Fusion Mechanism in Superheavy Mass Region

Abstract

58 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 a fluctuation-dissipation model taking into account the competition between the fusion and quasi-fission. We estimate the fusion-fission cross section σCN as σCN = π¯ h 2 2µ0Ecm ∞ ∑=0 (2l+ 1)TlPCN , (1) where µ0 denotes the reduced mass in the entrance channel and Ecm denotes the incident energy in center-of-mass frame. Tl is the barrier penetration coefficient of the lth partial wave through the 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 to be described by the Langevin equation, we treat z0 (distance between two potential centers), δ (deformation), and α (mass asymmetry 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 the Werner-Wheeler approximation for the velocity field, and the wall-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 Pb reaction, 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 for the 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 are denoted by (+) point and (×) points, respectively. The shadow box denotes the fusion box which is defined as the inside of the fission saddle point, {z< 0.6, δ< 0.2, |α|< 0.25}. We can see