Charge distribution of fission products in the reaction 209Bi(12C, fission)

J morg nucl. Chem,, ]977, Vol. 39, pp. ~21-924. Pergamon Press.

Printed in Great Britain

CHARGE DISTRIBUTION OF FISSION PRODUCTS IN THE REACTION 2°9Bi(12C, FISSION) C. L. BRANQUINHOt and V. J. ROBINSON Chemistry Department, The University, Manchester M13 9PL, England

(Received 28 July 1976) Abstract--The yields of about twenty five fission products in the system 2°9Bi(1~C,fission) have been measured by y-ray analysis without chemical separation, at excitation energies of 40, 53 and 66 MeV in the 22~Ac* compound nucleus. The data were used to calculate the most probable charge Zp for each mass number. On the assumption that Zp varies monotonically with A, simple functions were tested and two were found to account adequately for the data. These functions were used to calculate the mean number of emitted neutrons (if) at each energy, ff increases with energy at a rate of about 0.054 neutrons MeV ~. The nature of the charge distribution in the primary fragments is discussed briefly.

INTRODUCTION

EXPERIMENTAL

In a previous paper [1], charge dispersion and distribution parameters in the fission of z°gBi by t2C were reported. These results were mainly based on data obtained from antimony and yttrium isotopes, and the present work was undertaken to examine the charge distribution function over a wider mass range. There is a large number of different hypotheses which attempt to explain the way that the charge of the fissioning nucleus is divided between the two fragments. Conceptually the simplest is the U C D (unchanged charge distribution) hypothesis[2] which assumes that the average charge to mass ratio of fission fragments is independent of mass number. Most other hypotheses assume that some redistribution of charge takes place during fission, such that the lighter fragment has the greater charge density. This does indeed seem to be borne out experimentally, particularly in low energy systems [3]. A crucial point which is not always made explicit is whether the arguments refer to the primary fragments (before neutron emission) or to the final products (after neutron evaporation). Radiochemical yield measurements give information only about the products, whereas the hypotheses of charge division nearly always refer to the primary fragments. It is generally assumed that no charged particles are emitted from fission fragments, so that a fragment (Z,, AI) emits v neutrons to give a product (ZI, A2), where A~ = A2 + v. Thus in order to relate charge to mass ratios of products and fragments, a knowledge of the numbers of neutrons emitted from individual fragments is required. Such detailed information is rarely available, even the average numbers of neutrons from fragments of different mass have been reported for only a few systems [3-10]. In this paper we have assumed that the most probable charge Zp of a fission product is a simple function of the product mass number. The experimental data is compared with several such functions, each of which has also been used to calculate the mean average number of neutrons, ty, at three different energies.

(a) Irradiations. These were carried out on the Manchester heavy ion linear accelerator. The target arrangement was similar to that reported previously [1]. A magnetically analysed C~ beam with a time-averaged current of 100-200 nanoamps irradiated the sandwiched Bi foil for 1-2 hr. Beam currents were monitored with a Faraday cup and appropriate corrections for variations were made in the yiehi calculations. (b) Counting. After irradiation, the target and catcher foils were mounted together in front of a high resolution Ge(Li) detector (2.2 KeV at 1332 KeV). In order to obtain information about both short and long-lived activities in the sample, a sequence involving increasing counting times was adopted. A typical sequence of counting periods was: 6 x 15 rain, 4 x 30 min, 3 x 60 min, 4 × 6 hr, 3 × 12 hr--upto 2 x 60 hr. In total about 30 spectra were obtained for each irradiation. The initial activity of the sample was very high and a large distance from source to detector was required to reduce pulse pile-up and dead time corrections. As the activity decayed this distance was decreased from 10cm to 5, 3 and finally l cm. Corrections for differences in counting efficiency were made by internal standardisation, using prominent y-rays of isotopes of known half life. These correction factors were in good agreement with those from standard sources counted under similar conditions and appeared to be independent of y energy in all cases. (c) Analysis of data. The y spectra were obviously very complex and contained upto 200 identifiable peaks. Peak areas, energies and half-lives were found using the SAMPO code[Ill, modified to deal with these large amounts of data. Assignments of y-rays to particular fission products were made on the basis of half life and energy, using standard tables[12-14]. In cases of single peaks decaying exponentially, this procedure was straightforward. However, in many cases a "peak" contained components of y-rays from more than one isotope. The SAMPO code was able to resolve these overlaps satisfactorily, even for y-rays as close as 1.5-2.00 KeV (depending on energy). Satisfactory exponential decays (with half lives in agreement with literature values) were obtained for all the y-rays used in yield calculations. (d) Calculation of yields. The fission yields f(Z,A) were: calculated from the experimental data using eqn (1):

dNz,A I~ N~perfz,A(l-e ~z ,') dt e~a~

(1],

where - (dNz.A/dt) is the rate of decay of isotope (Z, A) at the end of irradiation of time t; Iv is the peak area extrapolated back to the end of irradiation; e~ is the efficiency of the detector at the appropriate energy; a~ is the abundance of y-ray in the isotopic decay scheme.

fPermanent address: COPPE-Universidade Federal do Rio de Janeiro and Instituto de Engenharia Nuclear, Rio de Janeiro, Brazil. 92t

922

C.L. BRANQUINHO and V. J. ROBINSON

N~ is the number of target atoms, ~ the beam fluxand c~the fission cross section. The term N~/~r is constant for each irradiation and was not directly determined, so that only relative yields were obtained. These however, were converted to per cent yields by normalising the integrated mass yield to 200%. (e) Calculation of the most probable charge, Zp. The independent isotopic yield fz.A of a particular fission product is usually assumed to be given by 1

fz, A = fAx ~

exp

(z - zp

2o.z2

)~ (2)

where fA is the mass chain yield and ~rz and Z. are parameters defining the width and the most probable charge of the gaussian charge dispersion curve, respectively. In these experiments, there was usually only one isotopic yield for any mass number, so that to obtain Zp it was necessary to assume values of az and /A. ~rz is often taken to be independent of fragment mass number [3] and only slightly dependent on the excitation energy of the fissioning nucleus[15]. In the present study the most satisfactory results were obtained using the relation ~rz = 0.565 + 0.0019Eo~.

(3)

where E~x is the compound nucleus excitation energy in MeV. This equation was applied to all mass numbers at each of the three excitation energies (40, 53 and 66 MeV). Values of fa were obtained from the equation IA = ~

1

exp

(A - ~)2

2o.^2 •

RESULTS AND DISCUSSION Experiments were carried out at three nC beam energies. Values of Zp were calculated from the yield data as outlined above and the results are shown in Table 1. Only those isotopes were included for which there are no known isomer states and for which absolute y abundances are available. For almost all the isotopes studied, the yield was either independent (stable or long-lived/3 precursors) or completely cumulative (shortlived/3 precursors). For each energy, about twenty five values of Zp were obtained, in the mass range 77-136. (1) Variation of Zp with A. Figure 1 shows a comparison of the data from experiment 3 with the predictions of various charge distribution hypotheses. Similar plots were found for the other two experiments. The ECD (equal charge displacemen0 calculations [16] were made using Coryell's values[17] of the most stable charge Zs for each A: the mean total number of neutrons (~) was taken as 8.0118]. For the UCD (unchanged charge distribution) calculations, it was simply assumed that Zp was directly proportional to A, i.e.

(4)

The mass yield parameters ~,, and 7, were evaluated using those isotopes for which the cumulative yields (i.e. including/3decaying precursors) were expected to be very close to the mass chain yield. The values of ~rA and A did not appear to vary significantly with energy and they were therefore taken to be constant, equal to 11.9 ainu and 106.5 ainu, respectively. Fortunately, calculated values of Zp are usually insensitive to these two parameters. The yield of a particular isotope (Z, A) may be independent or partly or wholly cumulative, depending on its own half life and those of its/3 precursors. A theoretical curve of the fractional independent chain yields (fz.AIfA) as a function of (Z-Z~) was calculated using eqn (2), with the appropriate value of ~rz (eqn (3)). The experimental isotopic yield was then corrected if necessary for accumulation from/~ precursors using an estimated value of Z~ to give an approximate value of fz.A. The resulting approximate fractional independent chain yield was then fitted to

l: : 3: :

0.4-3-

the theoretical curve to obtain a more accurate value of Z~. The procedure was repeated until Zp became constant and this was the value taken.

Zp = aA

(5)

with the value of " a " determined by a best fit to the data. It is clear from Fig. 1 that the ECD hypothesis gives a poor fit to the Zp data. The UCD hypothesis is rather better and this is in accord with the general picture that ECD is more useful for low energy fission while UCD applies to high energy systems. Nevertheless, as UCD is not entirely satisfactory, two other empirical formulae (eqns (6) and (7) below) were used to fit the data: Zp = b + cA

(6)

Zp = dA + eA 2.

(7)

or

Values of the parameters b, c, d, e were obtained by least squares fitting for each experiment. Equations (6)

UCD hypothesis ECD hypofno~ equetioa 6 equ~lon 7

o . e 0.42

o ..........

o

I

0.41

0.40 75

80

85

90

95

I00

105

I10

115

120

125

130

135

Product moss, A

Fig. 1. Comparison of several charge distribution hypotheses with experiment in the 2°gBilnC fission system at 66 MeV

923

Charge distribution of fission products Table I. Fractional independent yields and most probable charges of fission products in the ~BiI'2C reaction Experiment number

1

2

3

Excitation energy

40 MeV

53 MeV

66 MeV

Isotope

fa

fz, a

Ze

fZ,A

77Ge ~"Ge ~2Br 84Br 87Kr SSKr

1.55x10 -3 1.90×10 3 4.02x10 3

9.33x10 -4 7.69×10-" 1.14x10 3

32.35 32.48 34.33

9.23x10 " l.llxl0 ~ 1.84x10 ~

89Rb

91Sr *2Sr o2y ~Y ~4y 95Zr ~Nb ~Zr 97Nb "gMo ~°'Mo '°~Tc "ZAg mAg '~°Sb mSb t2'~Sb

'~q J26Sb 126I '2~Sb '28I '2"Cs "I '~Cs

5.60× 10 -3

8.74 x 10-~ 1.00×10 2 1.14×10 2 1.43 x 10 2 1.60x10 -2 1.60×10 -2 1.76 × 10-2 1.93x10 -2 2.10x 10-2 2.27×10 -2 2.44x 10-2 2.44x10 -z 2.75x10 -2 3.01×10 -2 3.28 × 10-2 3.01 x 10-z 2.89 x 10-2 1.76×10 -~ 1.43×10 -2 1.14X10 -2 1.14X 10-z 8.74x 10_3 8.74× 10-3 7.59×10 _3 6.54× 10-3 5.60x 10~ 4.02x10 -3 1.55 x 10-3

Z,o

fZ,A

32.37 7.91×10 4 3:2.25 1.06×10 3 34.60 2.45x10 3 . . . . 3.13 x 10 ~ 4.51 × I0 -3 36.33 4.12 × 10 3 36.45 4.65 x 10 3 3.81x10 3 36.58 2.99×10 ~ 36.80 -7.43x10 3 36.93 6.53x10 ~ 3'7.25 6.89X10 3 9.03× 10 3 37,85 9.66× 10 3 3'7.89 1.07X 10 2 7.43x10 -3 38.47 6.53×10 3 38.61 7.26x10 3 1.34x10 2 38.75 1.14x102 38.90 -1.23 x 10 2 38.83 1.06 x 10 2 38.73 1.04 x 10 ~ 1.04x10 ~ 39.33 1 . 0 4 x l 0 " 39.50 8.98x10 ~ 1.61 x 10-2 40.05 1.68× 10 2 39.90 -2.61×10 3 39.85 3.76×10 ~ 39.95 5.18x10 3 1.08x10 : 40.53 1.36x10 ~" 4(}.50 1.05x 10 2 1.38x10 ~ 40.68 9.66×10 ~ 411.35 1.32x10 2 2.34x 10 2 41.50 . . . . . 1.93×10 2 41.78 1.84×10 2 42.28 1.77x10 2 --2.37 x 10 ~" 43.35 -6.71 x 10 ~ 46.06 1.22 x 10 ~ 46.33 t.89 x 10 2 . . . . . 2.02 x 10 2 4.96x10 3 49.50 1.30x10 3 49.65 2.49x 10 3 5.94x10 3 50.38 7.16×10 ~ 5(I.55 7.80x10 ~ 6.32X10 3 51.40 6.10XI0 • 51.38 5.23X10 3 . . . . . 1.63 × 10 3 1.43× 10 3 52.10 1.01 x 10 3 52.23 6.75x 10 " 2.45X 10 3 52.12 2.95X 10 ~ 52.25 3.73 X 10 ~ 6.54x10 " 52.33 6.10x10 ' 52.38 -. . . . . 3.84x 10 3 2.27 x 10 -" 53.45 4.32 x 10 .4 53.63 8.65x 10 " 1.41xlO 4 53.82 1.04xlO ~ 53.95 7.06×10 ~ 7.17x 10 ~ 55.63 . . . . .

a n d (7) g a v e v e r y s i m i l a r r e s u l t s o v e r the m a s s r a n g e s t u d i e d a n d as c a n b e s e e n in Fig. 1 t h e s e e q u a t i o n s f o l l o w the t r e n d in the Zp d a t a r a t h e r m o r e c l o s e l y t h a n the U C D line. E q u a t i o n s (5), (6) a n d (7) c a n b e u s e d to e s t i m a t e the v a l u e of 17 as f o l l o w s . F o r t w o c o m p l e m e n t a r y p r o d u c t s , the s u m of the Ze v a l u e s is e q u a l to the c h a r g e of the f i s s i o n i n g n u c l e u s , p r o v i d e d (as a p p e a r s to be the case) t h a t c h a r g e d p a r t i c l e e m i s s i o n d u r i n g fission is negligible. H a v i n g c h o s e n a p a i r of c o m p l e m e n t a r y Zp v a l u e s , the c o m p l e m e n t a r y m a s s e s c a n b e o b t a i n e d f r o m the app r o p r i a t e e q u a t i o n . T h e v a l u e of ~7 is t h e n the d i f f e r e n c e

Zp 32.48 32.38 34.71 35.38 36.43 -37.29 38.05 38.55 -39.35 39.53 -40.10 40.60 40.60 42.33 -46.73 47.15 49.88 51.00 51.35 51.88 52.35 52.43 -53.30 53.90 54.10

b e t w e e n the m a s s of the c o m p o u n d n u c l e u s a n d the s u m of t h e s e c o m p l e m e n t a r y m a s s e s . T h e v a l u e s of ~7o b t a i n e d in this w a y , t o g e t h e r w i t h the v a l u e s of the v a r i o u s p a r a m e t e r s a, b, c, d, e at e a c h e n e r g y are s h o w n in T a b l e 2. E q u a t i o n s (5) a n d (6) p r e d i c t t h a t the a v e r a g e n u m b e r of n e u t r o n s is i n d e p e n d e n t of f r a g m e n t m a s s r a t i o w h i l e u s i n g e q n (7) w i t h the a p p r o p r i a t e v a l u e s of " d " a n d " e " it w a s f o u n d t h a t the n u m b e r of n e u t r o n s d e c r e a s e d w i t h i n c r e a s i n g a s y m m e t r y . The o v e r a l l ff f r o m eqn (7) w a s t h e r e f o r e o b t a i n e d b y t a k i n g a w e i g h t e d v a l u e o v e r all m a s s ratios.

Table 2. Charge distribution parameters and average number of neutrons emitted in the 2C9Bi/12C fission at three excitation energies Experiment number

a b c d e ~7 (eqn (5)) (eqn (6)) (eqn (7))

1

2

3

d d ~ (MeV/amu)

0.4159 1.5514 0.4003 0.4302 -13.87×10 5 7.00 6.42 6.56

0.4168 1.3443 0.4034 0.4291 _11.99×10 ~ 7.48 7.04 7.11

0.4181 1.0263 0.4080 0.4277 - 9 . 2 0 x 10 ~ 8.15 7.89 7.95

-----22.61 18.07 18.71

924

C.L. BRANQUINHO and V. J. ROBINSON

(2) Variation of ~ with excitation. By assuming that varies linearly with excitation the values in Table 2 were used to calculate d~/dEox. The results obtained are in the final column of Table 2. The value based on UCD (eqn (5)) is probably not reliable, because of the poor fit to the Zp data, but from the other results it appears that an increase of 18-19 MeV is needed to evaporate an extra neutron. This is in substantial agreement with the value found previously [1] and is considerably higher than for systems of higher masses. For example, a value of about 6.3 MeV/amu was suggested to be "universal" for fissile nuclei in the U - P u region[19]. Thus it seems that in heavy ion systems a considerable fraction of the excitation energy is dissipated in processes other than neutron emission. This is probably connected with the high angular momentum of these systems. In the first place, much of the angular momentum appears as orbital motion of the fragments, leading to increases in fragment kinetic energy. The remaining angular momentum will then appear as intrinsic spin of the fission fragments. This will tend to increase prompt 3' emission at the expense of neutron evaporation as the fragments get close to the "Yrast" levels [20, 21]. A similar effect to this has been observed in (HI, xn) spallation reactions, where the peaks of the excitation functions are shifted to higher energy as the mass of the heavy ion (and hence the angular momentum of the compound nucleus) increases [22]. (3) Charge distribution of the primary fragments. The present results give the most probable charge as a function of mass of the fission products. Without further experimental information on the variation of neutron number with fragment mass, it is not possible to draw any definite conclusions about the charge distribution of the primary fragments. We do not believe, however, that the UCD hypothesis can give an adequate description of this distribution in our system. This is because UCD can only be made consistent with our Zp data if it is assumed that the number of neutrons emitted from a fragment is approximately constant, independent of mass. It seems more likely that fewer neutrons are emitted by the light fragment than the heavy one, as has been observed in almost all previously studied cases[3-10]. If this is also true in our case, the Zp data would require the light fragment to have a greater charge density than the heavy fragment at scission. A similar effect occurs in low energy fission and is usually taken to be associated with the effects of the Z = 50 and N = 82 shells. It is improbable that such shell effects influence the charge distribution in the highly excited fissioning nuclei involved here. The conclusion to be drawn is that some movement of charge for heavy to light fragment takes place before

scission. The reason for this is not clear, as at present there is no completely satisfactory theory of charge division in fission at high excitation energies.

Acknowledgements--We wish to thank the staff of the Manchester Linear Accelerator for their help with irradiations and Mr. T. Morgan for preparing the targets. We are indebted to Dr. J. E. Freeman for valuable discussions, includingassistance with the 3' analysis programs. One of us (C.L.B.) acknowledgesthe financial support of The British Council. The Royal Society and S.R.C. provided funds for part of the cost of equipment.

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