Resonance Approximation Research Articles

Pointwise cross-section-based on-the-fly resonance interference treatment with intermediate resonance approximation

Abstract The effective cross sections (XSs) in the direct whole core calculation code nTRACER are evaluated by the equivalence theory-based resonance-integral-table method using the WIMS-based library as an alternative to the subgroup method. The background XSs, as well as the Dancoff correction factors, were evaluated by the enhanced neutron-current method. A method, with pointwise microscopic XSs on a union-lethargy grid, was used for the generation of resonance-interference factors (RIFs) for mixed resonant absorbers. This method was modified by the intermediate-resonance approximation by replacing the potential XSs for the non-absorbing moderator nuclides with the background XSs and neglecting the resonance-elastic scattering. The resonance-escape probability was implemented to incorporate the energy self-shielding effect in the spectrum. The XSs were improved using the proposed method as compared to the narrow resonance infinite mass-based method. The RIFs were improved by 1% in 235U, 7% in 239Pu, and >2% in 240Pu. To account for thermal feedback, a new feature was incorporated with the interpolation of pre-generated RIFs at the multigroup level and the results compared with the conventional resonance-interference model. This method provided adequate results in terms of XSs and k-eff. The results were verified first by the comparison of RIFs with the exact RIFs, and then comparing the XSs with the McCARD calculations for the homogeneous configurations, with burned fuel containing a mixture of resonant nuclides at different burnups and temperatures. The RIFs and XSs for the mixture showed good agreement, which verified the accuracy of the RIF evaluation using the proposed method. The method was then verified by comparing the XSs for the virtual environment for reactor application-benchmark pin-cell problem, as well as the heterogeneous pin cell containing burned fuel with McCARD. The method works well for homogeneous, as well as heterogeneous configurations.

On the Born-Oppenheimer approximation of diatomic molecular resonances

We give a new reduction of a general diatomic molecular Hamiltonian, without modifying it near the collision set of nuclei. The resulting effective Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator (the semiclassical parameter being the inverse of the square-root of the nuclear mass) and a semibounded operator localised in the elliptic region corresponding to the nuclear collision set. We also study its behaviour on exponential weights and give several applications where molecular resonances appear and can be well located.

Sensitivity of predictions in an effective model: Application to the chiral critical end point position in the Nambu-Jona-Lasinio model

The measurement of the position of the chiral critical end point (CEP) in the QCD phase diagram is under debate. While it is possible to predict its position by using effective models specifically built to reproduce some of the features of the underlying theory (QCD), the quality of the predictions (\textit{e.g.}, the CEP position) obtained by such effective models, depends on whether solving the model equations constitute a well- or ill-posed inverse problem. Considering these predictions as being inverse problems provides tools to evaluate if the problem is ill-conditioned, meaning that infinitesimal variations of the inputs of the model can cause comparatively large variations of the predictions. If it is ill-conditioned, it has major consequences because of finite variations that could come from experimental and/or theoretical errors. In the following, we shall apply such a reasoning on the predictions of a particular Nambu--Jona-Lasinio model within the mean field + ring approximations, with special attention to the prediction of the chiral CEP position in the $(T-\mu)$ plane. We find that the problem is ill-conditioned (\idest very sensitive to input variations) for the $T$-coordinate of the CEP, whereas, it is well-posed for the $\mu$-coordinate of the CEP. As a consequence, when the chiral condensate varies in a $10$ MeV range, $\mu_{CEP}$ varies far less. As an illustration to understand how problematic this could be, we show that the main consequence when taking into account finite variation of the inputs, is that the existence of the CEP itself cannot be predicted anymore: for a deviation as low as 0.6 \% with respect to vacuum phenomenology (well within the estimation of the first correction to the ring approximation) the CEP may or may not exist.

Resonant Dynamics and the Instability of Anti-de Sitter Spacetime.

We consider spherically symmetric Einstein-massless-scalar field equations with a negative cosmological constant in five dimensions and analyze the evolution of small perturbations of anti-de Sitter (AdS) spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing the instability of AdS under arbitrarily small perturbations.

Effect of generalized Breit interaction in dielectronicrecombination for highly charged ions

Dielectronic recombination (DR) for highly charged Fe, I, Ba, Bi and U ions are calculated with our developed codes. The calculations are based on isolate resonance approximation, and the free electrons are described with a fully relativistic distorted wave. The Auger decay rates are calculated in Coulomb plus generalized Breit interaction (GBI) and Møller interaction, respectively. The two-electron integrals in the imaginary parts of GBI and Møller interactions are derived to be the product of two one-electron integrals. By comparing our calculations with published theoretical and experimental results, residual relativistic and GBI effects are discussed. DR transitions through optical forbidden decays are investigated.

Dynamics of quantum transitions in Magnus representation

Dynamics of a two-level quantum system in an electromagnetic excitation field is investigated in the Magnus representation on the Bloch sphere. This approach leads to the general expressions for the probability of quantum transitions beyond the resonance approximation. The applications of these results to the interaction of a qubit with a monochromatic field as well as with the Gaussian pulse are presented.

An Improved Resonance Self-Shielding Calculation Method Based on Equivalence Theory

The deviation of the effective resonance cross section obtained by conventional equivalence theory for a heterogeneous system is analyzed. It is shown that several approximations commonly adopted in conventional equivalence theory account for the deviation at different levels, with the narrow resonance (NR) approximation being the main source of deviation. Based on the analysis, an improved method based on equivalence theory is proposed. It utilizes the resonance fine flux integral table to minimize the deviation caused by NR approximation. The validity of the method is confirmed by test calculations of effective resonance cross sections in different geometries and different energy group structures. The results of eigenvalue calculations on typical fuel pin cells show that the proposed improvement is effective in reducing the error of infinite multiplication factors of the pin cell. Since the resonance fine flux integral used in this method has already been obtained in calculating the resonance integral table and can be pre-tabulated in the process of generating the library, the implementation of the proposed method is simple and requires no additional calculations. It is useful for improving the accuracy of lattice physics codes based on the equivalence theory.

Resonant approximation of phase-shifted Bragg grating (PSBG) spectra

The resonance approximations of phase-shifted Bragg grating (PSBG) reflection and transmission coefficients are obtained as a function of frequency and wave-vector’s tangential components of incident light. The proposed theoretical description is verified using numerical simulations.

Assessing the accuracy of the Brodsky-Lepage prediction

We showed that a consistent set of short-distance conditions on the odd-intrinsic parity resonance chiral Lagrangian couplings can be derived in the large-NC limit and the single resonance approximation. These constraints are satisfied both by the VVP Green function and all its associated form-factors. Moreover, they are in agreement with earlier results found in the normal parity sector, which further supports the overall consistency of the approach. Here we take a new perspective and examine the consequences of these high-energy relations on the precise coefficient of the 1/Q2-term of meson form-factors, which rules their asymptotic behavior. In particular, we show that the coefficient derived using our consistent set of short-distance constraints is in remarkable accordance with the Brodsky-Lepage prediction, being alternative results for these coefficients disfavored.

Sensitivity and uncertainty analysis for UO2 and MOX fueled PWR cells

This paper discusses the improvement of a method for calculating sensitivity coefficients of neutronics parameters relative to infinite dilution cross-sections because the conventional method neglects resonance self-shielding effect. In this study, the self-shielding effect is taken into account by using the intermediate resonance approximation in order to get accurate results in both high and low energy groups. The improved method is applied to calculate sensitivity coefficients and uncertainties of eigenvalue responses for UO2 and MOX (ThO2–UO2 and PuO2–UO2) fueled pressurized water reactor cells. The verification of the improved method was performed by comparing the sensitivities with MCNP6 and TSUNAMI-1D. For uncertainty, calculation comparisons were done with TSUNAMI-1D, and we demonstrate that the differences are caused by the use of different covariance matrices.

Efficient and accurate treatment of weak pairs in local CCSD(T) calculations. II. Beyond the ring approximation.

In order to arrive at linear scaling of the computational cost with molecular size, local coupled cluster methods discriminate pairs of local molecular orbitals according to the spatial separation R of the latter. Only strong pairs are treated at the full coupled cluster level, whereas for weak pairs a lower level of theory (usually Møller-Plesset perturbation theory of second order, MP2) is used. Yet an MP2 treatment of weak pairs is inadequate in certain situations (for example, for describing π-stacking), which calls for an improved but still inexpensive method for dealing with the weak pairs. In a previous contribution, we proposed as a substituent for MP2 the LrCCD3 method, which is based on ring coupled cluster doubles (ring-CCD) and includes all third-order diagrams with energy contributions decaying not quicker than R(-6). In the present work, we explore a still more accurate method, which is based on the same principles. It turned out to be essential to abandon the restriction to ring-CCD, i.e., to include further CCD diagrams beyond the ring approximation. The occurring intermediates turn out to be formally very similar to LMP2 density matrices, such that an efficient evaluation of these non-ring CCD diagrams is possible. Furthermore, a computationally cheap a posteriori estimate for the fourth-order singles contribution to the weak pair energy, which also exhibits a decay behavior of R(-6), is introduced. The resulting method, denoted as LCCD[S]-R(-6), indeed provides a substantial improvement in accuracy over the previous LrCCD3 method at a relatively modest additional computational cost.

Levitating states of superconducting rings in the field of a fixed ring with constant current

We consider the possibility of designing a plasma trap with a magnetic system formed by super-conducting rings and coils levitating in the field of a fixed coaxial coil carrying constant current. An analytic dependence of the potential energy of such a system with one or two levitating superconducting rings having trapped preset magnetic fluxes on their coordinates in the uniform gravitational field is obtained in the thin ring approximation. Calculations performed in the Mathcad system show that equilibrium states of such a system exist for certain values of parameters. Levitating states of a single superconducting ring and two superconducting rings in the field of the coil with constant current are observed experimentally in positions corresponding to calculated values.

Flexible Pipes: Influence of the Pressure Armor in the Wet Collapse Resistance

When submitted to high external pressure, flexible pipes may collapse. If the external sheath is damaged, all the external pressure is directly applied on the internal polymeric layer that transmits the loading to the carcass layer, which can fail due to this effect, leading to wet collapse. This failure mode must be taken into account in a flexible pipe design. A model can be set up neglecting the influence of the pressure armor, but this assumption may underestimate the wet collapse pressure value. This work aims to include the pressure armor effect in the numerical prediction of wet collapse. The main contribution of the pressure armor to the flexible pipe resistance to collapse is to be a constraint to the radial displacement of the carcass and the internal polymeric layers. Two models were developed to find the wet collapse pressure in flexible pipes. A first study was done using a ring approximation three-dimensional (3D) finite element method (FEM) model. Comparisons are made with more simplified models using a 3D FEM equivalent ring approximation. The aim is to clarify the mechanical behavior of the pressure armor in the wet collapse scenario. Parametric studies of initial ovalization of carcass and initial gaps and interference between polymeric layer and pressure armor are made and discussed.

Electron-impact excitation and single- and multiple-ionization cross sections of heavy ions: Sn13+as an example

The cross sections of electron impact with Sn${}^{13+}$ resulting in the production of Sn${}^{13+}$-Sn${}^{16+}$ are investigated theoretically by using the fine-structure-level distorted-wave approximation from the threshold to 4000 eV. The electron-impact excitation, ionization, and resonant excitation processes are included in the cross sections. Contributions from different processes are determined by independent processes and isolated resonance approximations. The decay pathways and branching ratios for single and sequentially multiple autoionization for the final autoionized states are determined by detailed calculations. The cross section forming Sn${}^{13+}$ is the largest and next are those for Sn${}^{14+}$ and Sn${}^{15+}$. The double-ionization cross section forming Sn${}^{15+}$ is smaller than that forming Sn${}^{14+}$, yet the relative magnitude is larger at higher incident electron energy. A comparison with a recent measurement for the single-ionization cross section [A. Borovik, Jr. et al., J. Phys. B 46, 175201 (2013)] showed that accurate determination of the branching ratios for single and double autoionization and including contributions of the resonant excitation double autoionization are crucial to obtain accurate results.

Dirac fermion time-Floquet crystal: Manipulating Dirac points

We demonstrate how to control the spectra and current flow of Dirac electrons in both a graphene sheet and a topological insulator by applying either two linearly polarized laser fields with frequencies $\omega$ and $2\omega$ or a monochromatic (one-frequency) laser field together with a spatially periodic static potential(graphene/TI superlattice). Using the Floquet theory and the resonance approximation, we show that a Dirac point in the electron spectrum can be split into several Dirac points whose relative location in momentum space can be efficiently manipulated by changing the characteristics of the laser fields. In addition, the laser-field controlled Dirac fermion band structure -- Dirac fermion time-Floquet crystal -- allows the manipulation of the electron currents in graphene and topological insulators. Furthermore, the generation of dc currents of desirable intensity in a chosen direction occurs when applying the bi-harmonic laser field which can provide a straightforward experimental test of the predicted phenomena.

Consistent high-energy constraints in the anomalous QCD sector

The anomalous 〈VVP〉 Green function and related form-factors (π0→γ⁎γ⁎ and τ−→X−ντ vector form-factors, with X−=(KKπ)−, φ−γ, (φV)−) are analyzed in this letter in the large-NC limit. Within the single (vector and pseudoscalar) resonance approximation and the context of Resonance Chiral Theory, we show that all these observables overdetermine in a consistent way a unique set of compatible high-energy constraints for the resonance couplings. This result is in agreement with analogous relations found in the even intrinsic-parity sector of QCD like, e.g., FV2=3F2. The antisymmetric tensor formalism is considered for the spin-one resonance fields. Finally, we have also worked out and provide here the relation between the two bases of odd intrinsic-parity Lagrangian operators commonly employed in the literature.

VV′Pform factors in resonance chiral theory and theπ−η−η′light-by-light contribution to the muong−2

The description of the VV'P form factors (V,V' stands for vector particles and P for a pseudoscalar meson) for different particles virtualities remains a challenge for the theory of strong interactions. While their chiral limit is well understood, recent measurements of the gamma^* omega pi^0 and gamma^* gamma pi^0 form factors at high photon virtualities seem to depart from the simplest scaling behavior suggested by QCD. Here we attempt to describe them in their whole measured energy regimes within the Resonance Chiral Theory, a framework which naturally incorporates the chiral limit constraints and extends to higher energies by including the resonances as active fields. Specifically, we obtained an accurate description of the data up to 2 GeV on the former form factor by including three multiplets of vector resonances. Good agreement with measurements of the latter was possible even in the single resonance approximation, although we propose to measure the e^+e^- to mu^+mu^-pi^0 cross-section and di-muon invariant mass distribution to better characterize this form factor. We have then evaluated the pion exchange contribution to the muon g-2 obtaining (6.66\pm0.21)x10^{-10} with an accurate determination of the errors. We have also recalled that approximating the whole pion exchange by the pion pole contribution underestimates the corresponding result for the anomaly (by (15,20)%). Based on these results, we have predicted the eta^(\prime) transition form factors obtaining good agreement with data and obtained their respective contributions to the muon anomaly. In this way, the contribution of the three lightest pseudoscalars to it yields (10.47\pm0.54)x10^{-10}, in agreement with previous evaluations but with smaller error.

Quantum and classical phenomena in photoionization of carbon nanostructures

We present the results of investigation of electron excitations in various carbon-based nanoscale systems in the process of photoionization. As a case study, we consider a number of highly symmetric fullerenes, namely C20, C60 and C80, as well as aromatic hydrocarbons – benzene (C6H6) and coronene (C24H12). The calculations are performed within the ab initio TDDFT framework and model approach, based on the plasmon resonance approximation. Analysis of the results demonstrates that the main contribution to the photoionization spectra of nanoscale carbon systems is due to collective excitations of delocalized electrons, known as plasmons. Results of the model-based calculations are in close agreement with those of the more accurate quantum-chemical calculations and correspond also to the existing experimental data.

Improved ring approximation for the free energy in thermal scalar field theory

In a d-dimensional field theory at finite temperature T, with a interaction, we compute the contributions to the free energy in the ring approximation. These are calculated in a consistent manner, by evaluating the thermal self-energy in a similar approximation. The complete result can be expressed in closed form in terms of the Haber and Weldon functions . This result exhibits, to leading order, a non-analyticity in the coupling constant of the form or when d is even or odd, respectively.

Polylogarithm-Based Computation of Fano Resonance in Arrayed Dipole Scatterers

Efficient descriptions for Fano resonant properties of plasmonic arrays of nanoparticles could support selection of particle and array characteristics to achieve specific spectral outcomes. In contrast to conventional particle-by-particle computation of Fano resonances from arrayed particles, this work uses polylogarithms to assemble a semianalytical solution to the coupled dipole approximation for far-field Fano resonances from two-dimensional arrays by superposing results from discrete, one-dimensional chains of particles that comprise the array. This approach directly depicts the effects of discrete particle chains on the overall spectral features of an array, thus enhancing intuitive understanding of these effects, and reduces the computation time 56% relative to particle-by-particle evaluation. Fano resonance spectra calculated using polylogarithms are punctuated by more frequent, sharper oscillations and fine features due to summed contributions from distant interfering dipoles not present in spectra calculated using a necessarily finite number of particles. Chains more orthogonal to the axis of polarization contribute more Fano features due to broadband, sin2 θij dependent dipole scattering coupling to narrow diffracted modes. Overall, the approach improves accessibility and increases the speed of designing nanoparticle lattices for particular outcomes.