Langevin Calculations Research Articles

Connection of four-dimensional Langevin model and Hauser-Feshbach theory to describe statistical decay of fission fragments

ABSTRACT We have developed a novel theoretical method to obtain independent fission product yields and prompt neutron observables by connecting mass and total kinetic energy (TKE) distributions calculated by a four-dimensional Langevin dynamical model to a Hauser-Feshbach statistical decay model. In the Langevin calculations, mass distributions corresponding to the standard I and II modes were obtained separately and superposed to reproduce the fission fragment yield of spontaneous fission of 238 , 240 , 242 Pu and thermal neutron-induced fission of 239 Pu . This was achieved by using different neck parameters for these two modes in the two-center shell model shape parametrization, and a systematics of the superposing ratio was obtained as a function of N − Z / A of the fissioning nuclei. The Hauser-Feshbach calculations were performed using a nuclear reaction code TALYS for 239 Pu n , f reaction in the incident energy range from thermal up to 5 MeV , and the calculated prompt fission observables were compared with experimental and evaluated data. Although further improvements are needed for the most important nuclides, it turned out that the present methodology has the capability to prepare fission-related nuclear data for nuclides for which measurements are difficult.

Inertial energy dissipation in nuclear dynamics

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-dependent friction coefficients are confirmed by comparing to the existing experimental fission fragment yields. In conclusion, depending on the energy, the transition of energy dissipation mechanism from conventional viscous energy dissipation to inertial energy dissipation is shown.

Measurement of fission-fragment mass distributions in the multinucleon transfer channels of theO18+Np237reaction

Fission-fragment mass distributions for 23 nuclei ($^{234\ensuremath{-}237}\mathrm{U}$, $^{236\ensuremath{-}239}\mathrm{Np}$, $^{238\ensuremath{-}241}\mathrm{Pu}$, $^{240\ensuremath{-}243}\mathrm{Am}$, $^{242\ensuremath{-}245}\mathrm{Cm}$, and $^{244\ensuremath{-}246}\mathrm{Bk}$) were measured using the multinucleon transfer approach in the reaction of $^{18}\mathrm{O}+^{237}\mathrm{Np}$, and their excitation-energy dependence was obtained up to a maximum of 70 MeV. Among them, the low-energy fission of $^{236}\mathrm{Np}$, $^{238}\mathrm{Pu}$, and $^{245}\mathrm{Cm}$ is reported for the first time. The experimental data for all the studied nuclei were compared to the Langevin calculations. The calculation which takes into account the effects of multichance fission well reproduced the peak-to-valley ratio and mass-asymmetric peak positions of the distributions. The angular momentum given to the fissioning nucleus is also discussed.

Complex Langevin calculations in QCD at finite density

We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with β = 5.7 and four-flavor staggered fermions with degenerate quark mass ma = 0.01 and nonzero quark chemical potential μ. We confirm that a sufficient condition for correct convergence is satisfied for μ/T = 5.2 − 7.2 on a 83 × 16 lattice and μ/T = 1.6 − 9.6 on a 163 × 32 lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to μ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) × 4 (flavor) × 2 (spin) = 24. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

Modeling of Nuclear Reactions with Langevin Calculations

The mass angle distribution shows a strong correlation between mass and angle when quasifission events are dominant. Therefore, as long as quasifission events are dominant, the mass angle distribution is characterized in that diagonal correlation appears. This diagonal correlation could not be reproduced in our previous model that is before introducing $${{f}_{{{\text{ina}}}}}$$ and $$\gamma _{t}^{0}$$ model parameters. In this study, we clarify the indeterminate parameters included in the model to reproduce the diagonal correlation appearing in the mass angle distribution in the 48Ti + 186W reaction system. As a result, $${{f}_{{{\text{ina}}}}}$$ and $$\gamma _{t}^{0}$$ of model parameters found to be key parameters for MAD. it was also found that the balance between $${{f}_{{{\text{ina}}}}}$$ and $$\gamma _{t}^{0}$$ parameters values is important for the strong correlation between mass and angle.

Few-body physics on a spacetime lattice in the worldline approach

We formulate the physics of two species of non-relativistic hard-core bosons with attractive or repulsive delta function interactions on a space-time lattice in the worldline approach. We show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector if the chemical potential is tuned carefully. Since fermions can be treated as hard-core bosons up to a permutation sign, we apply this approach to study non-relativistic fermions. The fermion permutation sign is an observable in this approach and can be used to extract energies in each particle-number sector. In one dimension, non-relativistic fermions can only permute across boundaries, and so our approach does not suffer from sign problems in many cases, unlike the auxiliary field method. Using our approach, we discover limitations of the recently proposed complex Langevin calculations in one spatial dimension for some parameter regimes. In higher dimensions, our method suffers from the usual fermion sign problem. Here we provide evidence that it may be possible to alleviate this problem for few-body physics

Astrophysically motivated laboratory measurements of deuterium reacting with isotopologues of H

AbstractH2D+and D2H+are important chemical tracers of prestellar cores due to their pure rotational spectra that can be excited at the ~20 K temperature of these environments. The use of these molecules as probes of prestellar cores requires understanding the chemistry that forms and destroys these molecules. Of the eight key reactions that have been identified (Albertssonet al. 2013), five are thought to be well understood. The remaining three are the isotope exchange reactions of atomic D with H$${ + \over 3}$$, H2D+, and D2H+. Semi-classical results differ from the classical Langevin calculations by an order of magnitude (Moyanoet al.2004). To resolve this discrepancy, we have carried out laboratory measurements for these three reactions. Absolute cross sections were measured using a dual-source, merged fast-beams apparatus for relative collision energies between ~10 meV to ~10 eV (Hillenbrandet al.2019). A semi-empirical model was developed incorporating high level quantum mechanicalab initiocalculations for the zero-point-energy-corrected potential energy barrier in order to generate thermal rate coefficients for astrochemical models. Based on our studies, we find that these three reactions proceed too slowly at prestellar core temperatures to play a significant role in the deuteration of H$${ + \over 3}$$isotopologues.

Complex Langevin calculations in finite density QCD at large μ/T with the deformation technique

It is well known that investigating QCD at finite density by standard Monte Carlo methods is extremely difficult due to the sign problem. Some years ago, the complex Langevin method with gauge cooling was shown to work at high temperature, i.e., in the deconfined phase. The same method was also applied to QCD in the so-called heavy dense limit in the whole temperature region. In this paper we attempt to apply this method to the large $\mu/T$ regime with moderate quark mass using four-flavor staggered fermions on a $4^3\times 8$ lattice. While a straightforward application faces with the singular-drift problem, which spoils the validity of the method, we overcome this problem by the deformation technique proposed earlier. Explicit results for the quark number density and the chiral condensate obtained in this way for $3.2\leq \mu/T\leq 5.6$ are compared with the results for the phase-quenched model obtained by the standard rational hybrid Monte Carlo calculation. This reveals a clear difference, which is qualitatively consistent with the Silver Blaze phenomenon.

Polarized fermions in one dimension: Density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion

We calculate the finite-temperature density and polarization equations of state of one-dimensional fermions with a zero-range interaction, considering both attractive and repulsive regimes. In the path-integral formulation of the grand-canonical ensemble, a finite chemical potential asymmetry makes these systems intractable for standard Monte Carlo approaches due to the sign problem. Although the latter can be removed in one spatial dimension, we consider the one-dimensional situation in the present work to provide an efficient test for studies of the higher-dimensional counterparts. To overcome the sign problem, we use the complex Langevin approach, which we compare here with other approaches: imaginary-polarization studies, third-order perturbation theory, and the third-order virial expansion. We find very good qualitative and quantitative agreement across all methods in the regimes studied, which supports their validity.

The 4-dimensional Langevin approach to low energy nuclear fission

We applied the four-dimensional Langevin approach to the description of fission of 235U by neutrons and calculated the dependence of the excitation energy of fission fragments on their mass number. For this we have fitted the compact just-before-scission configuration obtained by the Langevin calculations by the two separated fragments and calculated the intrinsic excitation and the deformation energy of each fragment accurately taking into account the shell and pairing effects and their dependence on the temperature and mass of the fragments. For the sharing of energy between the fission fragments we have used the simplest and most reliable assumption - the temperature of each fragment immediately after the neck rupture is the same as the temperature of mother nucleus just before scission. The calculated excitation energy of fission fragments clearly demonstrates the saw-tooth structure in the dependence on fragment mass number.

Polarized fermions in one dimension: Density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion

Polarized fermions in one dimension: Density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion

Fission observables from 4D Langevin calculations with macroscopic transport coefficients

We have extended the Langevin equations to 4 dimensions (4D) by allowing the independent deformation for the left (δ1) and right fragments (δ2) of the fissioning nucleus. At the moment we are only able to use them in conjunction with the macroscopic transport coefficients. Nevertheless, we can see a considerable improvement in the preliminary results for the fission observables, especially those related to the total kinetic energy (TKE) of fission fragments. By plotting the TKE distributions we have revealed the super-long fission modes in236U and super-short fission modes in257Fm. By plotting the distribution ofδagainst the fragment’s TKE we have noted a correlation between the values ofδand Brosa’s fission modes. We have found that the standard fission modes correspond to prolate tips of the light fragments while the complementary heavy fragments have oblate fission tips. On the other hand, if both fragments were prolate at the tips, we get super-long fission modes. If both fragments were oblate at the tips, we get super-short fission modes.

Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin

We calculate the pressure and density of polarized non-relativistic systems of two-component fermions coupled via a contact interaction at finite temperature. For the unpolarized one-dimensional system with an attractive interaction, we perform a thirdorder lattice perturbation theory calculation and assess its convergence by comparing with hybrid Monte Carlo. In that regime, we also demonstrate agreement with real Langevin. For the repulsive unpolarized one-dimensional system, where there is a so-called complex phase problem, we present lattice perturbation theory as well as complex Langevin calculations. For our studies, we employ a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick’s theorem for perturbative calculations, which generates the diagrammatic expansion at any order. We find excellent agreement between the results from our perturbative calculations and stochastic studies in the weakly interacting regime. In addition, we show predictions for the strong coupling regime as well as for the polarized one-dimensional system. Finally, we show a first estimate for the equation of state in three dimensions where we focus on the polarized unitary Fermi gas.

Analysis of the total kinetic energy of fission fragments with the Langevin equation

We analyzed the total kinetic energy (TKE) of fission fragments with three-dimensional Langevin calculations for a series of actinides and Fm isotopes at various excitation energies. This allowed us to establish systematic trends of TKE with $Z^2/A^{1/3}$ of the fissioning system and as a function of excitation energy. In the mass-energy distributions of fission fragments we see the contributions from the standard, super-long, and super-short (in the case of $^{258}$Fm) fission modes. For the fission fragments mass distribution of $^{258}$Fm we obtained a single peak mass distribution. The decomposition of TKE into the prescission kinetic energy and Coulomb repulsion showed that decrease of TKE with growing excitation energy is accompanied by a decrease of prescission kinetic energy. It was also found that transport coefficients (friction and inertia tensors) calculated by a microscopic model and by macroscopic models give drastically different behavior of TKE as a function of excitation energy. The results obtained with microscopic transport coefficients are much closer to experimental data than those calculated with macroscopic ones.

Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of nonrelativistic fermions in one dimension

We analyze the pressure and density equations of state of unpolarized non-relativistic fermions at finite temperature in one spatial dimension. For attractively interacting regimes, we perform a third-order lattice perturbation theory calculation, assess its convergence properties by comparing with hybrid Monte Carlo results (there is no sign problem in this regime), and demonstrate agreement with real Langevin calculations. For repulsive interactions, we present lattice perturbation theory results as well as complex Langevin calculations, with a modified action to prevent uncontrolled excursions in the complex plane. Although perturbation theory is a common tool, our implementation of it is unconventional; we use a Hubbard-Stratonovich transformation to decouple the system and automate the application of Wick's theorem, thus generating the diagrammatic expansion, including symmetry factors, at any desired order. We also present an efficient technique to tackle nested Matsubara frequency sums without relying on contour integration, which is independent of dimension and applies to both relativistic and non-relativistic systems, as well as all energy-independent interactions. We find exceptional agreement between perturbative and non-perturbative results at weak couplings, and furnish predictions based on complex Langevin at strong couplings. We additionally present perturbative calculations of up to the fifth-order virial coefficient for repulsive and attractive couplings. Both the lattice perturbation theory and complex Langevin formalisms can easily be extended to a variety of situations including polarized systems, bosons, and higher dimension.

Investigation of dissipation in the tilting degree of freedom from four-dimensional Langevin dynamics of heavy-ion-induced fission

A four-dimensional dynamical model based on Langevin equations was applied to calculate a wide set of experimental observables for heavy fissioning compound nuclei. Three collective shape coordinates plus the tilting coordinate were considered dynamically from the ground state deformation to the scission into fission fragments. A modified one-body mechanism for nuclear dissipation with a reduction coefficient ks of the contribution from a ‘wall’ formula was used for shapes parameters. Different possibilities of deformation-dependent dissipation coefficient for the tilting coordinate () were investigated. Presented results demonstrate that the influence of the ks and γK parameters on the calculated quantities can be selectively probed. The nuclear viscosity with respect to the nuclear shape parameters influences the , the fission fragment mass–energy distribution parameters, and the angular distribution of fission fragments. At the same time the viscosity coefficient γK affects the angular distribution of fission fragments only. The independence of anisotropy on the fission fragment mass is found at both Langevin calculations performed with deformation-dependent and constant γK coefficients.

On some limitations of current Langevin calculations

The multi-dimensional Langevin approach is among the most powerful approach for understanding nuclear dynamics, in general, and fission, in particular. This work is devoted to a meticulous study of some limitations of current Langevin models. Evidence for the occurrence of potential spurious features is demonstrated. These are the results of a puzzling interplay involving the transport coefficients which govern the dynamics, on the one hand, and the modelling of nuclear shapes and scission, on the other hand. We reveal the conditions under which, and the mechanism by which, the result can be biased by practical aspects of the implementation of the theory. The implications of this study for the interpretation of experimental data are also discussed. As critical and cautious analysis of the predictions is recommended, and we comment on a strategy for identifying possible bias.

Pre- and post- scission particle emission in 3D Langevin calculations with various macroscopic potentials

Thefission dynamics described by solving differential equations of the Langevin type in three dimensional space of the deformation parameters is very sensitive on the choice of the macroscopic components such as potential energy models. The mass or charge distribution or total kinetic energy has been already shown to be different when one uses the Finite Range Liquid Drop Model or Lublin - Strasbourg Drop model. Also the shape-dependent congruence or shape-dependent Wigner energy andA 0 terms are important especially for the fission of medium mass nuclei. We would like to make step forward and answer the question about the varying of the post-scission multiplicity by including different PES. Up to now there are only few experimental data for the medium mass nuclei where the pre- and post- scission emission has been estimated and isotopic distributions have been shown. The isotopic distributions of the fission products for light compound nucleus such as 111 In with two beam energies (E

Mass-energy distribution of fragments within Langevin dynamics of fission induced by heavy ions

A stochastic approach based on four-dimensional Langevin fission dynamics is applied to calculating mass-energy distributions of fragments originating from the fission of excited compound nuclei. In the model under investigation, the coordinate K representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of the {c, h, α} parametrization. The evolution of the orientation degree of freedom (K mode) is described by means of the Langevin equation in the overdamped regime. The tensor of friction is calculated under the assumption of the reducedmechanismof one-body dissipation in the wall-plus-window model. The calculations are performed for two values of the coefficient that takes into account the reduction of the contribution from the wall formula: k s = 0.25 and k s = 1.0. Calculations with a modified wall-plus-window formula are also performed, and the quantity measuring the degree to which the single-particle motion of nucleons within the nuclear system being considered is chaotic is used for k s in this calculation. Fusion-fission reactions leading to the production of compound nuclei are considered for values of the parameter Z 2/A in the range between 21 and 44. So wide a range is chosen in order to perform a comparative analysis not only for heavy but also for light compound nuclei in the vicinity of the Businaro-Gallone point. For all of the reactions considered in the present study, the calculations performed within four-dimensional Langevin dynamics faithfully reproduce mass-energy and mass distributions obtained experimentally. The inclusion of the K mode in the Langevin equation leads to an increase in the variances of mass and energy distributions in relation to what one obtains from three-dimensional Langevin calculations. The results of the calculations where one associates k s with the measure of chaoticity in the single-particle motion of nucleons within the nuclear system under study are in good agreement for variances of mass distributions. The results of calculations for the correlations between the prescission neutron multiplicity and the fission-fragment mass, 〈n pre(M)〉, and between, this multiplicity and the kinetic energy of fission fragments, 〈n pre(E k )〉, are also presented.

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

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.