Volume 60B, number 5 PHYSICS LETTERS 16 February 1976

T O T A L K I N E T I C E N E R G I E S A N D M A S S Y I E L D D I S T R I B U T I O N S

O F 2 5 2 C f F I S S I O N F R A G M E N T S

P. DAVID, J. DEBRUS, F. LOBKE, H. MOMMSEN and R. SCHOENMACKERS Insitut ffir Strahlen- und Kernphysik der Universita't Bonn, D-53 Bonn, Nussallee 14-16, Germany

Received 29 December 1975

The variation in the mass yield distribution of the spontaneous fission of 2S2cf as a function of the total kinetic energy (TKE) of the two fragments is investigated. With increasing TKE the peaks of the mass yield distributions become narrower.

On the way from the saddle point configuration down to the scission configuration the mass ratio of the future fission fragments is believed to be conserved as it was built up at the second barrier for asymmetric deformations of nuclei in the mass region A ~ 240 leading to asymmetric mass yield distributions. As pointed out by Maruhn et al. [ 1 ] semi-empirical shell model calculations are able to reproduce experimental heavy-to-light mass ratios, but these calculations do not consider fluctuations around the preferred mass asym- metries which contribute to the spread of the final mass yield distributions. Introducing a collective

coordinate ~ = (A 1 - A 2)/(A 1 +A 2) where A 1 and A 2 are the masses of the nascent fragments Maruhn et al. describe the mass flow which gives rise to mass asym- metry fluctuations. The~results of their calculations very well reproduce the most favourable heavy-to-light fragment ratios but the final mass yield distributions are smaller than the experimental data. Also statisti- cal calculations of fission mass yield distributions [2, 3] do not give the right widths.

Therefore it seems worthwhile to investigate care- fully the positions of the peaks and the widths of fission fragment mass yield distributions. In this letter we report the variation in the mass yield distri- but ion of the spontaneous fission of 252Cf as a func- tion of the total kinetic energy (TKE) of the two fragments. The measurements where done with a 252Cf source [4] placed between two silicon surface detectors. Pulse heights of coincident events were stored on magnetic tape for subsequent computer processing. The fragment masses and the TKE for each event were calculated according to the method of Plasil et al. [5] and stored in a 50 × 50 matr ix for

further investigation. The correction due to neutron emission was made by constructing a smooth function approximating the data of Gavron and Fraenkel [6] with ~-(A) varying from g = 1 to P- ~ 3 in the mass region region of interest. Mass yield distributions as function of the TKE were obtained from the calculated matrix. The positions of the light and heavy mass peaks, A L and A H, and the corresponding widths were calculated by a least-squares fit o f a double humped Gaussian with equal standard deviations for the two mass peaks to the mass yield distributions.

In fig. 1 the standard deviation o (and the corre- sponding FWHM) of the mass peaks and the mean positions A L and A H of the light and heavy mass peaks are presented. Least-squares fits of second order poly- noms to the data are shown as dashed lines. A mass yield distribution integrated from E k = 160 to 210 MeV and the distribution of the average TKE as func- tions of the mass A are shown in fig. 2 (closed circles) compared with data obtained by Gavron and Fraenkel [6] (open squares).

Our integrated mass distribution is broader (o = 7.37 -+ 0.01 u) compared to the data of Gavron and Fraenkel (a = 6.77 u) or to the data presented by Unik et al. [7] (o ~ 7.2 u) and therefore the peaks of our mass yield distribution are somewhat flatter. This may be due to the experimental resolution and due to the integration range o f E k = 160 to 210 MeV. If the lower integration limit is increased by 10 MeV the standard deviation decreases by approximately 4% to o = 7.13 -+ 0.02 u.

Table 1 summarizes average masses of the light and heavy fragments, the variances of the mass yield distri- butions and the average and variance of the TKE dis-

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Volume 60B, number 5 PHYSICS LETTERS 16 February 1976

. , , , , i , , , , i , , ,~ i , , , , i , , , ,

u .

8 ~ ' 1 20

7

G "i-#...___t_. 15

= . : : : ' , . . . . . . . . , t , . . . . . . . .

I<C 115

~i'~e ~ 1 110 . i~,t ° (IZ. 2) ..t .b.lk4

105 . ~ " 11~7) e ~

100 ~ {152) -II

170 180 190 2 0 0

E K [ M e V ]

Fig. 1. Standard deviation (o) and mean positions of the light (A L) and heavy (,4 H) mass peaks for the spontaneous fission of 2S2Cf as function of the TKE of the fission fragments.

tributions. Our results are compared to those of Gavron and Fraenkel [6], Schmitt et al. [8], Whet- stone [9] and Reisdor fe t al. [10].

The most notable feature of our measurements is the dependence of the standard deviation u of the mass yield distributions on the total kinetic energy of the fission fragments. With increasing TKE the peaks of the mass yield distributions become narrower up to E k ~ 195 MeV from where they stay constant. From a least-squares fit this energy dependence is given by do /dE k = a + b E k with a = - 0 . 7 5 + 0.01 and b = (3.7 + 0.1) × 10 -3 . From the bo t tom of fig. 1 it can be seen that with increasing TKE the peaks of the mass yield distributions shift to the symmetric point. At E k = 185 MeV this energy dependence is given by

dZL/d.g k = 0.28 + 0.03 and dArt /dE k = - 0 . 2 8 -+ 0.03 for the light and heavy peak, respectively.

A first hint to this behaviour of the widths and mean positions of fission fragment mass yield distri- butions has been given by Deruyt ter et al. [11] who presented the mass yield distributions of thermal neutron induced fission of 239pu and of the spon- taneous fission of 240pu. The shift of the positions of the mass peaks to the symmetric point with increasing

446

200

o

X 190

<[

ttUx 180

170

2

• ~ 0.5

0.2

0.1

f '4 D

I J I I t I i I

eel o

o •

• o

t o

o

I l l II O0

o

• o

t ~

o

!

L I l I I I I I

90 100 110 120 130 1/,0 150 160

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Fig. 2. Energy integrated mass distribution and average TKE as function of mass A for the spontaneous fission of 2S2cf (closed circles) compared to data of ref. [6] (open circles). For mass yields ~ 0.3% statistical errors are to small to be shown.

TKE is also observed in thermal neutron induced fission of 255Fm [12] and in the spontaneous fission of 257Fm [13].

High kinetic energies of fission fragments are obvi- ously related to low internal excitation energy of the fragments. This is exp.erimentally shown by Nifenecker et al. [14] in the decrease of the number of emitted neutrons and the decrease of the total "),-ray energy with increasing TKE. Also the decrease of the widths of the mass yield distributions observed in our work may be caused by the reduction of internal excitation energy, since approaching the magic nucleon numbers Z = 50 and N = 82 fragments will be more resistant to deformation and less energy will go to internal excita- tion and fewer neutrons will be emitted leading to

Volume 60B, number 5 PHYSICS LETTERS 16 February 1976

Table 1 Comparison of the average light and heavy fragment mass, A L and AH, the standard deviation OA, the average TKE Ek, its standard deviation OF.k, and the average kinetic energies of the light and heavy fragments E L and E H with the standard deviations OEL and oEH.

butions. This may explain the levelling out of the width distribution in fig. 1.

The measured width distribution may be helpful for calculations in statistical and dynamic fission models.

Present ref. [6] ref. [81 ref. [91 ref. [101 results

AL(U) 108.6 AH(U) 143.4 OA(U) 7.37(7.13) Ek(MeV) 186.8 OEk(MeV) 11.17 EL(MeV) 104.6 OEL(MeV) 6.56 EH(MeV) 79.7 OEH(MeV) 9.35

109.0 1 0 8 . 6 108.4 108.54 143.0 1 4 3 . 4 1 4 3 . 6 143.46

6.77 6.72 6.77 6.8 183.7 1 8 6 . 5 1 8 6 . 6 185.8

11.06 12.0 11.3 -

narrower fragment mass yield distributions. Above

E k ~ 195 MeV the decrease of the widths flattens out. The observed peak-to-valley ratios decrease linear with increasing TKE from P/V = 36 -+ 6 for the energy

regionE k = 1 6 0 - 170 MeV toP/V= 11.5 -+ 1.0 for E k = 200 - 210 MeV. This and the flattening out of the width distribution may be due to the growing influence of the symmetric fission mode. The TKE of near symmetric mass splits is approximately 2 - 6 MeV lower with respect to the TKE of the masses in the maxima of the mass yield distribution (see top of fig. 2). For the fragments originating from the sym- metric fission the internal excitation energy seems to be increased leading to higher numbers of emitted neutrons and therefore to broader mass yield distri-

Financial support by the Bundesministerium for Forschung und Technologic is gratefully acknowledged.

References

[ 1] J. Maruhn, W. Greiner, P. Lichtner and D. Drechsel, Proc. 3rd IAEA Symp. on Physics and chemistry of fission, Rochester 1973, Vol. I, p. 569.

[2] A.S. Jensen and T. D4ssing, ibid, p. 409. [3] P. Fong, Phys. Rev. C10 (1974) 1122. [4] Fabricated in the Bureau Central des Mesures NucMaires,

Geel, Belgium. [5] F. Plasil, R.L. Fergusson, F. Pleasonton and H.W. Schmitt,

Phys. Rev. C7 (1973) 1193. [6] A. Gavron and Z. Fraenkel, Phys. Rev. C9 (1974) 632. [7] J.P. Unik et al., Proc. 3rd IAEA Symp. on Physics and chem-

istry of fission, Rochester 1973, Vol. II, p. 19. [8] H.W. Schmitt, W.E. Kiker and C.W. Williams, Phys. Rev.

137 (1965) B837. [9] S.L. Whetstone, Phys. Rev. 131 (1963) 1232.

[10] W. Reisdorf, J.P. Unik, H.C. Griffin and L.E. Glendenin, Nucl. Phys. A177 (1971) 337.

[11] A.J. Deruytter and G. Wegner-Penning, Proc. 3rd IAEA Symp. of Physics and chemistry of fission, Rochester 1973, Vol. II, p. 51.

[12] R.C. Ragaini, E.K. Hulet, R.W. Lougheed and J. Wild, Phys. Rev. C9 (1974) 399.

[13] J.P. Balgna, G.P. Ford, D.C. Hoffmann and J.D. Knight, Phys. Rev. Lett. 26 (1971) 145.

[14] H. Nifenecker, C. Signarbieux, R. Babinet and J. Poitou, Proc. 3rd IAEA Symp. on Physics and chemistry of fission, Rochester 1973, Vol. II, p. 117.

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