Journal of Nuclear and Radiochemical Sciences,Vol. 3, No. 1, pp. 99–101, 2002

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Systematic Study of Anomalous Fragment Anisotropies in Near- and Sub-barrier
Fusion-fission Reactions
H. Q. Zhang,∗ Z. H. Liu, J. C. Xu, M. Ruan, C. J. Lin, and X. Qian
China Institute of Atomic Energy, P.O. Box 275(10), Beijing 102413, China
Received: December 8, 2001; In Final Form: February 26, 2002
The fission cross sections and fragment angular distributions for the complete fusion-fission reactions of11
B + 238 U,237 Np, 12 C + 237 Np, 16 O + 232 Th,238 U, and 19 F + 232 Th at near- and sub-barrier energies have been measured by the fragment folding angle technique. It is revealed that the anomalous anisotropies of fission fragments
in latter three systems are existence. Based on the experimental observations and Døssing and Randrup’s theory, a
new version model of preequilibrium fission is put forward to explain the anomaly.

1. Introduction
We have succeeded in separating complete fusion-fission (FF)and transfer fission (TF) events by the fragment folding angletechnique.1 The fission cross sections and fragment angular distributions for the FF reactions of 11 B + 238 U,237 Np, 12 C + 237 Np,
16O + 232 Th,238 U, and 19 F + 232 Th at near- and sub-barrier energies have been measured. It is found that standard theories
can reproduce the experimental data for the former three systems, but not simultaneously explain both fusion-fission excitation functions and fragment anisotropies for the rest systems.
In the latter case, the experiments provided the conclusive evidence of anomalous anisotropies of fission fragments in nearand sub-barrier FF reactions. The comparison of 11 B + 237 Np
and 16 O + 232 Th gave strict evidence of the entrance-channel dependence of fragment anisotropies. Based on the experimental
observation and the model presented by Døssing and Randrup,2
we put forward a new version model of preequilibrium fission3
to explain this anomaly.
2. Experimental Procedure
The experiments were carried out using the collimated 11 B,C, 16 O, and 19 F beams from HI-13 tandem accelerator at CIAE.
The 232 Th, 238 U, and 237 Np targets were about 350 µg/cm2 thickness. Fission fragments were detected by two X-Y position sensitive double grid avalanche counters (DGAC) with an active
area of 25 cm × 20 cm, placed at either side of the beam. The
distances from the centers of these counters to the target were
15 cm (forward counter) and 16 cm (backward counter), andthe corresponding angle coverages were 10◦ ≤ θLab ≤ 90◦ and−75◦ ≤ θLab ≤ −160◦ , respectively. According to the fragment
folding angle distributions,1 the FF events were successfully
separated from the TF events. A Si(Au) detector was placedat −20◦ relative to the beam direction as a monitor to detect theelastic scattering. The measured FF angular distributions werefitted and extrapolated to 180◦ in terms of the Legendre polynomial with the even terms up to P6 (cos θ), and the corresponding
fragment anisotropies, Aexp , were obtained. The FF cross sections were achieved by integrating the Legendre polynomial andnormalizing to the Rutherford scattering cross sections.
12

3. Experimental Results
3.1. Fusion-fission Excitation Functions. The experimental complete fusion-fission excitation functions for all six systems4 can be well reproduced by the CCDEF code calculations
considering the nuclear static deformations and inelastic channels couplings, as shown in Figure 1. For each bombarding
energy, the compound nuclei angular momentum distributions∗Corresponding author. E-mail: huan@iris.ciae.ac.cn. FAX: +8610-6935-7787.

 
σF (J) and their mean square angular momentum J 2 theory wereobtained from these calculations.
3.2. Anisotropies of FF Angular Distributions. The
anisotropy of the FF fragment angular distribution W (θ) is de◦). The anisotropy A is characterized by thefined as Aexp = WW(180(90◦ )approximate relation,
 2
JAtheory = 1 +.
(1)
4K02
In the calculation of the saddle-point transition statistic (SPTS)
model, the K distribution is Gaussian with a variance
K02 = Ieff Tsad /h̄2 ,(2)where the effective moment of inertia Ieff = I I⊥ /(I⊥ − I ), andI and I⊥ are the moments of inertia rotating around the symmetric and perpendicular axes of the nucleus at the saddle point,respectively. The K is the projection of angular momentum J
on the symmetric axis of fissioning nucleus. Tsad is the nucleartemperature at the saddle point, E + Q − B (J) − E 1/2c.m.
fnTsad =,(3)ACN /8where Q and B f (J) are the reaction Q value and the fission barrier height, respectively. The B f , I and I⊥ can be calculated
in terms of the rotating finite-range model (RFRM). ACN is themass number of the composite system and En the energy carriedaway by the pre-saddle fission neutrons.
The dependence of the ratio, Aexp /Atheory versus Ec.m. /VB for
all six systems4 is shown in Figure 2. Where Ec.m. is centerof-mass energy and VB the fusion barrier. In the figure, α isP,
the entrance-channel mass asymmetry defined as α = AATT −A+APαBG the Businaro-Gallone critical mass asymmetry and about
0.9 for the range of nuclei studied. The reaction systems withα in different side of αBG have different characters. It canbe seen from the figure that the Aexp are in general agreementwith Atheory for the α > αBG reaction systems of 11 B + 238 U,237 Np
and 12 C + 237 Np. But for the α < αBG systems, Aexp are obviously larger than Atheory at sub-barrier energy whereas trends toAtheory at energy above the barrier. Therefore, the present experiments have provided the conclusive evidence of anomalous
anisotropies for the α < αBG systems in near- and sub-barrier FF
reactions.
We compared the anisotropy data of 11 B + 237 Np (α = 0.91)
and 16 O + 232 Th (α = 0.87) both of which form the same compound nucleus 248 Cf at the same excitation energies but α ison the different side of αBG .3 The results show that there exists great difference in anisotropy between the two systems, asshown in Figure 3. The experiment provides a strict evidenceof the entrance-channel dependence of anisotropies in FF reactions. It indicates that non-compound-nucleus fission withc 2002 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 6/30/2002

100 J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

Zhang

Figure 1. Fusion-fission excitation functions for all six systems. The solid curves are the results of the CCDEF code calculations.

Figure 3. Comparison of anisotropy data of 11 B + 237 Np and 16 O + 232 Thsystems. The solid and dashed lines are the predictions of SPTS for
11B + 237 Np and 16 O + 232 Th, respectively.
Figure 2. Aexp /Atheory versus Ec.m. /VB for all six systems.

memory of the entrance channel for the systems with α < αBG isoriginally responsible for the anomalous anisotropies observedat near- and sub-barrier energies.
4. Preequilibrium Fission Model for Low AngularMomentum
As pointed out by Ramamurthy et al.,5 a characterized evidence of preequilibrium fission would show the entrancechannel dependence of fragment anisotropies for targetprojectile combination across the Businaro-Gallone ridge inmass degree of freedom. This is clearly verified by our experiments. We mentioned in our previous work3, 4 that, in somecases, the relaxation time of K degree of freedom may be larger
than fission lifetime. If the relaxation process of K is taken into
account, the variance of K distribution, σ2K can be expressed as,
σ2K = K02 1 − exp(−t/τK ) ,(4)where τK is the relaxation time of K degree of freedom and K02
the statistical equilibrium value of σ2K , assuming equilibrium atthe saddle point. Døssing and Randrup2 studied the dynamicalevolution of angular momentum in damping nuclear reactions
and derived the coupled equations which governed the evolution of K distribution. They have gotten the expression of τK
depending on the rotational frequency ωR . Under some approximations,3, 4 the variance equation for preequilibrium (quasi) fission was obtained,
σ2K (J) = K02 1 − exp(−gJ 2 ) ,(5)2Ieff ). The constant 2.238 MeV−1 waswhere g = 2.238I2 /(I⊥obtained by using Back’s experimental fragment anisotropy andmean square angular momentum data6 at Ec.m. = 94.1 MeV forthe 16 O + 232 Th fusion-fission reaction.
The Atheory values for the 16 O + 232 Th,238 U and 19 F + 232 Th systems with α < αBG were recalculated with eq 5 and comparedwith the experimental data. The results for other three systems
with α > αBG were calculated by the SPTS model. All the results are displayed in Figure 4. It is evident in the figure that thetheoretical predictions of the fragment anisotropies are in general agreement with the measured ones. Therefore, the anomalous anisotropies of fission fragments in near- and sub-barrier
FF reaction systems with α < αBG are successfully explained bymeans of our preequilibrium fission model.

Systematic Study of Anomalous Fragment Anisotropies

J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

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channel dependence for target-projectile combination across theBusinaro-Gallone ridge. Based on the observation and Døssing
and Randrup’s theory, we put forward a new version model ofpreequilibrium fission to solve the anomalous anisotropy problem.
Acknowledgement. This work was supported by the National Nature Science Fundation of China under Contract No.
19275607 and partly by the Major State Basic Research Development Program under Grand No. G200077400.
References

Figure 4. Same as Figure 2 but Aexp /Atheory are recalculated for theα < αBG systems.

5. Summary
In this work, we have successfully separated the FF and TF
events in terms of the fragment folding angle technique, andmeasured the FF cross sections and fragment angular distributions for the 11 B + 238 U,237 Np, 12 C + 237 Np, 16 O + 232 Th,238 U, and19F + 232 Th systems at near- and sub-barrier energies. All theexperimental fusion-fission excitation functions can be well reproduced by the coupled-channels theory. As for the fragment
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