Problems In Nuclear Physics Research Articles

Nonautonomous Volterra Series Expansion of the Variable Phase Approximation and its Application to the Nucleon-Nucleon Inverse Scattering Problem

Abstract In this paper, the nonlinear Volterra series expansion is extended and used to describe certain types of nonautonomous differential equations related to the inverse scattering problem in nuclear physics. The nonautonomous Volterra series expansion lets us determine a dynamic, polynomial approximation of the variable phase approximation (VPA), which is used to determine the phase shifts from nuclear potentials through first-order nonlinear differential equations. By using the first-order Volterra expansion, a robust approximation is formulated to the inverse scattering problem for weak potentials and/or high energies. The method is then extended with the help of radial basis function neural networks by applying a nonlinear transformation on the measured phase shifts to be able to model the scattering system with a linear approximation given by the first-order Volterra expansion. The method is applied to describe the ${}^1S_0$ NN potentials in neutron+proton scattering below 200 MeV laboratory kinetic energies, giving physically sensible potentials and below $1\%$ averaged relative error between the recalculated and the measured phase shifts.

Nuclear Physics in the Era of Quantum Computing and Quantum Machine Learning

AbstractIn this paper, the application of quantum simulations and quantum machine learning is explored to solve problems in low‐energy nuclear physics. The use of quantum computing to address nuclear physics problems is still in its infancy, and particularly, the application of quantum machine learning (QML) in the realm of low‐energy nuclear physics is almost nonexistent. Three specific examples are presented where the utilization of quantum computing and QML provides, or can potentially provide in the future, a computational advantage: i) determining the phase/shape in schematic nuclear models, ii) calculating the ground state energy of a nuclear shell model‐type Hamiltonian, and iii) identifying particles or determining trajectories in nuclear physics experiments.

The most important achievements in research on fundamental problems of nuclear physics over the past 25 years and their future prospects

The most important achievements in research on fundamental problems of nuclear physics over the past 25 years and their future prospects

The most important achievements in research on fundamental problems of nuclear physics over the past 25 years and their future prospects

The most important achievements in research on fundamental problems of nuclear physics over the past 25 years and their future prospects

Isospin dependence in single-nucleon removal cross sections explained through valence-core destruction effects

The discrepancy between experimental data and theoretical calculations in one-nucleon removal reactions at intermediate energies (quantified by the so-called “quenching factors”) and its dependence on the isospin asymmetry of the nuclei has been an open problem in nuclear physics for the last fifteen years. In this work, we propose an explanation for this long-standing problem, which relies on the inclusion of the process of core destruction due to its interaction with the removed nucleon. To include this effect, we extend the commonly used eikonal formalism via an effective nucleon density, and apply it to a series of nucleon knockout reactions. The effect of core destruction is found to depend strongly on the binding energy of the removed nucleon, leading to a significant reduction of the cross section for deeply bound nucleons, which reduces the isospin dependence of the “quenching factors”, making them more consistent with the trends found in transfer and (p,pN) reactions.

Bessel functions of first kind and their Anuj transforms

Various problems of Statistics, Mathematics, Radio Physics, Nuclear Physics, Atomic Physics, Fluid Mechanics, Engineering and Science can easily handle by applying integral transform techniques on their mathematical models. Problems of heat equation, Schrodinger equation, Laplace equation, Helmholtz equation and wave equation have solutions in terms of Bessel functions. To solve such equations by integral transform methods, we need to know the integral transform of Bessel functions. In this paper, authors discuss Bessel functions of first kind and determine their Anuj transforms.

О суммировании 3j-символов Вигнера

Within the framework of the theory of irreducible tensor operators, using well -known general analytical results for double sums of products of two 3j-Wigner symbols, analytical expressions for single j m sums m for the valuesj1 j2 1 andj 2 parameters of the upper row 3j Wigner symbol are specified.The expressions obtained supplement the well-known analytical results of the theory of angular momentum and are in demand in solving, in particular, such problems of atomic physics as the construction of a nonrelativistic quantum theory of single and double bremsstrahlung when a photon is scattered by an atom (atomic ion).

Cluster formation in neutron-rich Be and B isotopes

Abstract Evaluating the formation of clusters in finite and infinite nuclear systems is a fundamental problem in nuclear physics, and the variation in clustering in the isotope chain up to the neutron drip-line is one such intriguing phenomenon. Recently, experiments performed using the (p, pα) reactions have revealed a negative correlation between α-cluster formation and neutron number in Sn isotopes, showing a trend opposite to that theoretically predicted for Be and B isotopes. Although the observed charge radii of the Be and B isotopes suggest the formation of clusters as the neutron drip-line is approached, these radii themselves are not a physical quantity that can directly probe the cluster structure. Here, we directly investigate the cluster formation in Be and B isotopes to elucidate the possibility of clustering as the neutron drip-line is approached. It has been shown that the sum of the S-factors (i.e., S(α), S(6He), and S(8He)) increases as the neutron drip-line approaches, in agreement with those of previous studies. The results indicate that the excess neutrons contribute to the formation of 6He and 8He clusters as well as α clusters. Thus, S(α) is not sufficient to estimate the enhancement of clustering in Be and B isotopes.

An efficient digital twin based on machine learning SVD autoencoder and generalised latent assimilation for nuclear reactor physics

This paper proposes an approach that combines reduced-order models with machine learning in order to create an digital twin to predict the power distribution over the core during the operation stage. The operational digital twin is designed to solve forward problems given input operation parameters, as well as to solve inverse problems given some observations of the power field. The forward model is non-intrusive and realised using SVD autoencoder reduced order model with the combination of machine learning methods, namely, k-nearest-neighbours and decision trees to build the input–output map. For model parameter estimation, the inverse model is based on a generalised latent assimilation method. The proposed approach is able to make use of the non intrusive reduced order model and the online measurements of the power field. The effectiveness in the sense of accuracy and real-time solver of the digital twin is illustrated through a real engineering problem in nuclear reactor physics — reactor core simulation in the life cycle of HPR1000 affected by input parameters, i.e., control rod inserting step, burnup, power level and inlet temperature of the coolant, which shows potential applications for on-line monitoring purpose.

Unbiasedness and optimization of regional weight cancellation.

The Monte Carlo method is often used to simulate systems which can be modeled by random walks. To calculate observables, in many implementations the "walkers" carry a statistical weight which is generally assumed to be positive. Some random walk simulations, however, may require walkers to have positive or negative weights: it has been shown that the presence of a mixture of positive and negative weights can impede the statistical convergence, and special weight-cancellation techniques must be adopted to overcome these issues. In a recent work we demonstrated the usefulness of one such method, exact regional weight cancellation, to solve eigenvalue problems in nuclear reactor physics in three spatial dimensions. The method previously exhibited had several limitations (including multigroup transport and isotropic scattering) and needed homogeneous cuboid cancellation regions. In this paper we lift the previous limitations, in view of applying exact regional cancellation to more realistic continuous-energy neutron transport problems. This extended regional cancellation framework is used to optimize the efficiency of the weight cancellation. Our findings are illustrated on a benchmark configuration for reactor physics.

The New Complex Integral Transform "Complex Sadik Transform" and It's Applications

In this paper, we introduce a new complex integral transform namely ”Complex Sadik Transform”. Theproperties of this transformation are investigated. This complex integral transformation is used to reducethe core problem to a simple algebraic equation. The answer to this primary problem can than be obtainedby solving this algebraic equation and applying the inverse of complex Sadik transformation. Finally,the complex Sadik integral transformation is applied and used to find the solution of linear higher orderordinary differential equations. As well as, we present and discuss, some important real life problemssuch as: pharmacokinetics problem ,nuclear physics problem and Beams Probem

A New Constraint on the Nuclear Equation of State from Statistical Distributions of Compact Remnants of Supernovae

Understanding how matter behaves at the highest densities and temperatures is a major open problem in both nuclear physics and relativistic astrophysics. Our understanding of such behavior is often encapsulated in the so-called high-temperature nuclear equation of state (EOS), which influences compact binary mergers, core-collapse supernovae, and other phenomena. Our focus is on the type (either black hole or neutron star) and mass of the remnant of the core collapse of a massive star. For each six candidates of equations of state, we use a very large suite of spherically symmetric supernova models to generate a sample of synthetic populations of such remnants. We then compare these synthetic populations to the observed remnant population. Our study provides a novel constraint on the high-temperature nuclear EOS and describes which EOS candidates are more or less favored by an information-theoretic metric.

Microscopic description of cluster decays based on the generator coordinate method

\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 $\alpha$-decays. \noindent\textbf{Methods:} Based on the Gamow theory, we evaluate the preformation probability of a cluster with GCM while the penetrability of the Coulomb barrier is estimated with a potential model. To this end, we employ Skyrme interactions and solve the one-dimensional Hill-Wheeler equation with the mass octupole field. We also take into account the dynamical effects of the pairing correlation using BCS wavefunctions constructed with an increased strength of the pairing interaction. \noindent\textbf{Results:} We apply this scheme to the cluster decay of $^{222}$Ra, i.e., $^{222}$Ra$\to^{14}$C+$^{208}$Pb, to show that the experimental decay rate can be reproduced within about two order of magnitude. We also briefly discuss the cluster radioactivities of the $^{228}$Th and $^{232}$U nuclei. For these actinide nuclei, we find that the present calculations reproduce the decay rates with the same order of magnitude and within two or three order of magnitude, respectively. \noindent\textbf{Conclusions:} The method presented in this paper provides a promising way to describe microscopically cluster decays of heavy nuclei.

Systematical analysis of (n,2n) reaction cross sections for 14-15 MeV neutrons

Fast neutron induced nuclear reaction cross section data are necessary for both nuclear energy technology and the understanding of fundamental nuclear physics problems. The information of (n,2n) cross sections is quite essential in nuclear technology as a significant portion of the fission neutron spectrum lies above the threshold of (n,2n) reaction for mostof the reactor materials. These cross section data are required in shielding and breeding calculations. Radioactive nuclides produced in the reactor usually have short half-life. So, direct measurement of their neutron cross sections is difficult. Therefore, model formulae are important to predict these cross sections theoretically. In this work, in the framework of the statistical model we deduced some theoretical formulae for the (n,2n) cross section using the evaporation model, constant nuclear temperatureapproximation and Weizsäker’s formula for binding energy. The model formulae were utilized for systematical analysis of known experimental data of the (n,2n) cross sections at 14 - 15 MeV energy.

Applications of group theory in crystallography

Group theory is a powerful tool for studying symmetric physical systems. Such systems include, in particular, molecules and crystals with symmetry. Group theory serves to explain the most important characteristics of atomic spectra. Group theory is also applied to the problems of atomic and nuclear physics. This paper gives examples of the use of the apparatus of group theory in research on crystallography, quantum mechanics, elementary particle physics. In particular, in these studies matrix groups and representations of unitary groups are actively used. For such groups we give an overview of the results on their recognition by the spectrum (by the orders of the elements of the group). This direction has been intensively developed in recent years both in our country and abroad. Recognition of finite simple non-Abelian groups by spectrum has been studied for last thirty years in Yekaterinburg at the Institute of Mathematics and Mechanics of the Ural Division of the Russian Academy of Sciences, in Chelyabinsk Federal University and in the Novosibirsk Institute of Mathematics of Siberian Division of the Russian Academy of Sciences. Some simple non-Abelian groups are not recognizable by their spectra. We have proposed an approach for recognizing groups by the bottom layer. The bottom layer of a group is the set of its elements of prime orders. A group is called recognizable by the bottom layer under additional conditions if it is uniquely restored by the bottom layer under these conditions. The paper considers some examples of simple non-Abelian finite groups that are not recognizable by spectra. For these examples, simultaneous recognition by spectrum and by the bottom layer is proved.

Data-Enabled Physics-Informed Machine Learning for Reduced-Order Modeling Digital Twin: Application to Nuclear Reactor Physics

This paper proposes an approach that combines reduced-order models with machine learning in order to create physics-informed digital twins to predict high-dimensional output quantities of interest, such as neutron flux and power distributions in nuclear reactor cores. The digital twin is designed to solve forward problems given input parameters, as well as to solve inverse problems given some extra measurements. Offline, we use reduced-order modeling, namely, the proper orthogonal decomposition, to assemble physics-based computational models that are accurate enough for the fast predictive digital twin. The machine learning techniques, namely, k-nearest-neighbors and decision trees, are used to formulate the input-parameter-dependent coefficients of the reduced basis, after which the high-fidelity fields are able to be reconstructed. Online, we use the real-time input parameters to rapidly reconstruct the neutron field in the core based on the adapted physics-based digital twin. The effectiveness of the framework is illustrated through a real engineering problem in nuclear reactor physics—reactor core simulation in the life cycle of the HPR1000 governed by the two-group neutron diffusion equations affected by input parameters, i.e., burnup, control rod inserting step, power level, and temperature of the coolant—which shows potential applications for online monitoring purposes.

Generalized Empirical Interpolation Method With H1 Regularization: Application to Nuclear Reactor Physics

The generalized empirical interpolation method (GEIM) can be used to estimate the physical field by combining observation data acquired from the physical system itself and a reduced model of the underlying physical system. In presence of observation noise, the estimation error of the GEIM is blurred even diverged. We propose to address this issue by imposing a smooth constraint, namely, to constrain the H1 semi-norm of the reconstructed field of the reduced model. The efficiency of the approach, which we will call the H1 regularization GEIM (R-GEIM), is illustrated by numerical experiments of a typical IAEA benchmark problem in nuclear reactor physics. A theoretical analysis of the proposed R-GEIM will be presented in future works.

The Calculation of Double Nonlinearity and Material Anisotropy Influence on the Temperature Distribution in the Cylinder Under High Temperature Heat Exchange

At the present stage of the development of technology, it is necessary to ensure the strength, reliability and durability of the structure that successfully functions under conditions of high-temperature heat exchange as maximum as possible. In this regard, graphite structural elements are widely used, and they are also applied for parts of space and aircraft, jet and rocket engines. The transversely isotropic graphite cylinder used in this work has a unique set of qualities that make it indispensable for problems in nuclear physics and power engineering; however, in the calculation of thermal engineering practice, it has not been studied enough, since it contains a large scatter of thermophysical characteristics for various grades of graphite. The aim of the study, including the basis of the developed method for solving boundary value problems of doubly nonlinear unsteady thermal conductivity, is to consider the effect of temperature dependences of the thermophysical characteristics of the material on temperature, zonal radiative-convective heat transfer and anisotropy on the distribution of temperature fields along the length, at the center and surface of a semi-infinite solid cylinder. The essence of this method is that the Goodman’s and Kirchhoff’s transformations are applied to the problem posed converted to a dimensionless form, then the relative temperature and functions from it, are expanded in the series of sines on the a priori interval, then the superposition principle is applied, after which the original setting is converted to a set of linearized problems with reduced thermophysical characteristics. Linear problems are solved by the method of integral transformations, which are summed up. The upper limit of the priori interval is determined from the condition that the relative temperature obtained from the solution of the problem Fo ® ¥ takes the value of the upper limit of the a priori interval. A large number of numerical calculations in the Matlab environment graphically show changes in the relative temperature on the axis and surface of the cylinder in a wide range of Fourier criteria. It is found that with an increase in the Fourier criterion, the character of heating changes qualitatively from the axis to the surface of the cylinder, both in terms of nonlinearities and anisotropy. For the case of double nonlinearity, the location of the temperature fields at different anisotropies in comparison with an isotropic material is shown graphically.

Nucleon-nucleon potentials from Δ -full chiral effective-field-theory and implications

We closely investigate NN potentials based upon the Delta-full version of chiral effective field theory. We find that recently constructed NN potentials of this kind, which (when applied together with three-nucleon forces) were presented as predicting accurate binding energies and radii for a range of nuclei from A=16 to A=132 and providing accurate equations of state for nuclear matter, yield a chi^2/datum of 60 for the reproduction of the pp data below 100 MeV laboratory energy. This chi^2 is more than three times what the Hamada-Johnston potential of the year of 1962 achieved already some 60 years ago. We perceive this historical fact as concerning in view of the current emphasis on precision. We are able to trace the very large chi^2 as well as the apparent success of the potentials in nuclear structure to unrealistic predictions for P-wave states, in which the Delta-full NNLO potentials are off by up to 40 times the NNLO truncation errors. In fact, we show that, the worse the description of the P-wave states, the better the predictions in nuclear structure. Thus, these potentials cannot be seen as the solution to the outstanding problems in current miscroscopic nuclear structure physics.

Two Reliable Techniques for Solving Conformable Space-Time Fractional PHI-4 Model Arising in Nuclear Physics via β-derivative

Nowadays, nonlinear fractional partial differential equations have been highly using for modelling of physical phenomena. Therefore, it is very important to achieve exact solutions of fractional differential equations for understanding complex phenomena in mathematical physics. In this study, new exact traveling wave solutions are reached of space-time fractional Phi-4 equation indicated by Atangana’s conformable derivative using two powerful different techniques. These are the functional variable method and the first integral method. Obtaining new solutions of this equation show that method is effective to understanding other nonlinear complex problems in particle and nuclear physics.