Self-consistent Mean Field Research Articles

Nuclear structure study of some tin isotopes using the self-consistent mean field method

Hartree-Fock calculations for even-even Tin isotopes usingSkyrme density dependent effective nucleon-nucleon interaction arediscussed systematically. Skyrme interaction and the general formulafor the mean energy of a spherical nucleus are described. The chargeand matter densities with their corresponding rms radii and thenuclear skin for Sn isotopes are studied and compared with theexperimental data. The potential energy curves obtained withinclusion of the pairing force between the like nucleons in Hartree-Fock-Bogoliubov approach are also discussed.

A study of shell structure in normal to exotic nuclides within relativistic Hartree–Bogoliubov approximation

The purpose of this work is to study theoretically the shell structure of even–even isotopes in Si, S, Ar and Ca and isotones at neutron number N = 0, 28, 50 and 82. We employed Covariant Relativistic self-consistent mean field models analogous to Kohn–Sham density functional theory to construct the Nuclear Density Functionals from Lagrangian densities based on meson exchange and point coupling models. The pairing correlations of nucleons are considered by the relativistic Hartree–Bogoliubov functional based on quasi-particle operators of Bogoliubov transformations. The theoretical calculations of shell closure parameter [Formula: see text](N) and the differential variation of the two-neutron separation energy [Formula: see text](Z, N) provide recognizable signature of shell closure at N = 14 and 20 in case of Si, N = 14, 20 and 28 in S, Ar and Ca isotopes and are consistent with recent experimental investigations of new sub-shell gaps.

Solute Diffusion by Self-Interstitial Defects and Radiation-Induced Segregation in Ferritic Fe- <i>X</i> ( <i>X</i>=Cr, Cu, Mn, Ni, P, Si) Dilute Alloys

This work investigates solute transport due to self-interstitial defects and radiation induced segregation tendencies in dilute ferritic alloys, by computing the transport coefficients of each system based on ab initio calculations of binding energies and migration rates. The implementation of the self-consistent mean field method in the KineCluE code allows to extend the calculation of transport coefficients to arbitrary interaction ranges, crystal structures, and diffusion mechanisms. The results show that the diffusivity of P, Mn, and Cr solute atoms is dominated by the dumbbell mechanism, that of Cu by vacancies, while the two mechanisms might be in competition for Ni and Si, despite the fact that the corresponding mixed dumbbells are not stable. Systematic enrichment at defect sinks is expected for P and Mn solutes due to dumbbell diffusion, and for Si due mainly to vacancy drag. Vacancy drag is also responsible for Cu and Ni enrichment below 1085 K. The RIS behavior of Cr is the outcome of a fine balance between dumbbell enrichment and vacancy depletion. Therefore, for dilute Cr concentrations global enrichment occurs below 540 K, and depletion above. This threshold temperature grows with solute concentration. The findings are in agreement with experimental observations of RIS and clustering phenomena, and confirm that solute-defect kinetic coupling plays an important role in the formation of solute clusters in reactor pressure vessel steels and other alloys.

Fusion cross section for Ni-based reactions within the relativistic mean-field formalism

In this theoretical study, we establish an interrelationship between the nucleon-nucleon interaction potential and the nuclear fusion reaction cross-sections at low energies. The axially deformed self-consistent relativistic mean field with non-linear NL3$^*$ force is used to calculate the density distribution of the projectile and target nuclei for fusion. The Wong formula is used to estimate the fusion cross-section and barrier distribution from the nucleus-nucleus optical potential for Ni-based systems, which are known for fusion hindrance phenomena. The results of the application of the so obtained nucleus-nucleus optical potential for the fusion cross-section from the recently developed relativistic $NN-$interaction (R3Y) are compared with the well-known, phenomenological M3Y effective $NN$ potential. We found a relatively good results from R3Y interactions below the barrier energies as compare to the M3Y potential concerning the experimental data. We also observe the density dependence on the nuclear interaction potential in terms of nucleon-nucleon optical potentials.

A semi-analytical modelling of cutting using crystal plasticity theory and flow line approach

A semi-analytical model for orthogonal cutting taking into account microstructure evolution and its influence on the chip formation process is developed for polycrystalline materials. To describe the 2D material flow in the chip, a thermomechanical crystal plasticity constitutive model was combined with the flow line approach. The microstructure evolution, as well as material flow stress and temperature rise, are obtained through a Visco-Plastic Self-Consistent (VPSC) mean field crystal plasticity model combined with a Mechanical Threshold Stress (MTS) physical-based hardening law. The proposed approach allows capturing in a relative simple way the variations of thermomechanical fields such as stress, strain, strain rate and temperature in the primary shear zone. The model validation is conducted by successful comparisons with experimental results of Shi and Liu [63] in terms of cutting forces and chip thickness during orthogonal cutting of a HY 100 steel alloy. The predicted results indicate that equivalent strain and temperature increase from the chip free surface to the tool tip. In contrast, the equivalent stress exhibits a reverse trend.

Broadened region for robust optical bistability in a nonlocal core and Kerr shell nanoparticle.

With the self-consistent mean field approximation in the framework of full-wave nonlocal scattering theory, we carry out a theoretical study on the optical bistability in a nonlocal nanoparticle coated with a Kerr-type nonlinear shell. A nonlocality-enhanced Fano profile is found in its scattering spectrum. We demonstrate the nonlocality-broadened bistable region in the geometrical parameter space. We perform the investigation of the nonlinear dependences of the near-field intensity and far-field scattering on the incident wavelength and find the input-wavelength-controllable as well as the input-field-intensity-controllable scattering. We check the stability of the nonlinear steady states and perform its temporal dynamical evolutions.

Metal-Insulator Transition in Copper Oxides Induced by Apex Displacements

High temperature superconductivity has been found in many kinds of compounds built from planes of Cu and O, separated by spacer layers. Understanding why critical temperatures are so high has been the subject of numerous investigations and extensive controversy. To realize high temperature superconductivity, parent compounds are either hole-doped, such as {La$_{2}$CuO$_4$} (LCO) with Sr (LSCO), or electron doped, such as {Nd$_{2}$CuO$_4$} (NCO) with Ce (NCCO). In the electron doped cuprates, the antiferromagnetic phase is much more robust than the superconducting phase. However, it was recently found that the reduction of residual out-of-plane apical oxygens dramatically affects the phase diagram, driving those compounds to a superconducting phase. Here we use a recently developed first principles method to explore how displacement of the apical oxygen (A-O) in LCO affects the optical gap, spin and charge susceptibilities, and superconducting order parameter. By combining quasiparticle self-consistent GW (QS\emph{GW}) and dynamical mean field theory (DMFT), that LCO is a Mott insulator; but small displacements of the apical oxygens drive the compound to a metallic state through a localization/delocalization transition, with a concomitant maximum $d$-wave order parameter at the transition. We address the question whether NCO can be seen as the limit of LCO with large apical displacements, and elucidate the deep physical reasons why the behaviour of NCO is so different than the hole doped materials. We shed new light on the recent correlation observed between T$_c$ and the charge transfer gap, while also providing a guide towards the design of optimized high-Tc superconductors. Further our results suggest that strong correlation, enough to induce Mott gap, may not be a prerequisite for high-Tc superconductivity.

Novel Theoretical Self‐Consistent Mean‐Field Approach to Describe the Conductivity of Carbon Fiber Filled Thermoplastics—PART I—Theory

AbstractA novel theoretical approach is shown which yields a nonlinear differential equation for the resistivity of carbon fiber filled composites below the percolation threshold as a function of the volume fraction of the filler and the fiber orientation. The solution of the equation is given analytically and a particular value for the exponent predicted. The theoretical concept can be transferred to other composite properties.

Effect of Interaction on the Majorana Zero Modes in the Kitaev Chain at Half Filling**Supported by the National Natural Science Foundation of China under Grant No 11274379, and the Research Funds of Renmin University of China under Grant No 14XNLQ07.

The one-dimensional interacting Kitaev chain at half filling is studied. The symmetry of the Hamiltonian is examined by dual transformations, and various physical quantities as a function of the fermion-fermion interaction U are calculated systematically using the density matrix renormalization group method. A special value of interaction Up is revealed in the topological region of the phase diagram. We show that at Up the ground states are strictly two-fold degenerate even though the chain length is finite and the zero-energy peak due to the Majorana zero modes is maximally enhanced and exactly localized at the end sites. Here Up may be attractive or repulsive depending on other system parameters. We also give a qualitative understanding of the effect of interaction under the self-consistent mean field framework.

Multiscale modeling of Radiation Induced Segregation in iron based alloys

In metallic alloys of fission or fusion reactors, microstructural evolution results from a dynamic equilibrium between thermodynamic forces and the production of defects by irradiation. The migration of defects can lead to the formation of clusters of defects (nano-cavities, dislocation loops, nano-precipitates) or variations in chemical composition close to the defect sinks, a phenomenon known as Radiation Induced Segregation (RIS). To predict the effect of irradiation conditions (type of irradiation particle, dose rate, temperature), phenomenological diffusion models exist that have to be assembled to give an overall description. Our objective is to describe these models and to propose numerical implementations to solve them starting at the atomic scale (DFT energy calculations, Kinetic Monte Carlo, Self-Consistent Mean Field approaches) to reach the mesoscopic one using the phase field modeling. This multi-scale approach is illustrated by a short review of recent studies focusing on dilute and concentrated iron based alloys.

Fission properties of superheavy nuclei for r -process calculations

We computed a new set of static fission properties suited for r-process calculations. The potential energy surfaces and collective inertias of 3640 nuclei in the superheavy region are obtained from Self-Consistent Mean-Field calculations using the Barcelona-Catania-Paris-Madrid energy density functional. The fission path is computed as a function of the quadrupole moment by minimizing the potential energy and exploring octupole and hexadecapole deformations. The spontaneous fission lifetimes are evaluated employing different schemes for the collective inertias and vibrational energy corrections. This allows to explore the sensitivity of the lifetimes to those quantities together with the collective ground state energy along the superheavy landscape. We computed neutron induced stellar reaction rates relevant for r-process nucleosynthesis using the statistical approach and study the impact of collective inertias. The competition between different reaction channels including neutron induced rates, spontaneous fission and alpha decay is discussed for typical r-process conditions.

Bubble nuclei within the self-consistent Hartree-Fock mean field plus pairing approach

The depletion of the nuclear density at its center, called the nuclear bubble, is studied within the Skyrme Hartree-Fock mean field consistently incorporating the superfluid pairing. The latter is obtained within the finite-temperature Bardeen-Cooper-Schrieffer theory and within the approach using the exact pairing. The numerical calculations are carried out for $^{22}\mathrm{O}$ and $^{34}\mathrm{Si}$ nuclei, whose bubble structures, caused by a very low occupancy of the $2{s}_{1/2}$ level, were previously predicted at $T=0$. Among 24 Skyrme interactions under consideration, the MSk3 is the only one which reproduces the experimentally measured occupancy of the $2{s}_{1/2}$ proton level as well as the binding energy, and consequently produces the most pronounced bubble structure in $^{34}\mathrm{Si}$. As compared to the approaches employing the same BSk14 interaction, our approach with exact pairing predicts a pairing effect which is stronger in $^{22}\mathrm{O}$ and weaker in $^{34}\mathrm{Si}$. The increase in temperature depletes the bubble structure and completely washes it out when the temperature reaches a critical value, at which the factor measuring the depletion of the nucleon density vanishes.

Surface properties of neutron-rich exotic nuclei within relativistic mean field formalisms

In this theoretical study, we establish a correlation between the neutron skin thickness and the nuclear symmetry energy for the even$-$even isotopes of Fe, Ni, Zn, Ge, Se and Kr within the framework of the axially deformed self-consistent relativistic mean field for the non-linear NL3$^*$ and density-dependent DD-ME1 interactions. The coherent density functional method is used to formulate the symmetry energy, the neutron pressure and the curvature of finite nuclei as a function of the nuclear radius. We have performed broad studies for the mass dependence on the symmetry energy in terms of the neutron-proton asymmetry for mass 70 $\leq$ A $\leq$ 96. From this analysis, we found a notable signature of a shell closure at $N$ = 50 in the isotopic chains of Fe, Ni, Zn, Ge, Se and Kr nuclei. The present study reveals an interrelationship between the characteristics of infinite nuclear matter and the neutron skin thickness of finite nuclei

Lorentz-symmetry test at Planck-scale suppression with a spin-polarized 133 Cs cold atom clock.

We present the results of a Local Lorentz Invariance (LLI) test performed with the 133Cs cold atom clock FO2 [1], hosted at SYRTE. Such test, relating the frequency shift between 133Cs hyperfine Zeeman substates to the Lorentz violating coefficients of the Standard Model Extension (SME), has already been realized in [2] and led to state-of-the-art constraints on several SME proton coefficients. In this second analysis we used an improved model, based on a second order Lorentz transformation and a SCRMF nuclear model, which enables us to extend the scope of the analysis from purely proton to both proton and neutron coefficients. We have also become sensitive to the isotropic coefficient ~cTT, another SME coefficient that was not constrained in [2]. The resulting limits on SME coefficients improve by up to 13 orders of magnitude the present maximal sensitivities for laboratory tests and reach the generally expected suppression scales at which signatures of Lorentz violation could appear [3].

Continuum approaches for modeling radiation-induced self-organization in materials: From the rate theory to the phase field approach

Abstract

Instability of Dirac semimetal phase under a strong magnetic field

The quantum limit can be easily reached in the Dirac semimetals under the magnetic field, which will lead to some exotic many-body physics due to the high degeneracy of the topological zeroth Landau bands (LBs). By solving the effective Hamiltonian, which is derived by tracing out the high energy degrees of freedom, at the self-consistent mean field level, we have systematically studied the instability of Dirac semimetal under a strong magnetic field. A charge density wave (CDW) phase and a polarized nematic phase formed by "exciton condensation" are predicted as the ground state for the tilted and untilted bands, respectively. Furthermore, we propose that, distinguished from the CDW phase, the polarized nematic phase can be identified in experiments by anisotropic transport and Raman scattering.

The anomalous optical conductivity in hole-doped cuprate superconductors

Based on the renormalized t-J model and self-consistent mean field theory, the doping and energy dependence of optical conductivity and effective electron number in cuprate superconductors are discussed. As the result of the presence of the pseudogap in normal state, the optical conductivity exhibits two main components from underdoping to overdoping, a narrow band peaked around zero energy and a broadband centered in the mid-infrared region which deviates the Drude formula. With increasing the doping concentration, the spectral weight of the optical conductivity suppressed strongly in underdoped region increases quickly, and the peak position of the mid-infrared band moves towards to the lower energy region, then incorporates into the narrow band centered in zero energy in the heavily overdoped region. By virtue of the integral, the effective electron number is obtained, and it increases monotonically from zero energy to mid-infrared characteristic energy with increasing energy, then shows a plateau feature when the energy is larger. In particular, the mid-infrared characteristic energy scales with the pseudogap, reflecting the presence of the mid-infrared band is the result of the pseudogap effect.

Temperature effects on nuclear pseudospin symmetry in the Dirac-Hartree-Bogoliubov formalism

We present finite temperature Dirac-Hartree-Bogoliubov (FTDHB) calculations for the tin isotope chain to study the dependence of pseudospin on the nuclear temperature. In the FTDHB calculation, the density dependence of the self-consistent relativistic mean fields, the pairing, and the vapor phase that takes into account the unbound nucleon states are considered self-consistently. The mean field potentials obtained in the FTDHB calculations are fit by Woods-Saxon (WS) potentials to examine how the WS parameters are related to the energy splitting of the pseudospin pairs as the temperature increases. We find that the nuclear potential surface diffuseness is the main driver for the pseudospin splittings and that it increases as the temperature grows. We conclude that pseudospin symmetry is better realized when the nuclear temperature increases. The results confirm the findings of previous works using RMF theory at $T=0$, namely that the correlation between the pseudospin splitting and the parameters of the Woods-Saxon potentials implies that pseudospin symmetry is a dynamical symmetry in nuclei. We show that the dynamical nature of the pseudospin symmetry remains when the temperature is considered in a realistic calculation of the tin isotopes, such as that of the Dirac-Hartree-Bogoliubov formalism.

Nuclear Matrix Elements for Tests of Local Lorentz Invariance Violation.

The nuclear matrix elements for the spin operator and the momentum quadrupole operator are important for the interpretation of precision atomic physics experiments that search for violations of local Lorentz and CPT symmetry and for new spin-dependent forces. We use the configuration-interaction nuclear shell model and self-consistent mean-field theory to calculate the momentum matrix elements for ^{21}Ne, ^{23}Na, ^{133}Cs, ^{173}Yb, and ^{201}Hg. We show that these momentum matrix are strongly suppressed by the many-body correlations, in contrast to the well-known enhancement of the spatial quadrupole nuclear matrix elements.

Topological charge-density and spin-density waves in InAs/GaSb quantum wells under an in-plane magnetic field

We study interaction effect of quantum spin Hall state in InAs/GaSb quantum wells under an in-plane magnetic field by using the self-consistent mean field theory. We construct a phase diagram as a function of intra-layer and inter-layer interactions, and identify two novel phases, a charge/spin density wave phase and an exciton condensate phase. The charge/spin density wave phase is topologically non-trivial with helical edge transport at the boundary, while the exciton condensate phase is topologically trivial. The Zeeman effect is strongly renormalized due to interaction in certain parameter regimes of the system, leading to a much smaller g-factor, which may stabilize the helical edge transport.