R-matrix Theory Research Articles

Measurements and parametrization of the 16O(d,d0)16O differential cross section

The differential cross section of the deuteron elastic scattering on oxygen was studied, experimentally, in the energy range of 1.5 – 2.5 MeV, in order for the theoretical study to be accomplished in the energy range 1.9–2.5 MeV for the scattering angles of 130°, 140°, 150°, 160° and 170°.The experiment was performed at the Tandem 5.5 MV Accelerator of the N.C.S.R. “Demokritos” in Athens, Greece. The theoretical study was accomplished in order to extend the pre-existing evaluation, which stopped at 1.98 MeV, up to 2.5 MeV. The used code implements the R-matrix theory along with optical model calculations.

Scattering matrix pole expansions for complex wave numbers inR-matrix theory

In this follow-up article to [Shadow poles in the alternative parametrization of R-matrix theory, Ducru (2020)], we establish new results on scattering matrix pole expansions for complex wavenumbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory, and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wavenumbers. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift $\boldsymbol{S}$ and penetration $\boldsymbol{P}$ functions: the legacy Lane \& Thomas "force closure" approach, versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF. In this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and unveil new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii $a_c$. We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix -- cancelling spurious poles and guaranteeing generalized unitarity -- while still being able to close channels below thresholds.

Shadow poles in the alternative parametrization of R -matrix theory

Nuclear data libraries (ENDF, JEFF, JENDL, CENDL, etc.) document our phenomenological knowledge of nuclear cross sections as interpreted by R-matrix theory. The R-matrix scattering model can parameterize the energy dependence of the scattering matrix in different ways. This article establishes new results on three such sets of parameters: the Wigner-Eisenbud, the Brune, and the Siegert-Humblet parameters. We show how the latter two arise from invariance to the arbitrary boundary condition, and how they can trade-off more complex parameters for a simpler energy dependence parameterization: the scattering matrix pole expansion of Humblet and Rosenfeld. We establish that the scattering matrix's invariance to channel radius sets a partial differential equation on the widths of the Kapur-Peierls operator, which enables us to derive an explicit transformation of the Siegert-Humblet radioactive residue widths under a change of channel radius. Considering the continuation of the scattering matrix to complex wavenumbers, several new results are established. We unveil there exist more Brune parameters than previously thought, depending on the way the scattering matrix is continued to complex energies. This points to a broader conundrum in the field: how to analytically continue the scattering matrix while closing sub-threshold channels. We argue that, contrary to the Lane and Thomas legacy of force-closing sub-threshold channels which introduces spurious poles, analytic continuation is the physically correct way of defining the scattering matrix for complex wave numbers. To back this claim we establish thee results: analytic continuation cancels spurious poles, enforces the generalized unitarity conditions of Eden and Taylor, and closes massive particle channels below threshold by both quantum tunneling and from the definition of the cross section as the ratio of probability currents.

Systematic study of the [formula omitted]([formula omitted],p)[formula omitted] reaction for NRA applications

The differential cross sections of the first two proton groups of the 12C(3He,p)14N reaction were determined within the 3He energy range 1.34–2.86 MeV and for backward angles from 107o107o to 164o with 2o steps using two double sided silicon strip detectors. The results are presented in graphical form and they are also given as tables in the Appendix. Aiming to assist in the enrichment of the reaction database and the improvement of the differential cross section data quality, the determined cross sections were benchmarked with the measurement of thick target reaction yields from a pure glassy carbon target at two 3He energies, 2.0 and 2.7 MeV. Furthermore, the data were accompanied by R-Matrix theory calculations, allowing for cross section data interpolation with sufficient accuracy.

12C(20Ne, 16O)16O α-transfer reaction and astrophysical S-factors at 300keV

The [Formula: see text]C([Formula: see text]Ne, [Formula: see text]O)[Formula: see text]O reaction has been used for the first time to determine ANC of [Formula: see text]O levels. The [Formula: see text]C([Formula: see text]Ne, [Formula: see text]O)[Formula: see text]O [Formula: see text]-transfer angular distributions are measured at [Formula: see text][Formula: see text]MeV and used to determine the ANC of the ground, 6.05[Formula: see text]MeV ([Formula: see text]), 6.13[Formula: see text]MeV ([Formula: see text]), 6.92[Formula: see text]MeV ([Formula: see text]) and 7.12[Formula: see text]MeV ([Formula: see text]) states of [Formula: see text]O. The ANC values are [Formula: see text] [Formula: see text] [Formula: see text], [Formula: see text] [Formula: see text], [Formula: see text] [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text]. Astrophysical S-factors at 300[Formula: see text]keV are extracted [Formula: see text]) keV b and [Formula: see text] keV b[Formula: see text] using these ANC values by R-matrix theory.

An approach for performing resolved and unresolved resonance evaluation based on few or none experimental data available: Application to unstable and short-lived isotopes

Fluctuations in the neutron cross sections resulting from resonance structures have to be accounted for in the calculation of a nuclear system. Regardless of the approach used, deterministic or stochastic, the depression in the neutron flux due to the resonance effects in the cross section must be well understood for the purpose of providing a good understanding of the self-shielding effects and an accurate calculation of any nuclear system. The R-Matrix theory is the mechanism most appropriate to represent the resonance region providing a detailed description of the cross sections thru resonance parameters.The objective of this work is to present an alternative to generate resonance region evaluation on the basis of the R-matrix theory in the resolved and unresolved energy regions. The proposed methodology can be applied to situations where few or none experimental data are available such as the energy dependent neutron cross section. It leverages over the knowledge of information such as thermal cross section values, Westcott factor, resonance integral, coherent and incoherent scattering lengths, scattering radius, and more important, knowledge of average resonance parameters. The approach is demonstrated and validated with applications for an isotope with a well-known resonance evaluation, that is the 103Rh, and afterwards to an isotope with minimum experimental data available. The latter is the 156Eu isotope.

Nuclear Reactions of Astrophysical Interest

We present different reaction models commonly used in nuclear astrophysics, in particular for the nucleosynthesis of the light elements. Nuclear reactions involved in stellar evolution generally occur at energies much lower than the Coulomb barrier. This property makes the cross sections extremely small, and virtually impossible to be measured in the laboratory. We start with a general discussion of low-energy scattering, and define the various cross sections required for reaction networks (essentially radiative capture and transfer reactions). Then we present specific models. Microscopic theories are based on fundamental principles, such as a nucleon-nucleon interaction, and an exact account of the antisymmetrization between all nucleons. In this context, most calculations performed so far have been done in the cluster approximation, but recent works, referred to as “ab initio” models, go beyond this approximation. Microscopic models can be simplified by neglecting the internal structure of the colliding nuclei, which leads to the potential model, also named the optical model. An alternative approach for the theoretical analysis of the experimental data is based on the phenomenological R-matrix theory, where parameters are fitted to the existing data, and then used to extrapolate the cross sections down to stellar energies. Indirect approaches, such as the Trojan Horse method, are briefly outlined. Finally, we present some typical applications of the different models.

Anthony Milner Lane. 27 July 1928—9 February 2011

Tony Lane came from humble beginnings to become one of the world's leading theoretical nuclear physicists. His career in the Theoretical Physics Division at the Atomic Energy Research Establishment (AERE) at Harwell was characterized by his outstanding successes in explaining experimental nuclear data. He pioneered the understanding of the important nucleon capture reactions by introducing new mechanisms of direct and semi-direct capture and, together with colleagues, he greatly advanced knowledge of nuclear analogue states, and the role of isospin in nuclear physics. With R. G. Thomas, he wrote a comprehensive review of R-matrix theory, applied to analyse resonances in nuclear reactions, which became one of the most cited papers in physics. His book Nuclear theory gave a good account of the use of pairing force theory in nuclear physics, and its application to nuclear collective motion.

Dissociative Recombination of Cold HeH^{+} Ions.

The HeH^{+} cation is the simplest molecular prototype of the indirect dissociative recombination (DR) process that proceeds through electron capture into Rydberg states of the corresponding neutral molecule. This Letter develops the first application of our recently developed energy-dependent frame transformation theory to the indirect DR processes. The theoretical model is based on the multichannel quantum-defect theory with the vibrational basis states computed using exterior complex scaling of the nuclear Hamiltonian. The abinitio electronic R-matrix theory is adopted to compute quantum defects as functions of the collision energy and of the internuclear distance. The resulting DR rates are convolved over the beam energy distributions relevant to a recent experiment at the Cryogenic Storage Ring, giving good agreement between the experiment and the theory.

Probing photon interaction with H2O and D2O

Investigation of the valence state photoionization of water using vacuum ultraviolet and soft x-rays gives important information for spectroscopic analysis and studies of radiation loss and cell biology. In this article, the total and valence-shell photoionization cross sections of H2O and D2O, generating the states 2B1, 2A1 and 2B2, and their isotopic consequences are studied. The effect of bonding on valence state photoionization is also reported. The calculations were made using R-matrix theory for photon energies up to 40 eV. Electronic transitions below 20 eV were considered to account for the autoionizing Rydberg transitions. This is the first report to demonstrate the effect of bonding on valence state photoionization. For the isotopic partner (D2O), we observed a quantitative change in cross section. Comparisons are made with the previously available results and a reasonable agreement is found. The present study gives a comprehensive understanding of the photoionization of water, thus providing deep insight into different non-dissociative processes of the molecule in various environments.

Evaluation of differential cross-sections for light element reactions at low energies using R-matrix calculations: The case of 12C

The theoretical evaluation of diÆerential cross-section values for low-energy re- actions of light elements is of great importance in the fields of IBA (Ion Beam Analysis) and nuclear astrophysics. R-matrix theory is generally accepted as the most appropriate one for the analysis of resonance reactions in low-energy nuclear physics. In this approach, the configuration space of the scattering problem is divided into an internal region, corresponding to the compound nucleus, where the total wave function can be expanded into a complete set of eigenstates (in terms of unknown base functions, with the energy eigenvalues and the matrix elements of the base functions being adjustable parameters) and an external region, where the possible combinations of coupled particle pairs exist, corresponding to the reaction channels that emerge from the compound nucleus. This division of space is made by the choice of the boundary of the compound nucleus, i.e. an appropriate nuclear radius is chosen for each reaction channel. The R-matrix takes account of all the interactions which occur inside the nucleus. In the present work, results obtained in the specific case of elastic scattering and charged-particle nuclear reactions, namely for the 12C+p system are presented.

Calculation of electron scattering cross-section using different theoretical methods

Aiming at the simulation of the fine process of the electron transportation in gamma detectors, we calculate electron differential scattering cross-section (DCS) of several typical materials including Fe, ethylene and polyethylene. Based on two different calculation methods, which are partial wave methods based on Dirac equation and R-matrix theory, we find differences of the cross section at low energy region. The result indicates that both partial wave method and R-matrix theory associated with independent atom method (IAM) are not suitable for low energy electron impacting on strong coupled molecule, for example, electron-ethylene. For high energy electron interacting with atom and molecule, the result shows no critical difference because the kinetic energy of the incident electron is severely higher than the electron bound energy in molecule or the excitation energy of a certain atom.

Developments regarding three-body reaction channels within the R-matrix formalism

At low incident energies of nucleon-induced reaction cross sections exhibit a striking resonance structure which cannot properly be described by (semi-) microscopic models. Usually R-matrix theory is applied which provides a sufficiently 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 at rather low incident energies and are usually treated in approximative or effective way. In this contribution an extension to unequal masses of the R-matrix formulation of Glockle based on the Faddeev equation is performed and proper expressions for numerical implementation are given.

Double-continuum R-matrix theory and codes for many-electron atoms: ionizing electron collisions and time-dependent laser-induced double-ionization

SynopsisAn extension of ab initio many-electron R-matrix theory is described which is relevant both to the time-dependent description of excitation and single and double ionization of atoms in laser pulses, and to time-independent calculation of intermediate energy electron collisions where ionized states of the target atom can be excited. Corresponding general many-electron ‘inner region’ code modules have been developed for use in combination with existing R-matrix method codes for diverse applications with up to two electrons explicitly described by a continuum orbital basis.

Covariance generation for the prompt neutron multiplicity of 239Pu including the (n,γf) process

Fission cross section of 239Pu can be seen as a sum of the “immediate" fission and “two-step" (n,γf) reactions. In the Resolved Resonance Range of the reaction cross sections, the contribution of the (n,γf) process has an impact on the determination of the partial widths magnitude involved in the Reich-Moore approximation of the R-matrix theory. The present work aims to investigate this impact by using the CONRAD code and the partial width Γγf for the (n,γf) reaction calculated by Lynn et al. [1]. A special attention will be paid to the covariance matrix obtained on νp.

UKRmol+: A suite for modelling electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method

UKRmol+ is a new implementation of the time-independent UK R-matrix electron–molecule scattering code. Key features of the implementation are the use of quantum chemistry codes such as Molpro to provide target molecular orbitals; the optional use of mixed Gaussian — B-spline basis functions to represent the continuum and improved configuration and Hamiltonian generation. The code is described, and examples covering electron collisions from a range of targets, positron collisions and photoionization are presented. The codes are freely available as a tarball from Zenodo. Program summaryProgram Title: UKRmol+Program Files doi:http://dx.doi.org/10.17632/k3ny7zcfrb.1Code Ocean Capsule:https://doi.org/10.24433/CO.2477858.v1Licensing provisions: GNU GPLv3Programming language: Fortran 95 with use of some Fortran 2003 featuresExternal routines/libraries: LAPACK, BLAS; optionally MPI, ScaLAPACK, Arpack, SLEPcNature of problem: The computational study of electron and positron scattering from a molecule requires the determination of multicentric time-independent wavefunctions describing the target+projectile system. These wavefunctions can also be used to calculate photoionization cross sections (in this case the free particle is the ionized electron) or provide input for time-dependent calculations of laser-induced ultrafast processes.Solution method: We use the R-matrix method [1], that partitions space into an ‘inner’ and an ‘outer’ region. In the inner region (within a few tens of a0 of the nuclei at most) exchange and correlation are taken into account. In the outer region, where the free particle is distinguishable from the target electrons, a single-centre multipole potential describes its interaction with the molecule. The key computational step is the building and diagonalization of the target + free particle Hamiltonian in the inner region, making use of integrals generated using the GBTOlib library. The eigenpairs obtained are then used as input to the outer region suite to determine scattering quantities (K-matrices, etc.) or transition dipole moments and, from them, photoionization cross sections. The suite also generates input data for the R-matrix with time (RMT) suite [2].Additional comments: CMake scripts for the configuration, compilation, testing and installation of the suite are provided. This article describes the release version UKRmol-in 3.0, that uses GBTOlib 2.0, and UKRmol-out 3.0.Program repository available at: https://gitlab.com/UK-AMOR/UKRmolReferences[1] P. G. Burke, R-Matrix Theory of Atomic Collisions: Application to Atomic, Molecular and Optical Processes. Springer, 2011.[2] A. Brown, et al RMT: R-matrix with time-dependence. Solving the semi-relativistic, time-dependent Schrödinger equation for general, multi-electron atoms and molecules in intense, ultrashort, arbitrarily polarized laser pulses., Computer Phys. Comm., https://doi.org/10.1016/j.cpc.2019.107062.

No-core shell model calculations of the photonuclear cross section of 10B

Results of ab initio no-core, shell model calculations for the photonuclear cross section of 10B are presented using realistic two-nucleon (NN) chiral forces up to next-to-next-to-next-order (N3LO) softened by the similarity renormalization group method (SRG) with \( \lambda= 2.02\) fm-1. The electric-dipole response function is calculated using the Lanczos method, with the effects of the continuum included via neutron escape widths derived from R-matrix theory and using the Lorentz integral transform method. The calculated cross section agrees well with experimental data in terms of structure as well as in absolute peak height, \( \sigma_{\max}=4.85\) mb at photon energy \( \omega= 23.61\) MeV, and integrated cross section 85.36 MeV. mb. We also test the Brink hypothesis by calculating the electric-dipole response for the first nine positive-parity states with \( J \ne 0\) in 10B and verify that dipole excitations built upon the ground and excited states have similar characteristics.

Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the 7Be system

R-matrix theory is used to describe nuclear reactions in the resolved resonance region. It uses information on bound states and low energy resonances to accurately parametrize cross sections on the resonances as well as the non-resonant background. Since the seminal work of Lane and Thomas (1958), the approach has been widely used to analyze experimental cross-section data in a broad range of fields spanning nuclear reaction dynamics, nuclear astrophysics, ion beam analysis and their applications. Different R-matrix codes have been developed and used in these different applications with very little communication among the developers or practitioners on the capabilities, achievements or limitations of the codes. A limited comparison among three R-matrix codes on neutron-induced reactions was performed by the International Atomic Energy Agency (IAEA) International Evaluation of Neutron Cross Section Standards project (2007). Since then, significant progress has been made in their implementation of the R-matrix algorithms, and R-matrix codes have enhanced capabilities. In this paper we present, for the first time, the results of a comprehensive effort to verify the most widely used R-matrix codes in the various fields of nuclear science and applications: AMUR, AZURE2, CONRAD, EDA, FRESCO, GECCCOS, and SAMMY. In addition to the description of the capabilities of the codes and their specifications, we discuss the results of a joint exercise which was coordinated by the International Atomic Energy Agency. The aim of the exercise was to compare calculations of charged-particle reaction cross sections for the light composite system 7Be. The calculations were performed by the codes using identical input R-matrix parameters and other specifications and were limited to charged-particle channels.

Total Absorption Cross Section for UV Excitation of Sulfur Monoxide.

In a new study on sulfur monoxide, new ab initio potential energy curves are developed for excited states A3Π, B3Σ-, C3Π, and C'3Π and for three states that are unassigned in the literature, which we numerically name 33Σ-, 43Π, and 53Π. All these excited states have allowed transitions from ground state, X3Σ-. The ab initio calculations were performed using the MRCI-F12+Q/aug-cc-pV(5+d)Z level of theory implemented in MOLPRO2015. On the basis of close-coupling R-matrix theory, fine structure absorption cross sections of isotopically substituted sulfur monoxide are calculated for wavelengths of 190-300 nm. The spectra are shown at the highest possible resolution (FWHH ≈ 0.15-0.18 cm-1) for reference and future studies. The effects of self-shielding and possible mutual shielding are discussed.

Pulse-duration dependence of the double-to-single ionization ratio of Ne by intense 780-nm and 800-nm laser fields: Comparison of simulations with experiments

Accurate ab initio calculations of the ratio of double-to-single ionization of Ne atoms in strong laser fields are difficult due to the many-electron nature of the target. Here, with accurate total cross sections carefully evaluated by using the state-of-the-art many-electron R-matrix theory for both electron-impact ionization and electron-impact excitation of Ne+, we simulate the total double-ionization yields of Ne2+ in strong laser fields at 780 and 800 nm for pulse durations in the range from 7.5 to 200 fs based on the improved quantitative rescattering model. The corresponding single-ionization yields of Ne+ are calculated within the nonadiabatic tunneling model of Perelomov, Popov, and Terent'ev. The ratio of double-to-single ionization of Ne is then obtained from the calculated double- and single-ionization yields. By normalizing the ratio to the one calculated from solving the time-dependent Schrodinger equation for a short few-cycle pulse, we make quantitative comparisons of our results with experimental data to show that our model predicts the experimental findings very well. Finally, we analyze the pulse-duration dependence of the double-to-single ionization ratio.