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Register a new userFission modes of 256Fm and 258Fm in a microscopic approach
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Authors
L. Bonneau
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A static microscopic study of potential-energy surfaces within the Skyrme-Hartree-Fock-plus-BCS model is carried out for the 256Fm and 258Fm isotopes with the goal of deducing some properties of spontaneous fission. The calculated fission modes are found to be in agreement with the experimentaly observed asymmetric-to-symmetric transition in the fragment-mass distributions and with the high- and low-total-kinetic-energy modes experimentally observed in 258Fm. Most of the results are similar to those obtained in macroscopic-microscopic models as well as in recent Hartree-Fock-Bogolyubov calculations with the Gogny interaction, with a few differences in their interpretations. In particular an alternative explanation is proposed for the low-energy fission mode of 258Fm.
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This article reviews how nuclear fission is described within nuclear density functional theory. In spontaneous fission, half-lives are the main observables and quantum tunnelling the essential concept, while in induced fission the focus is on fragment properties and explicitly time-dependent approaches are needed. The cornerstone of the current microscopic theory of fission is the energy density functional formalism. Its basic tenets, including tools such as the HFB theory, effective two-body effective nuclear potentials, finite-temperature extensions and beyond mean-field corrections, are presented succinctly. The EDF approach is often combined with the hypothesis that the time-scale of the large amplitude collective motion driving the system to fission is slow compared to typical time-scales of nucleons inside the nucleus. In practice, this hypothesis of adiabaticity is implemented by introducing (a few) collective variables and mapping out the many-body Schrodinger equation into a collective Schrodinger-like equation for the nuclear wave-packet. Scission configurations indicate where the split occurs. This collective Schrodinger equation depends on an inertia tensor that includes the response of the system to small changes in the collective variables and also plays a special role in the determination of spontaneous fission half-lives. A trademark of the microscopic theory of fission is the tremendous amount of computing needed for practical applications. In particular, the successful implementation of the theories presented in this article requires a very precise numerical resolution of the HFB equations for large values of the collective variables. Finally, a selection of the most recent and representative results obtained for both spontaneous and induced fission is presented with the goal of emphasizing the coherence of the microscopic approaches employed.
We describe the fission dynamics of $^{240}$Pu within an implementation of the Density Functional Theory (DFT) extended to superfluid systems and real-time dynamics. We demonstrate the critical role played by the pairing correlations, which even though are not the driving force in this complex dynamics, are providing the essential lubricant, without which the nuclear shape evolution would come to a screeching halt. The evolution is found to be much slower than previously expected in this fully non-adiabatic treatment of nuclear dynamics, where there are no symmetry restrictions and all collective degrees of freedom (CDOF) are allowed to participate in the dynamics.
With a help of the selfconsistent Hartree-Fock-Bogoliubov (HFB) approach with the D1S effective Gogny interaction and the Generator Coordinate Method (GCM) we incorporate the transverse collective vibrations to the one-dimensional model of the fission-barrier penetrability based on the traditional WKB method. The average fission barrier corresponding to the least-energy path in the two-dimensional potential energy landscape as function of quadrupole and octupole degrees of freedom is modified by the influence of the transverse collective vibrations along the nuclear path to fission. The set of transverse vibrational states built in the fission valley corresponding to a successively increasing nuclear elongation produces the new energy barrier which is compared with the least-energy barrier. These collective states are given as the eigensolutions of the GCM purely vibrational Hamiltonian. In addition, the influence of the collective inertia on the fission properties is displayed, and it turns out to be the decisive condition for the possible transitions between different fission valleys.
Recent progresses in the description of the latter stage of nuclear fission are reported. Dynamical effects during the descent of the potential towards scission and in the formation of the fission fragments are studied with the time-dependent Hartree-Fock approach with dynamical pairing correlations at the BCS level. In particular, this approach is used to compute the final kinetic energy of the fission fragments. Comparison with experimental data on the fission of 258Fm are made.
In this letter, we outline a methodology to calculate microscopically mass and charge distributions of spontaneous fission yields. We combine the multi-dimensional minimization of collective action for fission with stochastic Langevin dynamics to track the relevant fission paths from the ground-state configuration up to scission. The nuclear potential energy and collective inertia governing the tunneling motion are obtained with nuclear density functional theory in the collective space of shape deformations and pairing. We obtain a quantitative agreement with experimental data and find that both the charge and mass distributions in the spontaneous fission of 240Pu are sensitive both to the dissipation in collective motion and to adiabatic characteristics.
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