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Register a new userMicroscopic modeling of mass and charge distributions in the spontaneous fission of 240Pu
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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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We show that the total kinetic energy (TKE) of nuclei after the spontaneous fission of $^{258}$Fm can be well reproduced using simple assumptions on the quantum collective phase-space explored by the nucleus after passing the fission barrier. Assuming energy conservation and phase-space exploration according to the stochastic mean-field approach, a set of initial densities is generated. Each density is then evolved in time using the nuclear time-dependent density-functional theory. This approach goes beyond mean-field by allowing spontaneous symmetry breaking as well as a wider dynamical phase-space exploration leading to larger fluctuations in collective space. The total kinetic energy and mass distributions are calculated. New information on the fission process: fluctuations in scission time, strong correlation between TKE and collective deformation of daughter nuclei as well as pre- and post-scission particle emission, are obtained.
Calculations are presented for the time evolution of $^{240}$Pu from the proximity of the outer saddle point until the fission fragments are well separated, using the time-dependent density functional theory extended to superfluid systems. We have tested three families of nuclear energy density functionals and found that all functionals exhibit a similar dynamics: the collective motion is highly dissipative and with little trace of inertial dynamics, due to the one-body dissipation mechanism alone. This finding justifies the validity of using the overdamped collective motion approach and to some extent the main assumptions in statistical models of fission. This conclusion is robust with respect to the nuclear energy density functional used. The configurations and interactions left out of the present theory framework only increase the role of the dissipative couplings. An unexpected finding is varying the pairing strength within a quite large range has only minor effects on the dynamics. We find notable differences in the excitation energy sharing between the fission fragments in the cases of spontaneous and induced fission. With increasing initial excitation energy of the fissioning nucleus more excitation energy is deposited in the heavy fragment, in agreement with experimental data on average neutron multiplicities.
Accurate knowledge of fission fragment yields is an essential ingredient of numerous applications ranging from the formation of elements in the r-process to fuel cycle optimization for nuclear energy. The need for a predictive theory applicable where no data is available is an incentive to develop a fully microscopic approach to fission dynamics. In this work, we calculate the pre-neutron emission charge and mass distributions of the fission fragments formed in the neutron-induced fission of 239Pu using a microscopic method based on nuclear energy density functional (EDF) method, where large amplitude collective motion is treated adiabatically using the time dependent generator coordinate method (TDGCM) under the Gaussian overlap approximation (GOA). Fission fragment distributions are extracted from the flux of the collective wave packet through the scission line. We find that the main characteristics of the fission charge and mass distributions can be well reproduced by existing energy functionals even in two-dimensional collective spaces. Theory and experiment agree typically within 2 mass units for the position of the asymmetric peak. As expected, calculations are sensitive to the structure of the initial state and the prescription for the collective inertia. We emphasize that results are also sensitive to the continuity of the collective landscape near scission. Our analysis confirms that the adiabatic approximation provides an effective scheme to compute fission fragment yields. It also suggests that, at least in the framework of nuclear DFT, three-dimensional collective spaces may be a prerequisite to reach 10% accuracy in predicting pre-neutron emission fission fragment yields.
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.
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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