Fission rate of excited nuclei at variable friction in the energy diffusion regime (original) (raw)

The influence of the boundary conditions on characteristics of nuclear fission

arXiv (Cornell University), 2023

In this paper, using a quasi-classical statistical approach based on the Langevin equation, we simulate the fission dynamics of selected even-even U, Pu, Cm, Cf and Fm actinide nuclei. As a preparatory part of the work, before solving the Langevin equations, the determination of transport parameters such as inertia and friction tensors within the hydrodynamic approach is performed. Potential energy surfaces are calculated within a macroscopic-microscopic approach in a threedimensional space of deformation parameters defined within the Fourier decomposition of the surface radius function in cylindrical coordinates. Using the Lublin-Strasbourg drop model, Strutinsky shell correction and BCS-like pairing energy model with the projection onto good particle number, we calculate the nuclear total potential energy surfaces (PES). The restoration of the particle number in the superfluid approach is realized within the Generator Coordinate Method (GCM) with the so called Gaussian Overlap Approximation (GOA). The final study is concerned with the effect of the starting point of the stochastic Langevin trajectory on its time evolution and, more importantly, the conditions for judging whether such a trajectory for a given time moment describes an already passed fission nucleus or not. Collecting a large number of such stochastic trajectories allows us to assess the resulting fragment mass distributions, which appear to be in good agreement with their experimental counterparts for light and intermediate actinides. More serious discrepancies are observed for single isotopes of californium and fermium. II. QUASI-CLASSICAL STOCHASTIC LANGEVIN APPROACH The exact determination of the relevant fission process deformation parameters and the collective inertia

Nuclear fission: The “onset of dissipation” from a microscopic point of view

2001

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, where the rate is determined by the Smoluchowski equation. Consequently, comparison with experimental results do not give information on the effective damping rate, as often claimed, but on a special combination of local stiffnesses and the friction coefficient calculated at the barrier.

Nuclear fission with diffusive dynamics

Physical Review C, 1992

We investigate the dynamics of nuclear fission, assuming purely diffusive motion up to the saddle point. The resulting Smoluchowski equation is solved for conditions appropriate to the ' 0+' Nd~'"Er reaction at 207 MeV. The solution is characterized by an equilibration time~0 for the system to reach steady state, and the fission decay rate in steady state, A. We find that the equilibration time~0 plays a very small role in determining the number of prescission neutrons. The diffusion coefficient extracted from the experimental data is larger than the theoretical in the work of Bush, Bertsch, and Brown by a factor of 5-11.

Velocity fluctuations of fission fragments

International Journal of Modern Physics E, 2016

We propose event by event velocity fluctuations of nuclear fission fragments as an additional interesting observable that gives access to the nuclear temperature in an independent way from spectral measurements and relates the diffusion and friction coefficients for the relative fragment coordinate in Kramers-like models (in which some aspects of fission can be understood as the diffusion of a collective variable through a potential barrier). We point out that neutron emission by the heavy fragments can be treated in effective theory if corrections to the velocity distribution are needed.

Fission of highly excited nuclei investigated in complete kinematic measurements

Fission is an extremely complex mechanism that requires a dynamical approach to describe the evolution of the process in terms of intrinsic and collective excitations of the nuclear constituents. In order to determine these effects a complex experimental setup was mounted at GSI, which allowed us for the first time the full identification in charge and mass of all fission fragments thanks to a magnetic separation and the use of the inverse kinematic technique. Moreover, we also measured the neutron multiplicities and the light-charged particles emitted in coincidence with fission. These complete kinematic measurements will be used to define sensitive observables to dissipative and transient effects in fission. In this manuscript we present the first results for the total fission cross sections. Reactions p+ Bychenkov V.S. Konshin V. A. Kotov A.A. Brandt R. Hagebo E. Gloris M. Pb+p 208 Reactions This work

Critical insight into the influence of the potential energy surface on fission dynamics

Physical Review C, 2011

The present work is dedicated to a careful investigation of the influence of the potential energy surface on the fission process. The time evolution of nuclei at high excitation energy and angular momentum is studied by means of three-dimensional Langevin calculations performed for two different parametrizations of the macroscopic potential: the Finite Range Liquid Drop Model (FRLDM) and the Lublin-Strasbourg Drop (LSD) prescription. Depending on the mass of the system, the topology of the potential throughout the deformation space of interest in fission is observed to noticeably differ within these two approaches, due to the treatment of curvature effects. When utilized in the dynamical calculation as the driving potential, the FRLDM and LSD models yield similar results in the heavy-mass region, whereas the predictions can be strongly dependent on the PES for medium-mass nuclei. In particular, the mass, charge and total kinetic energy distributions of the fission fragments are found to be narrower with the LSD prescription. The influence of critical model parameters on our findings is carefully investigated. The present study sheds light on the experimental conditions and signatures well suited for constraining the parametrization of the macroscopic potential. Its implication regarding the interpretation of available experimental data is briefly discussed.

Investigating the fission dynamics of the following neutron shell closed nuclei within a stochastic dynamical approach: 210Po, 212Rn, and 213Fr*

Chinese Physics C, 2022

Dissipative dynamics of nuclear fission is a well confirmed phenomenon described either by a Kramers-modified statistical model or by a dynamical model employing the Langevin equation. Though dynamical models as well as statistical models incorporating fission delay are found to explain the measured fission observables in many studies, it nonetheless shows conflicting results for shell closed nuclei in the mass region 200. Analysis of recent data for neutron shell closed nuclei in excitation energy range 40−80 MeV failed to arrive at a satisfactory description of the data and attributed the mismatch to shell effects and/or entrance channel effects, without reaching a definite conclusion. In the present work we show that a well established stochastic dynamical code simultaneously reproduces the available data of pre-scission neutron multiplicities, fission and evaporation residue excitation functions for neutron shell closed nuclei 210 Po and 212 Rn and their isotopes 206 Po and 214,216 Rn without the need for including any extra shell or entrance channel effects. The calculations are performed by using a phenomenological universal friction form factor with no ad-hoc adjustment of model parameters. However, we note significant deviation, beyond experimental errors, in some cases of Fr isotopes.

Effects of transients on particle emission prior to fission in a transport description of the fission process

Nuclear Physics A, 1984

Nuclear fission is described as a transport process over the fission barrier. The fission width is obtained from the time dependent probability flow over the saddle point. Its relation tith the Bohr-Wheeler formula is discussed in the case where asymptotically in time a quasistationary flow exists. Inthe converse situation the whole fission process becomes a transient phenomenon. In both cases the duration time T of the transient process is defined and semi-quantitative analytical estimates are derived and compared with direct numerical evaluations. It is shown that the effect of the finiteness of T has direct consequences on the neutron multiplicities resulting from a cascade de-excitation of a compound nucleus in a situation where the current would reach asymptotically a quasistationary regime at all steps of the de-excitation chain. With respect to predictions of the statistical model, enhancement of these multiplicities by factors 2 to 5 are obtained in the excitation energy range 100 to 200 MeV depending on the value of the nuclear friction 8.

Dynamical study of fission process and estimation of prescission neutron multiplicity

Physical Review C, 1998

The dynamics of fission has been studied by solving Euler-Lagrange equations with dissipation generated through one and two body nuclear friction. The average kinetic energies of the fission fragments, prescission neutron multiplicities and the mean energies of the prescission neutrons have been calculated and compared with experimental values and they agree quite well. A single value of friction coefficient has been used to reproduce the experimental data for both symmetric and asymmetric splitting of the fissioning systems over a wide range of masses and excitation energies. It has been observed that a stronger friction is required in the saddle to scission region as compared to that in the ground state to saddle region.