R-matrix Theory Research Articles

Prediction of a complete and self-consistent collision cross-section set of C5F10O by data-driven method

The lack of a complete and consistent set of electron–molecule collision cross sections for the new eco-friendly gas C5F10O hinders the study of its microscopic discharge mechanisms. In this paper, we first calculate the elastic collision and electronic excitation cross-sections of C5F10O based on R-matrix theory and estimate its total attachment cross-sections through pulsed Townsend measurement. By combining cross sections from other literature, we are able to compile an initial set of collision cross-sections for C5F10O. However, this initial set remains incomplete and requires refinement. Therefore, this work establishes a neutral network to solve the inverse swarm problem of deriving cross-sections from swarm parameters. The inversion model is trained using a substantial amount of collision cross-sections from the LXCat project. Using the model and the initial set for C5F10O, a complete and self-consistent collision cross-section set for the C5F10O gas is predicted for the first time, based on the measured electron swarm parameters of C5F10O/Ar mixtures. The proposed method is capable of predicting C5F10O’s unknown vibrational excitation cross-section without any prior knowledge, thus enhancing its completeness. The refined set can reproduce the electron swarm parameters within an acceptable range of uncertainty, thus verifying its self-consistency. The set will be made available in the LXCat database, which is expected to be significant for fundamental studies of its discharge mechanisms as well as applications of C5F10O.

Neutron resonance cross sections evaluation based on the phase shift deep neural network

Neutron resonance cross sections are essential in many nuclear science and application fields. Evaluated nuclear libraries usually derive neutron resonance parameters using R-matrix theory. However, determining these parameters and reconstructing the pointwise cross sections required for transport calculations is a time-consuming process. This paper presents a new method for fitting neutron resonance cross sections by using a phase shift deep neural network (PhaseDNN). The network presents resonance cross sections based on its network parameters. This approach allows for the quick calculation of cross section values from the given network parameters. Additionally, PhaseDNN can fit network parameters to experimental data to obtain a smooth resonance cross section curve. Therefore, it has the potential to be an alternative to R-matrix theory.

Low-Energy Electron Scattering from Pyrrole and Its Isomers.

Low-energy electron scattering from pyrrole and its isomers, such as 2-H pyrrole, cyclopropanecarbonitrile, and Z-2 butenenitrile, is explored in detail in this article. The electron interaction with the target molecules was studied through R-matrix theory. We have used minimal STO-3G and advanced DZP basis sets on a fine energy grid from 0.1 to 12 eV electron energy in the calculation. The properties of the STO-3G and DZP-based targets, such as their ionization energy, polarizability, dipole moment, rotational constant, principal moment of inertia, ground-state energy, and orbital energies, were investigated and compared to previously reported data. The elastic and inelastic channels showed the appearance of shape and Feshbach resonances for pyrrole and its isomers. The ultralow-energy region resonance was observed for Z-2 butenenitrile at 0.47 eV. With STO-3G and DZP basis sets, we estimated elastic, excitation, and momentum-transfer cross sections. The differential cross section for the present polar molecules was studied at 5 eV. The dissociative electron attachment channel for pyrrole and its isomers was studied for the pyrrolide anion. The data presented here will be helpful in astrophysical, astrochemical, atmospheric, and low-energy plasma modeling due to the presence of pyrrole and its isomers and the pyrrolide anion in the celestial bodies. The estimated data are also helpful in the biomedical field, radiation therapy, and pharmaceuticals.

Lawson criterion for different scenarios of using D-3He fuel in fusion reactors

The paper is devoted to refining the Lawson criterion for three scenarios of using D-3He fuel in fusion reactors (fully catalyzed and non-catalysed D-D cycles and a D-3He cycle with 3He self-supply). To this end, a new parameterization of the D + 3He → p + 4He fusion reaction cross-section and astrophysical factor has been developed based on the effective radius approximation (Landau-Smorodinsky-Bethe approximation), which is a model-free theoretical approach to investigating near-threshold nuclear reactions, including resonant reactions. In the framework of this approximation, experimental data from studies in the NACRE II and EXFOR libraries, believed to provide the most reliable results to date, have been described within the accuracy declared in the studies in question in the energy range of 0 to 1000 keV, and the fusion reactivity averaged over the Maxwell distribution has been calculated. The results obtained are in good agreement with the calculations based on the R-matrix theory and the NACRE II fusion reactivity data. For the fully catalyzed D-D cycle and the cycle with 3He self-supply, the Lawson criterion and the triple Lawson criterion have been calculated based on solving the equations of the stationary process kinetics in a fusion reactor for three fuel ions (D, 3He, and T) taking into account the potential for external supply of 3He and p and 4He impurity ions removed from the reaction zone. The parameters of the triple Lawson criterion found are as follows: nτT = 6.42∙1016 cm-3∙s∙keV (T = 54 keV) for the fully catalyzed D-D cycle, nτT = 1.03∙1017 cm-3∙s∙keV (T = 45 keV) for the cycle with 3He self-supply, and nτT = 4.89∙1016 cm-3∙s∙keV (T = 67 keV) for the non-catalyzed D-D cycle with equimolar D-3He fuel.

Applications of the R-Matrix Method in Integrable Systems

Based on work related to the R-matrix theory, we first abstract the Lax pairs proposed by Blaszak and Sergyeyev into a unified form. Then, a generalized zero-curvature equation expressed by the Poisson bracket is exhibited. As an application of this theory, a generalized (2+1)-dimensional integrable system is obtained, from which a resulting generalized Davey–Stewartson (DS) equation and a generalized Pavlov equation (gPe) are further obtained. Via the use of a nonisospectral zero-curvature-type equation, some (3+1) -dimensional integrable systems are produced. Next, we investigate the recursion operator of the gPe using an approach under the framework of the R-matrix theory. Furthermore, a type of solution for the resulting linearized equation of the gPe is produced by using its conserved densities. In addition, by applying a nonisospectral Lax pair, a (3+1)-dimensional integrable system is generated and reduced to a Boussinesq-type equation in which the recursion operators and the linearization are produced by using a Lie symmetry analysis; the resulting invertible mappings are presented as well. Finally, a Bäcklund transformation of the Boussinesq-type equation is constructed, which can be used to generate some exact solutions.

Dissociative recombination of N_2hbox {H}^+: a revisited study

Dissociative recombination of N_2H^+ is explored in a two-step theoretical study. In a first step, a diatomic (1D) rough model with a frozen NN bond and frozen angles is adopted, in the framework of the multichannel quantum defect theory (MQDT). The importance of the indirect mechanism and of the bending mode is revealed, in spite of the disagreement between our cross section and the experimental one. In the second step, we use our recently elaborated 3D approach based on the normal mode approximation combined with R-matrix theory and MQDT. This approach results in satisfactory agreement with storage-ring measurements, significantly better at very low energy than the former calculations.

Matter-antimatter rearrangements using the R-matrix method

Antihydrogen atoms, H―, are now routinely created and can be stored for long enough to allow comparison with ordinary matter. A major goal of these efforts is to test potential physics beyond the Standard Model. This will require further developments in the experiments including the accumulation of more antihydrogen atoms and their storage over longer times. The latter is limited by the unavoidable presence of normal hydrogen molecules. Interactions of H― with H2 lead to the destruction of the hard-won antimatter. Little is known about these interactions but quantitative information will be crucial in guiding experimental developments. Physically realistic modelling of rearrangement scattering of “heavy” antimatter particles (antiprotons, p―, and antihydrogen atoms) by normal matter molecules, such as H2 + H―→ Pn + Ps + H (where Pn represents protonium and Ps positronium), requires the development of new theoretical and computational methodologies. R-matrix theory offers a strong prospect for tackling such problems having proved itself in atomic, molecular and optical physics. It divides the problem into a computationally demanding but energy-independent inner region and simpler energy-dependent outer regions. We propose to adapt the new RmatReact ultracold chemistry approach for the more complex molecular matter-antimatter problems. Here, developments required for the inner region, the boundary and outer regions are outlined. We also report some preliminary bound-state calculations on the {p,p,p―} system and a study of the required mixed coordinate systems for the general effective 3-body case and their transformations at the R-matrix boundary surfaces.

Relativistic analytical R -matrix theory for strong-field ionization

The analytical R-matrix (ARM) theory has been known for an efficient description of the Coulomb effects of the atomic core in strong-field ionization in the nonrelativistic regime. We generalize the ARM theory into the relativistic domain aiming at the application to strong-field ionization of highly charged ions in ultrastrong laser fields. Comparison with the relativistic Coulomb-corrected strong-field approximations (SFA) is provided, highlighting the advantages and disadvantages. The weakly relativistic asymptotics and its accordance with the nondipole Coulomb-corrected SFA are examined. As an example of a physical application of the relativistic ARM, the Coulomb enhancement of tunneling ionization probability for highly charged ions at the cutoff of the direct channel is discussed.

A novel R-matrix formalism for three-body channels

At low incident neutron energies nuclear reaction cross sections exhibit a distinct resonance structure which cannot properly be described by (semi-)microscopic models. Usually R-matrix theory is applied which provides a suffi ciently accurate but phenomenological description of the resonance region. However, standard R-matrix theory is only suited for two-particle channels. Three- and many-particle channels which may occur in light nuclear systems even at rather low incident energies are usually treated in an approximative or effective way. In this contribution a novel R-matrix formalism for three-body channels and its application to nuclear systems will be presented. It is a generalized and significantly modified form of a proposal by W. Glöckle based on the Faddeev equations.

140,142Ce Neutron Cross Section Resolved Resonance Region Evaluation

A resolved resonance region evaluation of 140,142Ce was conducted by Oak Ridge National Laboratory. Requested by the US Nuclear Criticality Safety Program, this evaluation is based on recent high-resolution transmission and capture high-resolution measurements of natCe and 142Ce conducted at JRC-Geel at the Geel Linear Accelerator facility. It is also based on recently measured thermal constants available from the EXFOR database [1]. Starting from the resonance parameters from the ENDF/B-VIII.0 library [2] and following a preliminary R-matrix analysis [3], an updated set of resonance parameters and corresponding covariance information was derived by the fit of these experimental datasets using the Reich–Moore approximation of the R-matrix theory, as implemented in the SAMMY code system [4]. The resolved resonance region upper energy limit for 140Ce was kept at 200 keV, whereas the 142Ce resonance region was extended from 13 to 26 keV. This new evaluation was found to be in good agreement not only with several integral quantities of interest to the reactor physics community, but also with the stellar Maxwellian-averaged cross section [5].

Present status of an R-matrix analysis code AMUR for cross-section evaluation in resolved resonance region

An R-matrix analysis code AMUR is being progressed in terms of the correction on the experimental conditions to the theoretical calculations. In this work, new broadening options are presented both for cross-sections and angular distribution with given energy resolution. The code is also under development to analyze the J-PARC/ANNRI measurement with the double-bunch mode. In the final part, let me focus on understanding of the R-matrix theory itself, in which a role of distant poles is discussed in the simultaneous analysis of the same compound nucleus.

Covariances and parameter confidence intervals from light-element R-matrix evaluations

R-matrix parameter covariances for light elements with A 16 are calculated within the Wigner-Eisenbud multichannel unitary R-matrix theory. We review the theoretical foundation, numerical approach, and determination of the parameter covariances within this approach. We derive the relation between the parameter variance, as the diagonal elements of the covariance matrix, and the parameter confidence interval based upon the chi-squared distribution. Cross section covariances computed from the parameter confidence intervals are calculated for several compound systems and discussed.

A new R-matrix module for multi-channel calculations with GECCCOS

A versatile new R-matrix module for multi-channel reaction calculations was introduced into the code GECCCOS (GEneral Coupled-Channel COde System) which has been developed by the nuclear data group at TU-Wien to perform nuclear reaction calculations especially for light nuclear systems. It provides a tool for phenomenological R-matrix analyses of reaction data combined with calculations of a potential-based calculable R-matrix using the Lagrange-mesh technique. In addition it provides a platform for the development of non-standard extensions of R-matrix theory such as Reduced R-matrix analyses and the Hybrid R-matrix. A successful run of the code yields the complete S-matrix (collision matrix) as well as observables for unpolarized beams, angle-differential cross sections, excitation functions and, if existing, angle-integrated cross sections. Recently, extensions to polarization observables for spin-1/2 and spin-1 particles were implemented and tested. For phenomenological R-matrix analyses a separate module assembles calculated and available experimental values, automatically performs transformations with regard to reference frame and matching radii. Furthermore it allows to switch between incident channel and compound nucleus representation and provides the necessary feedback for the chi2 fitting process.

Ellipticity dependence of anticorrelation in the nonsequential double ionization of Ar.

Within the framework of the improved quantitative rescattering (QRS) model, we simulate the correlated two-electron momentum distributions (CMDs) for nonsequential double ionization (NSDI) of Ar by elliptically polarized laser pulses with a wavelength of 788 nm at an intensity of 0.7 × 1014 W/cm2 for the ellipticities ranging from 0 to 0.3. Only the CMDs for recollision excitation with subsequent ionization (RESI) are calculated and the contribution from recollision direct ionization is neglected. According to the QRS model, the CMD for RESI can be factorized as a product of the parallel momentum distribution (PMD) for the first released electron after recollision and the PMD for the second electron ionized from an excited state of the parent ion. The PMD for the first electron is obtained from the laser-free differential cross sections for electron impact excitation of Ar+ calculated using state-of-the-art many-electron R-matrix theory while that for the second electron is evaluated by solving the time-dependent Schrödinger equation. The results show that the CMDs for all the ellipticities considered here exhibit distinct anticorrelated back-to-back emission of the electrons along the major polarization direction, and the anticorrelation is more pronounced with increasing ellipticity. It is found that anticorrelation is attributed to the pattern of the PMD for the second electron ionized from the excited state that, in turn, is caused by the delayed recollision time with respect to the instant of the external field crossing. Our work shows that both the ionization potential of the excited parent ion and the laser intensity play important roles in the process.

Reconciling Conflicting Approaches for the Tunneling Time Delay in Strong Field Ionization.

Several recent attoclock experiments have investigated the fundamental question of a quantum mechanically induced time delay in tunneling ionization via extremely precise photoelectron momentum spectroscopy. The interpretations of those attoclock experimental results were controversially discussed, because the entanglement of the laser and Coulomb field did not allow for theoretical treatments without undisputed approximations. The method of semiclassical propagation matched with the tunneled wave function, the quasistatic Wigner theory, the analytical R-matrix theory, the backpropagation method, and the under-the-barrier recollision theory are the leading conceptual approaches put forward to treat this problem, however, with seemingly conflicting conclusions on the existence of a tunneling time delay. To resolve the contradicting conclusions of the different approaches, we consider a very simple tunneling scenario which is not plagued with complications stemming from the Coulomb potential of the atomic core, avoids consequent controversial approximations and, therefore, allows us to unequivocally identify the origin of the tunneling time delay.

Study of Charged Particles Scattering with Atomic Target

In this paper, we have reported the calculated results of anisotropy parameter (Pl) and angular momentum transfer parameter (L) for positron (electron) scattering by Calcium (Ca) atom using close coupling approximation method in the framework of R-matrix theory at 20eV. Since this theory has deep root in nuclear physics, it also provides better results in atomic and molecular physics. The authors have compared the reviewed results with available theoretical results. A good agreement between these results shows that the present method gives better understanding for the positron (electron)-atom scattering.

Generalizations of the R-Matrix Method to the Treatment of the Interaction of Short-Pulse Electromagnetic Radiation with Atoms

Since its initial development in the 1970s by Phil Burke and his collaborators, the R-matrix theory and associated computer codes have become the method of choice for the calculation of accurate data for general electron–atom/ion/molecule collision and photoionization processes. The use of a non-orthogonal set of orbitals based on B-splines, now called the B-spline R-matrix (BSR) approach, was pioneered by Zatsarinny. It has considerably extended the flexibility of the approach and improved particularly the treatment of complex many-electron atomic and ionic targets, for which accurate data are needed in many modelling applications for processes involving low-temperature plasmas. Both the original R-matrix approach and the BSR method have been extended to the interaction of short, intense electromagnetic (EM) radiation with atoms and molecules. Here, we provide an overview of the theoretical tools that were required to facilitate the extension of the theory to the time domain. As an example of a practical application, we show results for two-photon ionization of argon by intense short-pulse extreme ultraviolet radiation.

Neutron capture cross section measurements for <sup>nat</sup>Lu with different thickness

The C<sub>6</sub>D<sub>6</sub> detection system coupling with the pulse height weighting technique is widely used for experimentally measuring the neutron capture cross section. The thickness of sample used in the experiment directly affects the neutron beam time and the reliability of the experimental data. In the present work, we compare the lutetium (Lu) neutron capture reaction cross sections among the samles with different thickness, obtained by the C<sub>6</sub>D<sub>6</sub> detection system of the back-streaming white neutron beam line at China spallation Neutron Source (CSNS back-n). The light response of the detection system is simulated with the consideration of the sample thickness by GEANT4 Monte Carlo simulation code. The 4<sup>th</sup> order polynomial pulse weight functions for different samples are determined by using the above light response function. In the experiment, the high precision capture yield distributions in the resonance energy region are obtained by measuring the longer flight distance and background. The experimental resonance parameters are deduced by analyzing the capture yield distribution with the R-matrix theory. The comparisons of the results of capture yield and the resonance parameters between the two groups show that the resonance curve of 1.06mm <sup>nat</sup>Lu sample changes due to its thickness effect, and there is a large difference between the experimental resonance parameters and ENDF/B-VIII.0 database. However, the experimental results of 0.207mm <sup>nat</sup>Lu sample can well accord with the ENDF/B-VIII. 0 data.

Measurement of total neutron cross section of natural lithium at China Spallation Neutron Source Back-n facility

Lithium is one of the main materials of fuel carrier salt in molten salt reactors. Its neutron cross section provides an important basic datum for physical design of molten salt reactor core and for evaluating the safety of the core during operation. The total neutron cross sections of natural lithium samples with thickness values of 8.00 mm and 15.0 mm are measured, respectively, in an energy range from 0.4 eV to 20 MeV by using a neutron total cross section spectrometer (NTOX) with the transmission method at the Back-n white neutron source of China Spallation Neutron Source (CSNS Back-n) with a 76.0 m time-of-flight path. High quality experimental data are obtained, especially in the energy region of keV and below, which supply a significative supplement of the data, thereby providing more abundant and reliable experimental data for nuclear data evaluation of lithium. Additionally, a theoretical analysis is carried out under the guidance of 1/<i>v</i> law and the multilevel R-matrix theory. And the resonance parameters of n+<sup>6,7</sup>Li reaction around the energy of 260 keV are extracted from the measured data.

R -matrix theory with level-dependent boundary condition parameters

I present a new formalism of the R-matrix theory where the formal parameters for the resonance energies and widths are identical to the observed values. By allowing the boundary condition parameters to vary from level to level, the freedom required to adjust the formal parameters for the pole positions to the observed values is obtained. The basis of the resulting theory becomes nonorthogonal, and I describe the procedure to construct a consistent R-matrix theory with such a nonorthogonal basis. And by adjusting the normalization of the states that form the basis, the formal parameters for the reduced decay widths also become the same as those observed, leaving no formal parameters that are different from the observed ones. A demonstration of the developed theory to the elastic 12C+p scattering data is presented.