Journal of Nuclear and Radiochemical Sciences,Vol. 3, No. 1, pp. 17–18, 2002

17Fusion Mechanism in Superheavy Mass Region
Y. Aritomo∗,a,ba
Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japanb
Flerov Laboratory of Nuclear Reactions, JINR, Dubna 141980, Russia
Received: December 19, 2001; In Final Form: April 30, 2002
The fusion-fission process for synthesis of superheavy elements is studied on the basis of the fluctuation-dissipation
dynamics. Recently at Dubna the experiments on the fission of superheavy nuclei were carried out and they presented
the fusion-fission cross section. We calculated the fusion-fission cross section of these systems and compared withthese experimental data.

0.7

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(1)

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Figure 1. The potential energy surface of liquid drop model withshell correction energy in nuclear deformation space for 292 114. Theabscissa and the ordinate denote the separation between two potential
center and the mass asymmetry, respectively. Symbols are given in text.
The arrows indicate the fusion and fission trajectory.

that the fission fragment of Pb and Sn corresponds to α ∼ 0.4 andα ∼ 0.12, respectively, which are indicated in Figure 1. In thecalculation, the mean trajectory at E ∗ = 33 MeV goes to quasifission at α ∼ 0.4 passing the outer-saddle point, and the fission
fragment Pb is produced. Actually, we can find such Pb fragments in the experimental data at the excitation energy.2
At Dubna the experiments on the fission of superheavy nuclei
in the reaction 48 Ca + 244 Pu were carried out and they present
the fusion-fission cross section of compound nuclei which is derived from the mass symmetric fission fragments (A/2 ± 20).2
The subsequent important question is whether all of the mass
symmetric fission fragments come from the compound nuclei or0,80,70,60,593.12 %CNQF0,40,36.80 %DQF

0,80,60,20,10,00,0 0,20.08 %

0,40,4 0,60,20,8 1,0z

1,2 1,41,6 1,8a

where µ0 denotes the reduced mass in the entrance channel andEcm denotes the incident energy in center-of-mass frame. Tl isthe barrier penetration coefficient of the lth partial wave throughthe potential barrier. Tl is calculated with parabolic approximation of the combined Coulomb potential and proximity potential. PCN is the probability of forming a compound nucleus in
the competition with quasi-fission.
In this work, we employ the Langevin equation.3 We adopt
the three-dimensional nuclear deformation space with the twocenter parametrization. As the three collective parameters tobe described by the Langevin equation, we treat z0 (distance
between two potential centers), δ (deformation), and α (massasymmetry of the colliding partner); α = (A1 − A2 )/(A1 + A2 ),where A1 and A2 denote the mass number of target and projectile,
respectively. Hydrodynamical inertia tensor is adopted with theWerner-Wheeler approximation for the velocity field, and thewall-and-window one-body dissipation is adopted for the dissipation tensor.
For the purpose of the calibration of our calculation, firstly
we analyze the fusion-fission cross section for the 48 Ca + 208 Pbreaction, where we can utilize the enough data of fusion-fission
cross section.2 The calculation results of the mass distribution of
the fission fragments and the excitation function of the fusionfission cross section give a good agreement with the experimental data beyond the Bass barrier region.4
Next, we present the analysis of the 48 Ca + 244 Pu reaction. We
assume that both shapes of the target and the projectile are spherical at touching point of the colliding system. We also take into
account the temperature dependent shell correction energy forthe potential energy surface.3, 4 For example, at T = 0, the potential energy surface in the reaction 48 Ca + 244 Pu is shown in
Figure 1. z = δ = α = 0 corresponds to a spherical compound
nucleus. The contact point in the reaction and saddle points aredenoted by (+) point and (×) points, respectively. The shadow
box denotes the fusion box which is defined as the inside of thefission saddle point, {z < 0.6, δ < 0.2, |α| < 0.25}. We can see∗E-mail: aritomo@nt.phys.s.u-tokyo.ac.jp.

0.8B.G.

deltπh̄2 ∞(2l + 1)Tl PCN ,2µ0 Ecm ∑l=0alpha

σCN =0.8

alpha

The productions of superheavy elements Z = 114 and Z = 116
were announced by Dubna group.1 Also at Dubna the experiments on the fission of superheavy nuclei in the reactions 48 Ca + 208 Pb, 48 Ca + 238 U, 48 Ca + 244 Pu, 48 Ca + 248 Cm, and58
Fe + 248 Cm were carried out.2 The mass and the total kinetic energy distributions of fission fragments of these reactions
were measured. In this paper, we focus on the fusion-fission
process and try to reproduce the experimental data by using afluctuation-dissipation model taking into account the competition between the fusion and quasi-fission. We estimate thefusion-fission cross section σCN as

0,0

Figure 2. The samples of the trajectory in the three dimensional coordinate space at E ∗ = 33 MeV in the reaction 48 Ca + 244 Pu.

c 2002 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 6/30/2002

18J.Nucl.Radiochem.Sci.,Vol. 3, No. 1, 2002

Aritomo(a)103102101100103102(b)
100

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cal.
Exp.

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Cross section (mb)

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1010-3-4

010-5

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10-60150

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190

200210Mass A50*E (MeV)Figure 3. (a) The cross section by the calculation and the experiment in the reactions 48 Ca + 244 Pu. Lines and scatters are given in the text. (b) The
mass distribution of the fission fragments in the reaction 48 Ca + 244 Pu. The calculations and experimental data are denoted by the histogram and closed
circles, respectively.

not. As the final results of the experiments the mass symmetricfission fragments are detected, but there exists two possibilities
where it comes from. One is that the mass symmetric fission
fragments come from the compound nuclei and the other is thatthey come from the quasi-fission. In Figure 1, paths are presented. We try to check them by using three-dimensional trajectory calculation with Langevin equation.
Figure 2 shows the samples of the trajectory in the three dimensional coordinate space at E ∗ = 33 MeV. Nuclear shapes at
each points are shown in Figure 2. The probability of mass
asymmetric fission fragments occupies 93.12%, which corresponds to quasi-fission process (QF). The trajectories which go
to mass symmetric fission region occupy 6.8% of all trajectories. However, almost all trajectories of mass symmetric fission
process do not enter the fusion box. They go to the direction ofthe large deformation of fragments. We call such trajectories as“deep quasi-fission process” (DQF).4 That is to say, the deep
quasi-fission process contributes to the yield of the mass symmetric fission fragments.4, 5 In fact, at E ∗ = 33 MeV, only 0.08%
of all trajectories can enter to the spherical region or fusion box,
which is denoted by CN in Figure 2.
Figure 3(a) shows the cross section by the calculation and theexperiment in the reactions 48 Ca + 244 Pu. The open and closed
diamonds denote the capture cross section σcap and the crosssection σA/2±20 which derived by the yield of the mass symmetric fission fragments with A/2 ± 20 in the experiments, respectively.2 The σA/2±20 by the calculation is denoted by the solidline. It presents very good agreement with the experimental
data. The calculated fusion-fission cross section σCN is denotedby the dashed line. It is calculated by the trajectory crossing
the three-dimensional fusion box mentioned above. The fusionfission cross section σCN by the calculation is one or two ordermagnitude smaller than the cross section σA/2±20 . We see thatthe cross section σA/2±20 includes the deep quasi-fission events.
Such an information is very important to estimate the evaporation residue cross section.
Furthermore we try to calculate other systems, the reactions
48Ca + 238 U and 48 Ca + 248 Cm. Also in these case, the calculation
for the cross section σA/2±20 agrees with experimental data well.
And we can see that the calculation for the fusion-fission crosssection σCN also is one or two order magnitude smaller than thecross section σA/2±20 .4 Figure 3(b) shows the mass distributionof the fission fragments in the reaction 48 Ca + 244 Pu. The calculation result shows that mass asymmetric fission fragments aredominant, which agree with the experimental data.
The author is grateful to Prof. M. Ohta, Prof. Zagrebaev, andProf. Yu. Ts. Oganessian for their helpful suggestion and valuable discussion through the present works.
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