This article pertains to the most newly-discovered and most sensational mode of transmutation, in which the entry of a neutron into a massive atom-nucleus brings about an internal explosion in which the nucleus is “fissured” or divided into two fragments which share the total mass and charge between them in nearly equal proportions, (In all other modes of transmutation except those affecting the very lightest elements, the division is into fragments of very unequal mass and charge.) The conversion of rest-mass into kinetic energy, or (as is more commonly said) the release of energy, is unprecedented in scale. A multitude of radioactive bodies, many hitherto unknown, is formed; and there is spontaneous emission of fresh neutrons in great quantities, possibly sufficient to convert the process once initiated into a self-perpetuating one under realizable conditions.

http://ieeexplore.ieee.org/iel7/6731005/6769463/06769469.pdf

Nuclear fission

A thorough evaluation of stochastic resonance with tuning system parameters in bistable systems is presented as a nonlinear signal processor. It is shown that the output signal-to-noise ratio obtained by adjusting systems parameters can exceed that by tuning noise intensity, especially when the input noise intensity is already beyond the resonance region. It is demonstrated that the theory and the method presented here can markedly improve the output signal-to-noise ratio, and minimize phase lag as well as the distortion of the system output signal with multi-frequency.

Stochastic resonance with tuning system parameters: the application of bistable systems in signal processing

There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical avenues were the subject of a workshop held at the University of York in October 2019; this report summarises its findings and recommendations.

/pdf/future-of-nuclear-fission-theory-2xcrzztnh7.pdf

Future of nuclear fission theory

We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.

https://trace.tennessee.edu/cgi/viewcontent.cgi?article=2203&context=utk_graddiss

Surface symmetry energy of nuclear energy density functionals

A four-dimensional dynamical model based on Langevin equations was developed and applied to calculate a wide set of experimental observables for the reactions ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}\ensuremath{\rightarrow}{}^{224}\mathrm{Th}$ and ${}^{16}\mathrm{O}+{}^{232}\mathrm{Th}\ensuremath{\rightarrow}{}^{248}\mathrm{Cf}$ over a wide range of excitation energy. The fusion-fission and evaporation residue cross sections, fission fragment mass-energy distribution parameters, prescission neutron multiplicities, and anisotropy of angular distribution of fission fragments could be reasonably reproduced using a modified one-body mechanism for nuclear friction with a reduction coefficient of the contribution from a wall formula ${k}_{s}\ensuremath{\simeq}0.25$ and a dissipation coefficient for the orientation degree of freedom ($K$ coordinate) ${\ensuremath{\gamma}}_{K}\ensuremath{\simeq}$ 0.077 ${(\mathrm{MeV}\phantom{\rule{0.16em}{0ex}}\mathrm{zs})}^{\ensuremath{-}1/2}$. Inclusion of the $K$ coordinate into calculation of potential energy changes the stiffness of the nucleus with respect to mass asymmetry coordinate for the values of $K\ensuremath{\ne}0$ and results in a shift of the Businaro-Gallone point towards larger ${Z}^{2}/A$ values. The experimental data on the fission fragment mass-energy distribution parameters together with mean prescission neutron multiplicity for heavy fissioning nuclei are reproduced through the four-dimensional Langevin calculations more accurately than through three-dimensional calculations.

/pdf/four-dimensional-langevin-dynamics-of-heavy-ion-induced-1aztncmqbc.pdf

Four-dimensional Langevin dynamics of heavy-ion-induced fission

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 qualitative similarity between the phenomenological friction in nuclear fission and the chaos weighted wall formula. This provides further evidence for one body nature of the dissipative force acting in a fissioning nucleus.

Chaos modified wall formula damping of the surface motion of a cavity undergoing fissionlike shape evolutions

We present a modification of the wall formula for one body dissipation in order to include the effect of irregularity in the shape of the one body potential on the dissipation mechanism. We arrive at a dissipation rate which is a scaled version of the wall formula developed earlier by Blocki {ital et} {ital al}. We show that the scaling factor is determined by a measure of chaos in the single particle motion. As an illustration, we obtain this measure of chaos for particles in a multipole deformed cavity with a view to use the scaled wall formula to calculate the damping widths of multipole vibrations of the cavity wall. Considering the amplitudes of the vibrations typical of the giant resonances in nuclei, it is observed that the effect of the shape dependence is to strongly suppress the damping caused by the original wall formula. {copyright} {ital 1996 The American Physical Society.}

Shape dependence of single particle response and the one body limit of damping of multipole vibrations of a cavity

Nuclear symmetry energy from effective interaction and masses of isospin asymmetric nuclei

The validity of the chaos weighted wall formula developed for systems in which the particle motion is not fully randomized is tested. We consider an ideal gas in a cavity undergoing volume conserving shape oscillations and compare the energy transferred from the wall to the gas with the prediction of the chaos weighted wall formula. We find that the chaos weighted wall formula provides a fairly reliable description of one body dissipation for nearly integrable to highly chaotic systems. {copyright} {ital 1997} {ital The American Physical Society}

Chaos in single particle motion and one body dissipation

Photonuclear reactions at energies covering the giant dipole resonance (GDR) region are analyzed with an approach based on nuclear photoabsorption followed by the process of competition between light-particle evaporation and fission for the excited nucleus. The photoabsorption cross-section at energies covering the GDR region is contributed by both the Lorentz-type GDR cross-section and the quasi-deuteron cross-section. The evaporation-fission process of the compound nucleus is simulated in a Monte Carlo framework. Photofission reaction cross-sections are analyzed in a systematic manner in the energy range of ∼ 10-20 MeV for the actinides 232Th , 238U and 237Np . Photonuclear cross-sections for the medium-mass nuclei 63Cu and 64Zn , for which there are no fission events, are also presented. The study reproduces satisfactorily the available experimental data of photofission cross-sections at GDR energy region and the increasing trend of nuclear fissility with the fissility parameter Z
 2/A for the actinides.

Tapan Mukhopadhyay

Papers

Chaos modified wall formula damping of the surface motion of a cavity undergoing fissionlike shape evolutions

Shape dependence of single particle response and the one body limit of damping of multipole vibrations of a cavity

Nuclear symmetry energy from effective interaction and masses of isospin asymmetric nuclei

Chaos in single particle motion and one body dissipation

Photonuclear reactions of actinides in the giant dipole resonance region