mass 95 given by Walker[D]. In general, the agreement between the present results and those of the other groups is quite good. There is a marked discrepancy in 94Rb for which our value is aboul 20% higher than the other reported values. This might be due to the existence of an isomeric state in ~4Rb with a half-life of the order of 0.1 sec as also suspected by others[14]. Such an isomer will not interfere in the measurements of Siegert et al.[12] because they were counting atoms and not radioactivity; this is also the case for the measurements of Chaumont[15] which are based on ion counting. The present values for the yields of 97-98Rb are the most precise. The yield of ~Rb wa~; measured for the first time. Sr. The yields of Sr isotopes were normalized for "'St" with the fractional independent yield given by Siegert et a/.[12], multiplied by the chain yield given by Walker[13]. The only existing measurement in this region is that of Siegert et al.[12] and the agreement between the two different methods is reasonably good. Cs. For the normalization of the yields of Cs isotopes, we used the value given in the compilation of Amiel and Feldstein[3] for the yield of ~42Cs. Our values confirm the measurement of Chaumont[15] and Reeder et al. [1611 (see Table 1). We succeeded however, in extending the range to the yields of J47Cs and H"Cs. Ba. There is a dearth of fission yield data for Ba isotopes. The yields of ,4, ~49Ba were measured for the first time in the present work. For normalization, we used the yield of ~*(Ba given by Amiel and Feldstein[3]. The error intervals for ~47-t49Ba are asymmetric due to the systematic downward error caused by La contamination.

COMPARISON OF THE EXPERIMENTAL RESULTS TO THE ODD-EVEN SYSTEMATICS The systematics of charge distribution in fission is usually presented as a distribution of fractional in-. dependent yields as a function of Z in an isobaric mass chain. In this work isotopic yield distributions were measured and the connection between the isobaric anti isotopic mass distributions will now be shown. According to the odd-even systematics, the fractional independent yield is given by eqn (1). Z,, is very nearly a linear function of A [17]. This approximation is even better if we consider only the range of the isotopes of a certain element. Therefore Z, can be written, (4)

Z, - aA + b

Inserting this expression into eqn (1) we obtain,

FIY :.f

....

Lexp[ X'rw

(A- A">:] cla 2

I

(5'

where, Ap -

Z-b a

(6)

It may be inferred from eqn (5) that if the isobaric distribution of fractional independent yields is assumed

870

M. SHMID et al. Table 2. Independent fission yields of isotopes of Rb, Sr, Cs and Ba IElement

Mass

Present work

Others

(%)

(z) gb

Sr

Cs

Ba

92

3.24+_0.28

93

3.13~0.34

94

2.26+0.34

1.60T0.08 (a), 1.52_+0.05 (b) , 1.74_+0.03 (c)

95

0.89+-0. i0

0.89+_0. i0 (a) 0.639+0_. 025 (b), 0.841-0.03 (e)

96 97

0.35_+0.06 0.1C-k0.02

0.31+0.06 (a) , 0.131+_0.007 (b) , 0.186±0.009 (e)

98

0.036!-__0.009

0.05±0.03 (a) , 0.003+-0.006 (e)

99

0.0064+_0~0018

Measured for the first time

94 95

5.77+_1.6 4.45±0.13

4.20i-0.12 (a)

96

2.56±0.72

97

1.63_+0.46

3.67+0.16 (a) i. 85+_0.12 (a)

98

0.49_+0.14

99

0.18~0.06

0.87+_0.13 (a) 0,38+0,07 (a) O. 057_+0.038 (a)

3.01±0.ii (a), 3.29+0.075 (b), 2.7 _3+0.03 (c) 3.12±0.ii (a), 2.97±0.07 (b), 3.11+0.03 (c)

0.21_+0.06 (a), 0.035_+0.004 (b) , 0.047+0.006 (c)

4. 451-0.13 (a)

i00

0.057_+0.025

142

2,

34+-0,33

1.46±0.39 (d) , 2.38~0.07 (b) , 2.43+_0.06 (c)

143 144

1.45_+0.17 0. 43_-1"0,06

145 146

0.0380i-0.0076

0.98+0.17 (d), 1.45±0.06 (b), 1.36_+0.03 (c) 0.28+-0.08 (d) , 0.26+0.03 (c) 0 inn~0.055 (d) 0.057+0.010 (e) . . . . . 0.046 ' O.O191-O. 006 (c)

0.100+-O. 028

147 O. 0078!-'0.0019

Measured for the first time

148

0.0019+-0.0007

Measured for the first time

143

4.42+i.15

3.60+_0.41 (e)

144 145

3.9(F50.32 2.60T0.60

Measured for the first time

146

u. ~u10.34

. ^^+0.18 147

_ _+0 • 09

O. ~/_0.16 ^

. ^+0.04

148 u.-~_0.08 . . . . +0.017 149 U. U00_0. 029

3.90~0.32 (e)

Measured for the first time Measured for the first time Measured for the first time Measured for the first time

t')The independentyields given here are derived from the fractional independentyields in Ref. [12] using the chain yields from Ref. [13]. C~)Chaumont[15]. t~l'he independent yields given here are derived from the relative yields in Ref. [16] normalized to ~41Csfor Cs isotopes and to 93Rb for Rb isotopes using the recommended values of Amiel and Feldstein[3]. ~dTorman et al. [26]. (e~Amieland Feldstein[3]. to be Gaussian with a constant width parameter for all mass chains, then so is the isotopic distribution, with the width parameter given by c/a 2 and a most probable mass Ap given by ( Z - b)/a. In Fig. 3 the isotopic distributions of fractional independent yields of Rb, Sr, Cs and Ba, measured in the present work, are compared with the respective distributions calculated using the odd-even effect systematics. The values shown are the experimental independent yields divided by the chain yields recommended by Walker[13] and the calculated values are taken from Wolfsberg[18]. It is clearly seen that in the vicinity of the center of the distribution, the predictions of the odd-even systematics are in good agreement with the experimental results. This demonstrates clearly a proton odd-even effect of about 25% exhibited by the experimental yields. It should be noted, however, that for Sr the odd-even factor is a little too high.

One can observe a "wing effect" in Fig. 3, i.e. in the wings of the distributions the yields are in all cases higher than those predicted by the systematics and the decline of yield with mass is much more moderate than expected. It is also possible in Fig. 3 to observe a neutron odd-even effect which is most clearly seen for '4~'49Ba, 98.99Rb and '45-'47Cs as an upward deviation of the yields of even-N nuclides and downward deviation of the yields of odd-N nuclides from the fitted line (broken lines). Amiel and Feldstein[3] reported an average oddeven neutron effect of 8% in the thermal neutron fission of 2asU. Denschlag[17] recommends a smaller value of (4.4---3.4)% which is an average of values of several compilations of fission yield data. The values quoted above for the odd-even neutron effect are the deviation of the measured yields from the calculated yields assuming a Gaussian charge (or isotopic) distribution. This

871

Fission yield measurements of Rb, Sr, Cs and Ba i~otopes

'°°I

Rb

Cs

Id'

iO l

-2

IC)2

I0 >.-

,7 id 3

1(53

\ 164

16 5

165

I

92

L

142 ~s

i0 0

I0 °

i0 "~

~o

144 1443 MQss

148

-I

-4

IO 94

96

98

I00

MOSS

i43

145

~7

~49

Moss

Fig. 3. Isotope distributions of fractionl independent yields of Rb, Sr, Cs and Ba. (O) present work: (0) values calculated by the odd-even systematics[18]; (broken lines) lines fitted to the experimental points.

method of expressing the odd-even effect is applicable only to yields in the center of the distribution and cannot be used for yields in the wings because of the systematic deviation of these yields from the Gaussian distribution, as was found in the present work. However, for the wings the effect can be given a quantitative expression by calculating the deviations from the fitted lines in Fig. 3. The odd-even neutron effect evaluated in this way for the wings of Rb. Sr, Cs and Ba varies from 4 to 8%. It

should be borne in mind however that the error in yield values is 20% or more, so the value given here for the odd-even neutron effect is only an estimate. A CORRECTION TO THE SEMI-EMPIRICAL YIELD

SYSTEMATICS In order to derive a correction function for the dis-. tribution of fission yields, the natural logarithm of the FIY was plotted vs ( Z - Z , , ) 2 (Fig. 4). The solid lines in

M. SHMID et al.

872

that these yields are systematically higher than the corresponding yields in the wing of the heavy isotopes. The possibility that such asymmetry may be caused by prompt neutron emission will be discussed below. It may be noted that the yields of the isotopes 147-149Bado not fit the general trend. Their upward deviation is not completely explained by their error intervals. In order to represent the experimental charge distribution in a systematic way, a function which is a superposition of two Gaussians with a common center was used to fit the experimental data. The first Gaussian is given by the odd-even systematics while the coefficients of the second were derived by fitting a Gaussian to the values obtained by subtracting the first Gaussian from the experimental points. This procedure provides the following correction function for the calculation of fractional independent yields.

, ,4~o -2

l

,,aBo

I

,-Bo

-4 o i

c

FIY=fo.e.{A,exp[ (Z~-ZP)2]+A2exp[ (Z~-ZP)2]} "x x

\\ \,

-6

(7)

N. x

OddZ\ \ Even Z

\ xx x

\'x

7

8

oadz "~..

0

I

2

3

4

5

6

",~_,z~

9

c

I0

where c~ = 0.80-+ 0.14, A~ = (Trc,)- '/= as given by Wahl et aL [2], c2 = 2.57, and Az = 0.039, which were calculated as described above. This way of introducing the correction is convenient because in the center of the distribution, i.e. I Z - Z , [ ~< 1.5, the first term in eqn (7) is dominant and the equation reduces to eqn (1). In the wing of the distribution, the slow decline of yield with [ Z - Z , I is accounted for by the second term in eqn (7).

(Z-Zp) a

Fig. 4. Plot of In of fractional independent yields vs (Z-Zp) 2. (©) even-Z nuclides, Z-Zp <0 (heavy mass wing); (0) odd-Z nuclides, Z-Zp <0 (heavy mass wing); ([]) even-Z nuclides, Z-Zp >0 (fight mass wing); ( I ) odd-Z nuclides, Z-Zp >0

(light mass wing). Fig. 4 are the curves predicted by the odd-even systematics with the upper curve for even-Z nuclides and the lower curve for odd-Z nuclides, These are straight lines as is expected for fission yields following the oddeven systematics (see eqn 1). The experimental points are taken from the present work, and for ( Z - Z p ) 2 ~> 1.5, values measured by Siegert et a/.[12] are included as well. It should be noted that for this region there are no radiochemical independent yields data due to the reasons mentioned in the Introduction. There are a few values which were determined by mass spectrometric techniques[15, 16] but these were not considered here because of their relatively high uncertainties. The reason for these uncertainties is that the radioactive half-life of the nuclides in question are much shorter as compared to the reported delay-times[t5, 16]. The region ( Z - Z , ) 2 ~ 1.5 is thus covered by Siegert et al.[12] and the present work. The features observed in the isotopic distributions (Fig. 3) are also clearly seen in Fig. 4. For the central region of the distribution, i.e. for the (Z - Z,) 2 <~2.25, the agreement between the experimental yields and the systematics is good but for (Z-Z,)Z~>2.25 the "wing effect" is noticed. That is, the experimental yields are considerably higher than predicted by the systematics and their decline with Z - Z~ is more moderate. It should be noted that a "wing effect" also exists in the wing of light isotopes ( Z - Z p > 0). In addition, it can be seen

COMPARISONOF THE EXPERIMENTALRESULTSTO FISSIONMODELS All current fission models predict a Gaussian or nearly Gaussian shape for the distribution of yields as a function of charge in an isobaric mass chain[17]. The calculated widths, ~r, of the distributions for thermal neutron fission of z35U are in the range 0.38-0.55119,22]. Recently Facchini and Sassi[22] developed a partial equilibrium model which is a new version of the statistical model and provides calculated fractional independent yields for all products in the thermal neutron fission of 235U. This model was chosen for a comparison to the experimental data and since it shares the general features of the charge distribution with the other models, the comparison is also representative for these models. The comparison is shown in Fig. 5. In the center of the distribution the agreement is reasonably good although the odd-even effect fine structure is not accounted for. However, for yields in the wings of the distribution, i.e., those for which I Z - Z,I ~> 1.5, the calculated values are small compared with the experimental values and also the decline with IZ-Zpl is steeper. Thus the distributions predicted by theoretical models are too narrow to account for the behavior of yields in the wings of the distribution. THE EFFECT OF PROMPT NEUTRON EMISSION It might be argued against the comparison between experimental fission yields and the predictions of fission models that these models refer to the distribution of mass and charge in the primary fission fragments, while experimental results refer to fission products created after prompt neutron emission and the broadening of the distributions in the wings might be due to the effect of prompt neutron emission. The net effect of prompt neu-

873

Fission yield measurements of Rb, Sr, Cs and Ba isotopes

i

/'

IO"i

,l//

<

"

I'

/\

=O-Z

/ / i

r

i

A: 149

iO~ i

f

"/

/

!

,,,,48 i

56

toc !

,

55

6(-

58 Z

{

A=IOO

/

A=99

i0

~ll l

i

i i

,6"[ ;

1(53

57 Z

t

IO 4

L

59

,

t

~

I

L

42

4O Z

i ~ J~ ~ ~ , 37

39 Z

41

$

~6'i

v

/

/

{ A: 147

/ ,I

v

/

A=9~

/ ,eL 555

57 Z

59

I

,

,

55

t

J

57 Z

'!1 1 A=97

,_J

519 3,'

I

T,9 Z

Z

10 o

<'%

L0q

//

k\t,

iO-I

i

/

>- i0 -z /

& = 145

/

A= 144

/

ICP

i

59

57

.

54

Z 10° i~

~df

I

56

,

'

,d"

_,

L _,

37

Z

i

/

A =95

58 Z

Z?

io t

!,,

L 36

J

39

10° I

"

i

7 58

~...A

!/

A=96

id 3

1

55

I

t

4O

/

,/

A q43

ir

,I I

i

/

~=142

A:94

F

/

A:93

J / o L_~_

54

;,

56 Z

58

53

I

J

55 Z

57

d 36

38 Z

40

35

i

J

....

37

39

Fig. 5. Isobaric distibutions of fractional independent yields for A = 93-100 and A = 142-149. Solid tines--theoretical values of Faccini and Sassi[22] (O) present work; (A) Siegert et al.[12]; (rq,) Amiel and Feldstein[3].

tron emission is determined by the interplay of two opposite effects. On the one hand, the average number of neutrons emitted as a function of mass is an ascending function in both peaks of the mass distribution (see Ref.[23]) and this narrows the distributions after prompt neutron emission. On the other hand, for each mass the

distribution of the number of neutrons emitted around the average has a width which is not negligible and this broadens the final distribution so it is not definite that the final effect will be a broadening of the yield distribution. In order to evaluate quantitatively the effect of prompt neutron emission on the final distribution of yields, it is

874

M. SHMID et al.

convenient to calculate the effect for an isotopic distribution. This is because prompt neutron emission leaves the nuclides within the distribution of the same element. The calculations of the effect of prompt neutron emission were performed as follows. The distribution of the number of prompt neutrons emitted was assumed to be Gaussian for all mass chains and so the probability PA(V) of a fragment of mass A to emit v neutrons is given by, ,.f"+~/2~/2(O'AV2~')-' -exp[ ( V ' ~ z ) 2 J d v ' PA(V) = I.,

IO o

iO-I

I02

>_ K53

pC

(8) where ffa and ~ are, respectively, the average number and the width of the distribution of prompt neutrons emitted from a fragment with mass A. The width of these distributions was not measured for the thermal neutron fission of 235U and data exist only for the spontaneous fission of 252Cf. Nifenecker et a1.[23] report values of ~r~2 between 1.1 and 1.6 with small variations with mass. The value expected for ~35U(nthf) is much smaller because the average number of neutrons emitted is much smaller. The value adopted for these calculations was calculated by Terrel[24] using his summation method to be O'A2 = 0.6 independent of mass. The ~(A) function was taken from Musgrove et a1.[25]. The distribution of yields of fission products after prompt neutron emission was obtained from the distribution of yields of fission fragments prior to prompt neutron emission and the probability function Pa(v) using the equation, Yp(A) = ~ YF(A + v)P/~+v(v)

(9)

v-o

where Yp(A) and YF(A) are, respectively, the yields of a product and a fragment of mass A. The summation in eqn (9) does not go higher than four neutrons because the probability for the emission of more than four neutrons is negligible. The fragment yield distribution Y~(A), was obtained from the theoretical fractional independent yield of Facchini and Sassi[22] multiplied by the fragment mass distribution. This fragment mass distribution was obtained from the product mass distribution recommended by Walker[13] using the ~(A) function of Ref.[25] and the interpolation method of Facchini and Sassi[22]. For the calculation of the fragment mass distribution, the dispersion in the prompt neutron emission is not taken into account because in the mass region considered the mass yield is almost constant, and therefore prompt neutron emission does not modify the shape of the distribution but only displaces it to lower masses. The results of these calculations for the isotopic distribution of Rb together with experimental values are shown in Fig. 6. This distribution is a representative. example, the other isotopic distributions share the same features. It can be seen that prompt neutron emission broadens the distribution slightly. In the wing of heavy isotopes, the enhancement in the yields is small. The effect is more pronounced in the wing of light isotopes where the enhancement is up to a factor of 10 for the lightest isotopes. It may be concluded, as is evident from Fig. 6, that even with the inclusion of the effect of prompt neutron emission, the theoretically predicted values do not account for the behavior of yields in the

16' 86

t

i 88

I 90

I

i I J 92 94 Moss

i

t 96

I

J 98

Fig. 6. The effect of prompt neutron emission on the isotopic yield distribution of Rb. (solid line) theoretical values of Faccini and Sassi[22]; (broken line) theoretical values corrected for prompt neutron emission; (qb)experimental values. wings of the distribution. This effect explains, however, another feature of the yield distribution which was pointed out previously, the asymmetry of the curve. That is, yields in the wing of light masses are higher than corresponding yields in the wing of heavy masses, It can be concluded that prompt neutron emission does not explain the discrepancies between the predictions by fission models and the experimental yields in the wings of the distribution. Therefore the effect seems to originate in the fission process and should be accounted for by fission theory. Note added in proof--After this work was completed for publication some new fission yield measurements of Rb and Cs were published:- S. J. Balestrini, R. Decker, H. Wollnik, K. D. Wfinsch, G. Jung, E. Koglin and G. Siegert, Phys. Rev. C20, 2244 (1979).

REFERENCES 1. A, C. Wahl, R. L. Ferguson, D. R. Nethaway, D. E. Troutner and K. Wolfsberg, Phys. Rev. 126, 1112(1962). 2. A, C. Wahl, A. F. Norris, R. A. Rouse and J. C. Williams, Proc. 2nd Syrup. Physics and Chemistry of Fission, Vienna 1969, p. 813. IAEA, Vienna (1969). 3. S. Amiel and H. Feldstein, Proc. 3rd Syrup. Physics and Chemistry of Fission, Rochester 1973, Vol. II, p. 65. IAEA, Vienna (1974). 4. S. Amiel and H. Feldstein, Phys. Rev. Cll, 845 (1975). 5. K. Sistemich, Nucl. Instrum. Methods 139, 203 (1976). 6. S. Amiel, G. Engler, Y. Nir-El and M. Shmid, Nucl. Instrum. Methods 139, 305 (1976). 7. M. Shmid, Y. Nir-El, G. Engler and S. Amiel, Nucl. lnstrum. Methods 144,601 (1977). 8. M. Oron and S. Amid, Proc. 8th Int. Conf. Electromagnetic Isotope Separators and the Techniques of their Application, Marburg, p. 87 (1970). 9. S. Amiel, Ark. Fys. 36, 9 (1967). 10. G. Engler, Y. Nir-El, M. Shmid and S. Amiel,Phys. Rev. C19, 1948 (1979). 11. K. D. Wi.insch;private communication. 12. G. Siegert, H. Wollnik,J. Greif, R. Decker, G. Fiedler and B. Pfeiffer, Phys. Rev. C14, 1864(1976). 13. W. H. Walker, Proc. of a Panel on Fission Product Nuclear Data, Bologna 1973, Vol. I, p. 285. IAEA-169, Vienna (1974).

Fission yield measurements of Rb, Sr, Cs and B~ isotopes 14. K. Thiboult, private communication. 15. J. Chaumont, Ph.D. thesis, Faculte des Sciences d'Orsay, L niversit6 de Paris (1970), unpublished. 18. P. I~. Reeder, J. F, Wright and R. A. Andrel, Proc. Conf. Nuclear Cross Sections anti Technology, Washington D. C. Vol. I, p. 401 (1975). !7 H. O. Denschlag, Proc. 2nd Panel on Fission Product Nuclear Data. Petten 197.7', Vol. II, p. 421. IAEA-213, Vienna {1978). i8. K, Wolfsberg, LA-5553-MS (1974). 19. M. R. lyer and A. K. Ganguly, Phys. Rev. C3, 785 {1971). 20. P. Fong, Phys. Rer. 102, 434 (1956). 21. J. Wing and P. Fong, Phys. Rev. 157, 1038 (19671. 22. ti. Facchini and G. Sassi. Contribution to the IAEA conStlltants meeting on the l;,e of Nut'lear Theory in Neutron

23.

24. 25.

26.

27.

875

Nuclear Data Evaluation, Trieste, Vol. II, p. 391. IAEA-190, Vienna (1975), H. Nifenecker, C. Signarbieux, R. Babinet and J. Poitou. Proc. 3rd Symp. on Physics and Chemistry of Fission Rochester 1973, Vol. I1, p. 117. IAEA, Vienna (19741. J. Terrell, Phys. Rev. 127, 880 (1962). A. R. de L. Musgrove, J. L. Cook, G. D. Trimble, Proc. of ~,, Punel on Fission Product Nuclear Data, Bologna 1973. VoI. 1I, p. 163. IAEA-169, Vienna (1974), L. Forman, S. J. Balestrini, K. Wolfsberg and T. R Jeter, Proc. Conf. ¢~n the Properties of Nuclei Far from the Revion of Beta Stability, Leysin 1970, Vol. 1, p. 589. CERN 70-30 (1970). R, G, Wilson and G. R. Brewer, Ion Beams, p. 118 Wiley, N.Y. 11973h