Nuclear Physics A502 f 19891 315~324~ North Holland, Amsterdam

3152

1

252Cf FISSION REVISITED - NEW INSIGHTS INTO THE FISSION PROCESS

P. Glassel. R. Schmid-Fabian*. D. Schwalm

Physikalisches lnstitut der Universitit Heidelberg, FRG

D. Habs, H.U. v. Helmolt

Max-Planck-lnstitut fiir Kernphysik, Heidelberg, FRG

y-ray energies and multiplicities and neutron multiplicities from Cf spontaneous fission were measured with Nal detectors in 4% at the Heidetberg-Darmstadt Crystal Ball together with the mass and kinetic energy of the fission fragments. The correlation of neutron multiplicity with fragment mass and kinetic energy is presented and discussed in the context of nascent fragment deformation. The ~-multiplicity unfolded for individual fragments is found to be rather independent of mass. A high-energy component in the y-spectra is found in the vicinity of symmetric fission. The results are discussed in the framework of current fission models.

INTRODUCTION

Nuclear fission has been a subject of continuous interest and research for decades. Despite

of great efforts both experimentally and theoretically, many basic questions are still open. The

data reported here are part of a more comprehensive study of neutron and y-emission in 252Cf

spontaneous fission’ exploiting the unique features offered by the Heidelberg-Darmstadt Crystal

Ball*, namely the highly efficient detection of both neutrons and y’s in nearly 4~. We will

focus on a few selected, noteworthy results. Regarding neutron emission, we discuss the

correlation of neutron multiplicity with fragment total kinetic energy. A marked dependence

on fragment mass is found, which is probably linked to the deformation of the fragment at

scission. Concerning y-emission, we firstly address the issue of r-multiplicities vs. fragment

mass. Previous measurements have reported a sawtooth-like behavior for 252Cf3 spontaneous

fission and 235U(n,f)47 5, srmilar to the famous sawtooth in the neutron multiplicity, whereas

our data result in a multiplicity rather independent of fragment mass. Secondly, evidence for a

new high-energy component of the y-spectrum for mass splits near symmetry is presented which

could be associated with the y-deexcitation of highly deformed fragments.

2. EXPERIMENTAL SET-UP AND DATA ANALYSIS

The experiment was performed at the Heidelberg-Darmstadt Crystal Bal12, a 4x detector with

with up to 162 Nal(TI)-crystals and high efficiency for y’s and neutrons. The fission fragments

were measured in coincidence between a solid state detector, and an array of 7 low-pressure

position-sensitive parallel plate avalanche detectors with - 1.4~ solid angle6. The 252Cf source

with an activity of 600 fissions/s was produced by self-transfer onto a 0.22 pg/cm2 polypropylene

* Present address: Stratec GmbH, D-7534 Birkenfeld, FRG

~37S-9474/~9/~O~.SO !@ Else&s Science Publishers B.V. (North-Holland Physics Publishing Division)

316~ P. Gliissel et al. / “‘Cfj.ssion reuisited

foil. It was mounted with 1 mm distance directly onto the solid state detector and centered in

the Crystal Ball. For fragment 1, kinetic energy and time of arrival were measured in the solid

state detector with an intrinsic resolution of - 0.5 MeV and 150 ps (fwhm); for fragment 2, the

direction and time-of-flight (with respect to fragment 1) over typically 20 cm were measured

with 18 mrad and -300 ps resolution (quoted values are detector performances). A total of

1.2 . lo6 fission events were recorded.

In the rather involved calibration procedure, the data of Schmidt7 were used as start values for

the kinetic energy and velocity spectra. The velocity spectra had to be shifted by -0.01 cm/ns

(within the quoted errors) in order to achieve internal consistency of the data. The kinetic

energies are corrected for the (angle-dependent) energy loss in the carrier foil and the pulse

height defect employing the technique of Schmidt7, which was modified for our combination

of measured variables. The corrected energies are converted to pre-neutron values using the

fragment-mass dependent mean neutron multiplicities. The time-of-flight of fragment 2 was

corrected for the angle and mass-dependent time-of-flight and energy loss in the carrier foil

for fragment 1, for energy loss in the outer gas foil of the parallel plate detector, and for the

local variations of the signal propagation delay. Both the start (fragment 1) and the stop time

were corrected for walk effects. In addition, long-term drifts were software-stabilized both for

the kinetic energy and the time-of-flight. The overall resolutions achieved after all corrections

are 400 ps for time-of-flight and -1 MeV for kinetic energy resulting in a (pre-neutron) mass

resolution of 2.7 to 3.3 mass units, slightly varying with fragment mass.

As will be discussed below, apart from the mass resolution, the absolute mass scale is very

critical in the procedure determining fragment -y-multiplicity. It turns out that the asymmetry of

the set-up, with kinetic energy measured for one fragment and velocity for the other, seemingly

a disadvantage, is especially suited to control distortions of the mass scale caused by non-

linear effects (like energy losses in foils, walk effects and pulse height defects) for the following

reason: In a symmetric set-up, the distributions of fragment mass, kinetic energy or velocity

are necessarily invariant with respect to interchange of the fragments, irrespective of non-linear

effects, as long as the non-linearities are the same for the two halves of the set-up. In our

case, the nonlinearities inherent in the energy and time-of-flight measurement are fundamentally

different. This allows to check the level of correction due to these effects by comparing (i) the

distributions of the directly measured (and corrected) quantities (specifically El, “2) with the

corresponding calculated quantities (Ez, VI), and (ii) requiring the resulting mass spectrum to

be symmetric.

As an independent check of the absolute mass scale, the prominent 162-ns isomer 134Te

with a 4+-2+-O+ cascade was enhanced by a sum energy and delayed time cut. A signal of

- 3u is seen at m = 134. From the total of these checks we claim an error in the absolute

mass scale of < 0.5 u.

3. NEUTRON RESULTS

Although not intended for this purpose, the Crystal Ball with a neutron efficiency of 70 -

1.5

1.0 I>

0.5

0.0

1.5

1.0 I>

0.5

0.0

1.5

1.0 I>

0.5

0.0

1.5

1.0 I>

0.5

0.0

0 m = 156 --

l m = 102 -

: I : I : ; : I : I : I : I :

l m = 108 - . m = 126

I,I.I.I.I.I.I.I.I.I,I.I.I,II

150 160 170 180 190 200 210 150 160 170 180 190 200 210

TKE [MeVI TKE [MeVI

Fig. 1: Neutron multiplicity vs. TKE for selected fragment mass pairs. The full symbols refer to the heavy fragment.

75% and nearly 47r solid angle is quite suited for neutron multiplicity measurements. With a

mean neutron flight path of N 35 cm, there is good separation of neutrons and prompt y’s by

time-of-flight, but only limited neutron energy information. Scattering leads to an average of

N 1.4 detectors responding per emitted neutron, which is corrected by discarding the later of two

delayed hits in neighboring detectors. The time difference cuts in this rejection are chosen as to

reproduce the average neutron multiplicity ii = 3.77 taken from literature8. The contribution

from delayed y’s is subtracted using the data of Skarsvigg.

318c I? Glissel et al. / “‘CYf,fission revisited

Neutrons are assigned to the individual fragments by dividing the frame in which the fragment

separate with equal velocity in two hemispheres. This method gives good separation except for

the very slowest neutrons without sacrificing statistics. The validity of the neutron data is proven

by the resulting neutron sawtooth, which is in good agreement with published data.

0.08

0.06

0.02 - l

0.00 m ’ n ’ ’ ’ n ’ ’ ’ a ’ ’ ’ ’ ’ ’ ’ 80 90 100 I10 120 130 1LO 150 160 170

m [ul

Fig. 2: The slopes dii/dTKE of the least-squares fits of the data of Fig. 1

The neutron multiplicity ti for selected mass bins is plotted vs. TKE in Fig. 1. For each

mass, the relation is remarkably linear, the slopes, however, exhibit a marked mass dependence

(Fig. 2) similar to the well-known sawtooth Z vs. mass.

The linear correlation of the neutron multiplicity with TKE and its slope dependence on

fragment mass strongly support the random-neck-rupture model in its refined form with several

distinct fission pathslo. Recent calculations on the basis of experimental data lead to a pre-

scission shape of the following form: In the standard channel there are two rather hard spheres

with masses of about 80 and 130 mass units. The rest of the mass is in the neck. A rupture at

the thinnest part of the neck leads to the most frequent mass split of 109/143. If this pre-scission

shape is typical for the standard channel, it is obvious why the masses 126 and 80 are produced

with such a small yield. The variation of the TKE is created by the length of the neck. A long

neck corresponds to low values of the TKE while a short neck leads to a high TKE because

of the different coulomb repulsion of the spheres. If the neck ruptures near one of the spheres,

the corresponding fragment consists of the second sphere and the whole neck. This leads to

different variations of deformation energy with TKE, and consequently to different slopes of il

vs. TKE. If the neck ruptures near mass 130, e.g., the light fragment inherits most of the neck,

consequently it is very strongly elongated at low TKE and only weakly elongated when the

TKE is high, while the deformation of the mass 130 is nearly independent of TKE. This leads

to a small and the large slope for the heavy and the light fragment, respectively. In the opposite

case, when the neck ruptures near mass 80, the small and large TKE-dependence result for

mass 80 and 172, respectively. The remarkable uniformity of the TKE-dependence in the mass

region m = 108 - 120 is not so easy to explain. In the mass region 110 to 120 the fragments

have oblate ground-state deformations, but it is not clear whether there is a relation to the

deformation near the scission point. It is evident that the variation of the slopes of dis/dTKE

with mass contains much more information about the pre-scission shape of the nucleus than the

familiar B neutron saw-tooth.

4. GAMMA RESULTS

With a time resolution of the Crystal 8all of - 3 ns fwhm (for E, 5 1 MeV) and the

mentioned flight paths, prompt y’s (taken in the window -4 < t < 4 ns) are well separated

with a remaining neutron contamination of less than 1%. The lower cut-off on the y-energy is

at 150 keV.

4.1 y-Multiplicity

The ~-multiplicity My, corrected for efficiency and pile-up, for bhe sum of bolh ~~ugme~~~

vs. fragment mass m2 (fragment detected in the parallel plate detector) is shown in Fig. 3. The

total multiplicity exhibits a variation of about lo%, with lower multiplicity for symmetric and

very asymmetric mass splits, Most of this variation is due to y’s with E, < .8 MeV, the higher

energy y’s show a different trend.

For the assignment of individual fragment y-multiplicities &f?, historically two methods have

been employed: the collimator-method3, which uses a narrow collimator to look at only one

fragment after a short flight path of order a few tenths of a mm, and the Doppler-shift method4,

which exploits the shift of the y-energies and/or the change of the angular distribution due to

the fragment velocities, We have adapted the Doppler-shift method to the asymmetry of our

set-up: (i) the y-response is asymmetric due to the different pre-absorption in the solid state

and parallel plate detectors, (ii) a non-negligible fraction of the fragments are stopped in the

solid state detector before y-emission. For this reason, we compare the y’s emitted by light and

heavy fragments in a small cone of 30” (smeared by the 8” half angle of the individual Crystal

Ball modules) with respect to fragments detected in the parallel plate detector. This way, the

response functions cancel. The y-yield of the individual fragments is then calculated as

where m and ?it are corresponding fragments, Y,,, and YE are the measured y-yields in the

narrow cone about the direction of the fragments, and Pm@% are the mean projections of the

fragment velocity on the direction of the y in that cone.

The result of this unfolding procedure is shown in Fig. 4. Except for a small deviation near

the corresponding masses 121 and 131. it exhibits a rather flat behavior, compared to older data

(full line), which resemble the famous neutron sawtooth.

32oc P. G&se1 et al. / “-‘Cf fission revisited

6

E, > 1.5 Mei statistical l - . . . . .._ i . . . . . . l l l

I . t * I I I *. 1 * 1 * 1 * 1 1

go loo 110 120 130 1LO 150 160

m2 h_11

Fig. 3: y-multiplicity for both fragments vs. mass rn2 for selected individual y-energy ranges

On encountering such a discrepancy with older data, one has to ask what could have gone

wrong in our analysis or in the previous results. An important clue lies in the fact that in the

course of refining the calibration procedure of the fission detectors by including more and more

of the corrections mentioned above, premature glimpses on the unfolded ~-multiplicity showed,

quite unexpectedly, successively less and less ‘sawtoothness’. Since the internal consistency

checks were improved more and more, we finally had to accept the rather flat behavior of the

y-multiplicity.

321c

88

2-

~~ 0 “‘*““‘*‘*“’

90 100 110 120 130 140 150 160

m [ul

Fig. 4: Relative yield of prompt y-rays of individual fragments vs. fragment mass. Full line from ref. 3, dotted line see text.

The authors of ref. 4 were well aware of the fact that the absolute mass scale is crucial for

the observed effect. We are convinced, however, that in their symmetrical set-up there was no

possibility to check the absolute mass scale to the required accuracy. To quantify this argument,

we have deliberately distorted the mass scale by a shift of 2 units towards higher masses. The

resulting unfolded y-multiplicity exhibits a marked sawtooth (dotted line in Fig. 4).

For the completely independent collimator method of ref. 3, the following causes may be

relevant for the observed sawtooth: (i) The measurement looks only at the decay time interval

1. lo-l1 6 t, 5 7 + lo-l1 s, estimated to contain 60-70% of the y-yield. This fraction may be

mass-dependent. (ii) The delay and width of the observed time window and thus the observed

fraction of y’s depend on the velocity of the fragment passing the collimator. This effect is also

borne out by the peculiar shapes of the y-energy spectra in the observed window. (iii) Neutrons

are not identified, their contribution (-30% on average) is removed by subtraction. (iv) The

fragment mass was derived from an analog division of the energy signals and is thus subject to

distortions due to the pulse height defects and foil losses. It is well known today that the pulse

height defects are not smooth functions of atomic number 2.

4.2 Non-statistical high-energy y’s

The y-energy spectra for selected mass splits are plotted in Fig. 5. (For statistics reasons,

the spectra are not unfolded for the Nal detector response. For a comparison of different mass

splits, this is not important.) The spectra exhibit the familiar components: a low-energy bump

dominated by rotational and vibrational transitions occurring close to the Yrast line, and a steeply

falling high-energy tail of statistical y’s These high-energy tails exhibit a marked dependence

on fragment mass. The spectrum for very asymmetric fission (highest line) is purely exponential

above about 1.5 MeV up to 2 6 MeV, whereas, towards symmetric mass splits, a component

322c

HI8 -

lo7 -

--g lo6 -

-!+!! 105 -

-u z loL - >

L= 103 -

lo* -

10’ -

100 -

ml = 90 - 100 101 - 110 111 - 117 118 - 122

-I

Fig. 5: y-energy spectra (both fragments) for the listed ranges of the light fragment mass (top to bottom). The solid lines are a fit to the exponential part above 1.5 MeV, with the same slope for all masses.

above the exponential fall-off gets increasingly pronounced in the region E, 2 3 MeV. For

comparison, the best-fit slope for the purely exponential part of the spectra directly above 1.5

MeV for the more asymmetric cases is shown in all spectra. This slope is nearly the same for all

mass splits. The assumption of a constant exponential slope, though suggested by the spectra

in the region 1.5 < E, 2 2.5 to 5 MeV, is not necessary, however, to conclude the existence

of an enhancement for more symmetric mass splits. The spectra for the more symmetric mass

splits simply cannot be fitted with a single exponential slope in the region above 1.5 MeV.

To be sure that the observed enhancements are not produced by pile-up of neutrons with

prompt y-rays in the same detector, we have investigated the spectrum of energies deposited by

neutrons and its dependence on mass split. The near independence of the spectral shape and

absolute neutron yield from mass split clearly rules out such an explanation.

To quantify the enhancement, the 7-multiplicity for E, > 1.5 MeV was split in two

components: (i) the statistical component below the exponential fit (with constant slope),

already shown above in Fig. 3 (bottom), and (ii) the contribution above the pure exponential

fall-off, plotted in Fig. 6a, clearly concentrated near symmetric fission.

From fragment mass and kinetic energy distributions, there have been hints for a radiative

323C

01’ 3 ” ” ’ I-’ B ” ” ” 90 100 110 120 130 140 150 160

m id

Fig. 6: (a) Symmetrized y-yield (both fragments) of non-statistical high-energy r-rays vs. fragment mass (see text). (b) Fraction of fission events with 2 y-rays with E, > 3.5 MeV each.

deexcitation of fragments in ‘hot’ fission’l. Non-statistical high-energetic r-rays have been

suggested’* to be emitted by very elongated fragments when contracting to the less deformed

groundstate configuration. Th e random-neck-rupture model postulates a ‘super-long’ fission

path with extreme deformations of the nascent fragments for mass splits near symmetry with

a branching ratio of -40% at symmetry”. Since, in contrast to the ‘standard’ fission path,

symmetric scission configurations are predicted for this mode 10 , the simultaneous emission of

tuto such ‘contraction’-7’s by the two fragments should be likely. We have therefore investigated

the yield for events with two y-rays of ET > 3.5 MeV each. The mass dependence of this yield

[Fig. 6b) is very similar to the non-statistical high-energy component in Fig. 6a, again strongly

enhanced near symmetric fission in the region where the random-neck-rupture model predicts

the ‘super-long’ fission mode lo. A similar result has been reported by Brooks and Reines13 for

an experiment with two Nat-detectors and modest mass resolution.

5. CORRELATIONS OF NEUTRONS AND GAMMAS

As is well known, both the neutron multiplicity Ti and the y-multiplicity W, exhibit an

increase with excitation energy E’= Qsg - TKE, suggesting a positive correlation of P and

M7. Nifenecker, e.g., obtained K = 1.133 + 3 by correlating V and &f, (based on ref. 3) of

individual fragments14. As our data do not exhibit a marked mass dependence of 34,. this result

seems questionable now. Correlating ii,. and M, (summed for both fragments) vs. excitation

324~ P. Gliissel et al. / ‘“cfjission revisited

energy E*, we get a much smaller increase of N 0.16 7’s emitted per neutron. This positive

correlation points to an increase of the mean spin of the fragments l4 with excitation energy (or

deformation) and does not exclude a competition between neutrons and 7’s in the deexcitation

process. From the time scales of neutron and y-emission, a competition should be expected

for the overlap of the life-time ranges in the region lo-l4 - lo-l3 s. The high efficiency

of the Crystal Ball both for neutrons and y’s allows the investigation of this competition by

correlating MY and V on an event-by-event basis. Contrary to the relations above, a rather

linear, but negative correlation with a decrease of 0.02 emitted neutrons per 7 (multiplicities of

both fragments, corrected for neutron-y pile-up) is found, independent of the excitation energy

range. This is a first clear evidence of neutron-y competition in the last steps of deexcitation.

REFERENCES

1)

2)

3)

4)

5)

6)

7)

8)

9)

R. Schmid-Fabian, Thesis, Heidelberg 1987, and R. Schmid-Fabian, P. Glissel, D. Habs, H.U. v. Helmolt, D. Schwalm, to be published

V. Metag, D. Habs, K. Helmer, U. v. Helmolt, H.W. Heyn W. Hennerici, H.J. Hennrich, H.J. Himmele, E. Jaeschke,

Rr RB;~~ ~,~~e,i,“d,5c~~~~’

R. Albrecht, Proc. Symp. on Detectors in Heavy-Ion Reactions, Be& 1982, ed. v. Oertzen (Lecture Notes in Physics 178, Springer, Berlin 1983) p. 163

S.A.E. Johansson, Nucl. Phys. 84 (1965) 147

H. Maier-Leibnitz, H.W. Schmitt, P. Armbruster, Proc. Int. Symp. Phys. and Chem. of Fission, Salzburg 1965 (IAEA, Vienna 1965) Vol II, p. 143

F. Pleasonton, R.L. Ferguson, H.W. Schmitt, Phys. Rev. C6 (1972) 1023

R. Schmid-Fabian. Diplomarbeit, Heidelberg 1982

H.W. Schmitt, W.E. Kiker, C.W. Williams, Phys. Rev. 137B (1965) 837

R.R. Spencer, Proc. Int. Conf. on Nuclear Cross Sections for Technology, Knoxville, Tennessee, 1979 (NBS - 594, Washington, D.C. 1980) p. 728

K. Skarsvig, Nucl. Phys. Al53 (1970) 82

10) U. Brosa, S. Grossmann, A. Miiller, Z. Naturforsch. 41a (1986) 1341 U. Brosa, Phys. Rev. C38 (1988) 1944

11) P. Koczon. M. Mutterer, J.P. Theobald, P. Geltenbort, F. Gonnenwein. A. Oed. M.S. Moore, Phys. Lett. BlQl (1987) 249

12) R.W. Hasse, Invited Talk at the All-Union Symposium on Physics and Chemistry of Fission, Obninsk 1987

13) J.W. Brooks, jr., F. Reines. Phys. Rev. C7 (1973) 1579

14) H.A. Nifenecker, C. Signarbieux, M. Ribrag, J. Poitou, M. Matuszek, Nucl. Phys. A189 (1972) 285