Four-dimensional Langevin approach to low-energy nuclear fission of U236

Abstract

We developed a four-dimensional Langevin model which can treat the deformation of each fragment independently and applied it to low energy fission of 236 U, the compound system of the reaction n+ 235 U. The potential energy is calculated with the deformed two-center Woods-Saxon (TCWS) and the Nilsson type potential with the microscopic energy corrections following the Strutinsky method and BCS pairing. The transport coefficients are calculated by macroscopic prescriptions. It turned out that the deformation for the light and heavy fragments behaves differently, showing a sawtooth structure similar to that of the neutron multiplicities of the individual fragments ν(A). Furthermore, the measured total kinetic energy T KE(A) and its standard deviation are reproduced fairly well by the 4D Langevin model based on the TCWS potential in addition to the fission fragment mass distributions. The developed model allows a multi-parametric correlation analysis among, e.g., the three key fission observables, mass, TKE, and neutron multiplicity, which should be essential to elucidate several long-standing open problems in fission such as the sharing of the excitation energy between the fragments.

Nuclear Fission Dynamics: Past, Present, Needs, and Future

“…This behavior is apparently confirmed indirectly by experiments. In Langevin or Fokker-Planck [60][61][62][63][64][65], TDGCM [24,66], and scission-point [50][51][52][53] models the calculation of the FFs yields consider only a very limited range of nuclear shapes. In particular in such simulations one never introduces the octupole FF moments.…”

Unitary evolution with fluctuations and dissipation

“…In the quantum optics the dimensionally of the Hilbert spaces of interest is small ≈ O(1). In nuclear fission for example, the number of degrees of freedom in Langevin studies is between 2 to 5 [2][3][4][5]24], which would correspond in the case of a quantum treatment to wave functions of 2 to 5 spatial variables and density matrices depending on 4 to 10 spatial variables alone. The solution of a Lindblad equation, even after a reduction to a Monte Carlo wave function approach, in the case of nuclear fission becomes easily prohibitive numerically.…”

Accuracy of the analytical escape rate for a cusp barrier in the overdamping regime

“…The problem of the thermal decay of a metastable state (escape of a Brownian particle from a trap due to thermal fluctuations) is significant for different branches of natural sciences: in chemistry [1-3], biophysics [4,5], astrophysics [6], electronics [7,8], nuclear physics [9,10] etc. The decay rate is the principal characteristics of this process.…”