Starting from a quantum theory of dissipation for nuclear collective motion, the time-dependent generator coordinate method (TDGCM) is extended to allow for dissipation effects in the description of induced fission dynamics. The extension is based on a generalization of the GCM generating functions that includes excited states, and the resulting equation of motion in the collective coordinates and excitation energy. With the assumption of a narrow hamiltonian kernel, an expansion in a power series in collective momenta leads to a Schrödinger-like equation that explicitly includes a dissipation term, proportional to the momentum of the statistical wave function. An illustrative calculation is performed for induced fission of $^{228}$Th. The three-dimensional model space includes the axially-symmetric quadrupole and octupole shape variables, and the nuclear temperature. When compared to data for photo-induced fission of $^{228}$Th, the calculated fission yields demonstrate the important role of the additional term in the hamiltonian that explicitly takes into account the dissipation of energy of collective motion into intrinsic degrees of freedom.
Nuclear fission is still one of the most complex physical processes we can observe in nature due to the interplay of macroscopic and microscopic nuclear properties that decide the result. An example of this coupling is the presence of nuclear dissipation as an important ingredient that contributes to drive the dynamics and has a clear impact on the time of the process. However, different theoretical interpretations, and scarce experimental data make it poorly understood. In this letter, we present the first experimental determination of the dissipation energy in fission as a function of the fr…
The claim put forward in a recent paper by B. Jurado, K.-H. Schmidt and J. Benlliure that the transient effect of nuclear fission may be described simply as a relaxation process in the upright oscillator around the potential minimum is refuted. Some critical remarks on the relevance of this effect in general are added.
This work presents a microscopic study of dissipation in fission dynamical evolutions with the time-dependent Hartree-Fock+BCS method in terms of energy dependence and pairing dependence. The friction coefficients and dissipation energies are extracted by mapping the symmetric fission process of $^{258}$Fm into a classical equation of motion. Density-constrained calculations are used to obtain the dynamical potential. The obtained friction coefficients have a strong dependence of deformations, and averagely match the coefficients adopted in statistical models. The dissipation indeed increase w…
Semi-analytical expressions are suggested for the temperature dependence of those combinations of transport coefficients which govern the fission process. This is based on experience with numerical calculations within the linear response approach and the locally harmonic approximation. A reduced version of the latter is seen to comply with Kramers' simplified picture of fission. It is argued that for variable inertia his formula has to be generalized, as already required by the need that for overdamped motion the inertia must not appear at all. This situation may already occur above T=2 MeV, w…
We present the TDDFT+Langevin model that incorporates microscopic time-dependent density function theory (TDDFT) with macroscopic Langevin model. By extracting the energy-dependent dissipation effect from the TDDFT dynamics, quantum effects are introduced to the Langevin-type stochastic fission analysis. In this paper, by means of Skyrme nuclear effective interactions, the energy-dependent friction coefficients to be used in Langevin calculations are provided individually for 25 fission nuclei chosen from uranium, plutonium, curium, californium, and fermium isotopes. The validity of the energy…
Collective mass tensors derived in the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method are employed in a study of induced fission dynamics. Together with a collective potential determined in deformation-constrained self-consistent mean-field calculations based on nuclear energy density functionals, the mass tensors specify the collective Hamiltonian that governs the time evolution of the nuclear wave function from an initial state at equilibrium deformation, up to scission and the formation of fission fragments. In an illustrative calculation of l…
We solve the time-dependent Dirac equation for a muon which is initially bound to a fissioning actinide nucleus. The computations are carried out on a 3-D cartesian lattice utilizing the Basis-Spline collocation method. The muon dynamics is sensitive to the nuclear energy dissipation between the outer fission barrier and the scission point. From a comparison with experimental data we find a dissipated energy of about 10 MeV and a fission time delay due to friction of order $2 \times 10^{-21}$ s.
Following the formation of an excited muonic atom, inner shell transitions may proceed without photon emission by inverse internal conversion, i.e. the muonic excitation energy is transferred to the nucleus. In actinides, the 2p -> 1s and the 3d -> 1s muonic transitions result in excitation of the nuclear giant dipole and giant quadrupole resonances, respectively, which act as doorway states for fission. The nuclear excitation energy is typically 6.5 - 10 MeV. Because the muon lifetime is long compared to the timescale of prompt nuclear fission, the motion of the muon in the Coulomb field of t…
Evaporation residue cross-sections are calculated in a dynamical description of nuclear fission in the framework of the Langevin equation coupled with statistical evporation of light particles. A theoretical model of one-body nuclear friction which was developed earlier, namely the chaos-weighted wall formula, is used in this calculation for the 224Th nucleus. The evaporation residue cross-section is found to be very sensitive to the choice of nuclear friction. The present results indicate that the chaotic nature of the single-particle dynamics within the nuclear volume may provide an explanat…
A model is developed to calculate the total kinetic energy (TKE) distribution of fission fragments in the framework of the time-dependent generator coordinate method (TDGCM), extended to include dissipation effects in the description of induced fission dynamics. Starting from an expression for the dissipative term in the GCM Hamiltonian that determines the time evolution of a statistical collective wave function, derived in the first part of this work, the integrated flux of the probability current through the scission hyper-surface can be computed at different temperatures. The kinetic energy…
Fragment mass distributions from the fission of U and Pu isotopes at low excitation energies are studied using a dynamical model based on the fluctuation-dissipation theorem formulated as Langevin equations. The present calculations reproduced the overall trend of the asymmetric mass distribution without parameter adjustment for the first time using the Langevin approach. The Langevin trajectories show a complicated time evolution on the potential surface, which causes the time delay of fission, showing that dynamical treatment is vital. It was found that the shell effect of the potential ener…
The general problem of dissipation in macroscopic large-amplitude collective motion and its relation to energy diffusion of intrinsic degrees of freedom of a nucleus is studied. By applying the cranking approach to the nuclear many body system, a set of coupled dynamical equations for the collective classical variables and the quantum mechanical occupancies of the intrinsic nuclear states is derived. Different dynamical regimes of the intrinsic nuclear motion and its consequences on time properties of collective dissipation are discussed. The approach is applied to the descant of the nucleus f…
Decay of $^{210}$Po compound nucleus formed in light and heavy-ion induced fusion reactions has been analyzed simultaneously using a consistent prescription for fission barrier and nuclear level density incorporating shell correction and its damping with excitation energy. Good description of all the excitation functions have been achieved with a fission barrier of 21.9 $\pm$ 0.2 MeV. For this barrier height, the predicted statistical pre-fission neutrons in heavy-ion fusion-fission are much smaller than the experimental values, implying the presence of dynamical neutrons due to dissipation ev…
Since its beginnings, fission theory has asumed that low-energy induced fission takes place through transition-state channels at the barrier tops. Neverthess, up to now there is no microscopic theory applicable to those conditions. We suggest that modern reaction theory is suitable for this purpose, and propose a methodology based on a configuration-interaction framework using the Generator Coordinate Method (GCM). Simple reaction-theoretic models are constructed with the Gaussian Overlap Approximation (GOA) to parameterize both the dynamics within the channels and their incoherent couplings t…
In order to describe heavy-ion fusion reactions around the Coulomb barrier with an actinide target nucleus, we propose a model which combines the coupled-channels approach and a fluctuation-dissipation model for dynamical calculations. This model takes into account couplings to the collective states of the interacting nuclei in the penetration of the Coulomb barrier and the subsequent dynamical evolution of a nuclear shape from the contact configuration. In the fluctuation-dissipation model with a Langevin equation, the effect of nuclear orientation at the initial impact on the prolately defor…
Energy dissipative processes play a key role in how quantum many-body systems dynamically evolve towards equilibrium. In closed quantum systems, such processes are attributed to the transfer of energy from collective motion to single-particle degrees of freedom; however, the quantum many-body dynamics of this evolutionary process are poorly understood. To explore energy dissipative phenomena and equilibration dynamics in one such system, an experimental investigation of deep-inelastic and fusion-fission outcomes in the $^{58}$Ni+$^{60}$Ni reaction has been carried out. Experimental outcomes ha…
The role of dynamical pairing in induced fission dynamics is investigated using the time-dependent generator coordinate method in the Gaussian overlap approximation, based on the microscopic framework of nuclear energy density functionals. A calculation of fragment charge yields for induced fission of $^{228}$Th is performed in a three-dimensional space of collective coordinates that, in addition to the axial quadrupole and octupole intrinsic deformations of the nuclear density, also includes an isoscalar pairing degree of freedom. It is shown that the inclusion of dynamical pairing has a pron…
Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with a Kramers-modified statistical model which takes into account the collective motion of the system about the ground state; the temperature dependence of the location of fission transition points; and the orientation degree of freedom. We see no evidence to suggest that the nuclear viscosity departs from the surface-plus-window dissipation model. The strong increase in the nuclear viscosity above a temperature of ~1 MeV deduced by others is an artifact generated by an inadequate fission model.
Random walks on five-dimensional potential-energy surfaces were recently found to yield fission-fragment mass distributions that are in remarkable agreement with experimental data. Within the framework of the Smoluchowski equation of motion, which is appropriate for highly dissipative evolutions, we discuss the physical justification for that treatment and investigate the sensitivity of the resulting mass yields to a variety of model ingredients, including in particular the dimensionality and discretization of the shape space and the structure of the dissipation tensor. The mass yields are fou…
The dynamics of low-energy induced fission is explored using a consistent microscopic framework that combines the time-dependent generator coordinate method (TDGCM) and time-dependent nuclear density functional theory (TDDFT). While the former presents a fully quantum mechanical approach that describes the entire fission process as an adiabatic evolution of collective degrees of freedom, the latter models the dissipative dynamics of the final stage of fission by propagating the nucleons independently toward scission and beyond. By combining the two methods, based on the same nuclear energy den…
Low-energy positive and negative parity collective states in the equilibrium minimum, and the dynamics of induced fission of actinide nuclei are investigated in a unified theoretical framework based on the generator coordinate method (GCM) with the Gaussian overlap approximation (GOA). The collective potential and inertia tensor, both at zero and finite temperature, are computed using the self-consistent multidimensionally constrained relativistic mean field (MDC-RMF) model, based on the energy density functional DD-PC1. Pairing correlations are treated in the BCS approximation with a separabl…
Presence of closed proton and/or neutron shells causes deviation from macroscopic properties of nuclei which are understood in terms of the liquid drop model. It is important to investigate experimentally the stabilizing effects of shell closure, if any, against fission. This work aims to investigate probable effects of proton shell ($Z = 82$) closure in the compound nucleus, in enhancing survival probability of the evaporation residues formed in heavy ion-induced fusion-fission reactions. Evaporation residue cross sections have been measured for the reactions $^{19}$F+$^{180}$Hf, $^{19}$F+$^{…
Neutron- and proton-induced fission cross-sections of separated isotopes of tungsten (182W, 183W, 184W, and 186W) and natural tungsten relative to 209Bi have been measured in the incident nucleon energy region 50-200 MeV using fission chambers based on thin-film breakdown counters (TFBC) at quasi-monoenergetic neutrons from the 7Li(p,n) reaction and at the proton beams of The Svedberg Laboratory (TSL), Uppsala University (Uppsala, Sweden). The preliminary experimental data are presented in comparison with the recent data for nuclei in the lead-bismuth region, as well as with predictions by the…
This work attempts to overcome the existing inconsistencies in modelling decay of fissile nucleus by inclusion of important physical effects in the model and through a systematic analysis of a large set of data over a wide range of CN mass (ACN). The model includes shell effect in the level density (LD) parameter, shell correction in the fission barrier, effect of the orientation degree of freedom of the CN spin (Kor), collective enhancement of level density (CELD) and dissipation in fission. Input parameters are not tuned to reproduce observables from specific reaction(s) and the reduced diss…
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 bo…
The time-dependent generator coordinate method with the gaussian overlap approximation (TDGCM+GOA) formalism is applied to describe the fission of $^{252}$Cf. We perform analysis of fission from the initial states laying in the energetic range from the ground state to the state located 4 MeV above the fission barrier. The fission fragment mass distributions, obtained for different parity, energy of levels and types of mixed states, are calculated and compared with experimental data. The impact of the total time of wave packet propagation on the final results is studied as well. The weak depend…
The chaos weighted wall formula developed earlier for systems with partially chaotic single particle motion is applied to large amplitude collective motions similar to those in nuclear fission. Considering an ideal gas in a cavity undergoing fission-like shape evolutions, the irreversible energy transfer to the gas is dynamically calculated and compared with the prediction of the chaos weighted wall formula. We conclude that the chaos weighted wall formula provides a fairly accurate description of one body dissipation in dynamical systems similar to fissioning nuclei. We also find a qualitativ…
Excited nuclear fragments are emitted during nuclear fission. The de-excitation of these fission fragments takes place as sequential emission of neutrons followed by photons. A correlation between neutron and photon multiplicities accompanying fission is thus expected. Fission event generators based on established statistical nuclear physics models predict a negative event-by-event correlation in neutron-photon multiplicity. A survey of published experimental results of an event-by-event covariance between the neutron and photon multiplicities emitted following the spontaneous fission of $^{25…
A statistical model description of heavy ion induced fusion-fission reactions is presented where shell effects, collective enhancement of level density, tilting away effect of compound nuclear spin and dissipation are included. It is shown that the inclusion of all these effects provides a consistent picture of fission where fission hindrance is required to explain the experimental values of both pre-scission neutron multiplicities and evaporation residue cross-sections in contrast to some of the earlier works where a fission hindrance is required for pre-scission neutrons but a fission enhanc…
Spontaneous fission barriers, quadrupole inertia, and zero-point quadrupole-energy corrections are calculated for 252,256,258Fm in the framework of the self-consistent Skyrme-Hartree-Fock+BCS theory. Two ways of computing dynamical inertia are employed: the Gaussian Overlap Approximation to the Generator Coordinate Method and cranking ansatz. The Skyrme results are compared with those of the Gogny-Hartree-Fock-Bogolyubov model.
\noindent\textbf{Background:} While many phenomenological models for nuclear fission have been developed, a microscopic understanding of fission has remained one of the most challenging problems in nuclear physics. \noindent\textbf{Purpose:} We investigate an applicability of the generator coordinate method (GCM) as a microscopic theory for cluster radioactivities of heavy nuclei, which can be regarded as a fission with large mass asymmetry, that is, a phenomenon in between fission and $α$-decays. \noindent\textbf{Methods:} Based on the Gamow theory, we evaluate the preformation probability of…
An outstanding problem in the theory of nuclear fission is understanding the Hamiltonian dynamics at the scission point. Here we apply the Generator Coordinate Method to calculate decay widths for pre-scission configurations into the two-fragment continuum. Transitions that are allowed under diabatic dynamics can have widths up to several MeV. For non-diabatic decays through the pairing interaction, typical widths to a specific final state channel are 2-3 orders of magnitude smaller. The nucleus U-236 is taken as a representative example in the calculations.
The collective dynamics of low energy fission in 238U is described within a time-dependent formalism based on the Gaussian Overlap Approximation of the time-dependent Generator Coordinate Method. The intrinsic deformed configurations of the nucleus are determined from the self-consistent Hartree-Fock-Bogoliubov procedure employing the effective force D1S with constraints on the quadrupole and octupole moments. Fragment kinetic energy and mass distributions are calculated and compared with experimental evaluations. The effect of the collective dynamics along the fission paths and the influence …
Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and…
Presently, it is well established that fission of excited nuclei is a dynamical process being a subject of fluctuations and dissipation. In the literature, there are indications that, at the compact nucleus shapes, the strength of nuclear friction is significantly reduced in comparison with the prediction of the one-body approach. Thus, one can expect that at small deformations the nuclear fission process occurs in the so-called "energy diffusion regime". The purpose of our present work is to compare an approximate analytical formula for the fission rate in this regime with the quasistationary…
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…
Predicting the properties of neutron-rich nuclei far from the valley of stability is one of the major challenges of modern nuclear theory. In heavy and superheavy nuclei, a difference of only a few neutrons is sufficient to change the dominant fission mode. A theoretical approach capable of predicting such rapid transitions for neutron-rich systems would be a valuable tool to better understand r-process nucleosynthesis or the decay of super-heavy elements. In this work, we investigate for the first time the transition from asymmetric to symmetric fission through the calculation of primary fiss…
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 so…
The non-perturbative method to compute Adiabatic Time Dependent Hartree Fock Bogoliubov (ATDHFB) collective inertias is extended to the Generator Coordinate Method (GCM) including the case of density dependent forces. The two inertias schemes are computed along the fission path of the $^{234}$U and compared with the perturbative results. We find that the non-perturbative schemes predict very similar collective inertias with a much richer structure than the one predicted by perturbative calculations. Moreover, the non-perturbative inertias show an extraordinary similitude with the exact GCM ine…
The fission of highly excited compound nuclei formed in heavy ion induced fusion reactions has emerged as a topic of considerable interest in the recent years. Dissipative dynamical models based on the Langevin equation were developed and were applied successfully for fission dynamics of highly excited heavy nuclei. However, Wall Friction(WF), the standard version of nuclear friction when incorporated in the Langevin dynamical model was not able to reproduce simultaneously experimental data for both prescission neutron multiplicity and fission probability. Consequently, an empirical reduction …
A brief description of the IntraNuclear cascade, preequilibrium, evaporation, fission, coalescence, and Fermi breakup models used by the last versions of our CEM and LAQGSM event generators is presented, with a focus on our latest development of all these models. The recently developed "S" and "G" versions of our codes, that consider multifragmentation of nuclei formed after the preequilibrium stage of reactions when their excitation energy is above 2A MeV using the Statistical Multifragmentation Model (SMM) code by Botvina et al. ("S" stands for SMM) and the fission-like binary-decay model GE…
The time-dependent energy density functional with pairing allows to describe a large variety of phenomena from small to large amplitude collective motion. Here, we briefly summarize the recent progresses made in the field using the TD-BCS approach. A focus is made on the mapping of the microscopic mean-field dynamic to the macroscopic dynamic in collective space. A method is developed to extract the collective mass parameter from TD-EDF. Illustration is made on the fission of $^{258}$Fm. The collective mass and collective momentum associated to quadrupole deformation including non-adiabatic ef…
A theory of the competition between fusion and quasi-fission in a heavy fusing system is proposed, which is based on a master equation and the two-center shell model. Fusion and quasi-fission arise from a diffusion process in an ensemble of nuclear shapes, each of which evolves towards the thermal equilibrium. The master equation describes the diffusion of the nuclear shapes due to quantum and thermal fluctuations. Other crucial physical effects like dissipation, ground-state shell effects, diabatic effects and rotational effects are also incorporated into the theory. The fusing system moves i…
Static and dynamic aspects of the fission process of $^{226}$Th are analyzed in a self-consistent framework based on relativistic energy density functionals. Constrained relativistic mean-field (RMF) calculations in the collective space of axially symmetric quadrupole and octupole deformations, based on the energy density functional PC-PK1 and a $δ$-force pairing, are performed to determine the potential energy surface of the fissioning nucleus, the scission line, the single-nucleon wave functions, energies and occupation probabilities, as functions of deformation parameters. Induced fission d…
A description of the IntraNuclear Cascade (INC), preequilibrium, evaporation, fission, coalescence, and Fermi breakup models used by the latest versions of our CEM03.03 and LAQGSM03.03 event generators is presented, with a focus on our most recent developments of these models. The recently developed "S" and "G" versions of our codes, that consider multifragmentation of nuclei formed after the preequilibrium stage of reactions when their excitation energy is above 2A MeV using the Statistical Multifragmentation Model (SMM) code by Botvina et al. ("S" stands for SMM) and the fission-like binary-…
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 a…
We present a description of nuclear spontaneous fission, and generally of quantum tunneling, in terms of instantons - periodic imaginary-time solutions to time-dependent mean-field equations - that allows for a comparison with more familiar and used generator coordinate (GCM) and adiabatic time-dependent Hartree-Fock (ATDHF) methods. It is shown that the action functional whose value for the instanton is the quasiclassical estimate of the decay exponent fulfils the minimum principle when additional constraints are imposed on trial fission paths. In analogy with mechanics, these are conditions …
