R-matrix Approach Research Articles

Superelastic electron scattering from laser-excited cesium atoms

We present results from a joint experimental and theoretical investigation of superelastic electron scattering from laser-excited Cs atoms in the (6p){sup 2}P{sub 3/2} state. Comparison of the measured pseudo-Stokes parameters P{sub 1}, P{sub 2}, and P{sub 3} and the total degree of polarization P{sup +} for incident energies of 5.5 eV and 13.5 eV, respectively, with theoretical predictions based upon a nonrelativistic convergent close-coupling method and a 24-state semirelativistic Breit-Pauli R-matrix approach indicates that driving channel coupling to convergence for these observables is more important than accounting for relativistic effects.

Vibrational excitation and dissociative recombination of the LiH + ion

LiH+ is one of the remaining enigmas among small, simple molecules, in its unexpectedly high dissociative recombination (DR) rate. The dissociative recombination process, in which a colliding electron is captured, results in dissociation and destruction of the molecule. The conventional mechanism characteristic of most species with a high DR rate, which normally involves direct capture into a dissociative resonance potential curve, is absent here. For this reason, this is a prototype for indirect DR that must instead proceed through Rydberg capture pathways. We apply ab initio multichannel quantum defect theory (MQDT), in combination with a rovibrational frame transformation based on Siegert pseudostates, to treat indirect DR for this fundamental diatomic ion. The starting point is a set of ab initio quantum defects determined using the R-matrix approach, functions of the internuclear distance. The calculated DR rate coefficient agrees with recent experimental data [S. Krohn, et al., Phys. Rev. Lett. 86, 4005 (2001)]. Found to play a key role are complex resonance manifolds that couple closed channels having both high and low principal quantum numbers, of the same type studied in molecular Rydberg spectroscopy by Jungen and co-workers over the years.

Quantum effect of intramolecular high-frequency vibrational modes on diffusion-controlled electron transfer rate: From the weak to the strong electronic coupling regions

The Sumi-Marcus theory is extended by introducing two approaches to investigate electron transfer reactions from weak-to-strong electronic coupling regime. One of these approaches is the quantum R-matrix theory, useful for dealing with the intramolecular vibrational motions in the whole electronic coupling domain. The other is the split operator approach that is employed to solve the reaction-diffusion equation. The approaches are then applied to electron transfer in the Marcus inverted regime to investigate the nuclear tunneling effect on the long time rate and the survival probabilities. The numerical results illustrate that the adiabatic suppression obtained from the R-matrix approach is much smaller than that from the Landau-Zener theory whereas it cannot be predicted by the perturbation theory. The jointed effects of the electronic coupling and solvent relaxation time on the rates are also explored.

Electron-impact study of PH3: an R-matrix approach

We present elastic cross sections for scattering of electrons by a phosphine (PH3) molecule using the R-matrix method for incident electron energies in the range 0.025–15 eV. We find a shape resonance in 2E scattering symmetry in the static-exchange (SE) and static-exchange plus polarization (SEP) approximations whose resonance positions are 5.57 eV and 2.34 eV, respectively. The Born correction is applied for the elastic transition to account for partial waves higher than l = 4 excluded in the R-matrix calculation. A comparison of our results in both approximations is carried out with other theoretical and the experimental work. Our calculations also reproduce the Ramsauer–Townsend effect that reflects the accuracy of electron–electron correlation included in our theoretical treatment.

Indirect Dissociative Recombination ofLiH+Molecules Fueled by Complex Resonance Manifolds

The LiH$^{+}$ molecule is prototypical of the indirect dissociative recombination (DR) process, in which a colliding electron destroys the molecule through Rydberg capture pathways. This Letter develops the first quantitative test of the Siegert state multichannel quantum defect theory description of indirect DR for a diatomic molecular ion. The R-matrix approach is adopted to calculate ab-initio quantum defects, functions of the internuclear distance that characterize both Rydberg states and the zero-energy collisions of electrons with LiH$^{+}$ ions. The calculated DR rate coefficient agrees accurately with recent experimental data (S. Krohn et al, Phys. Rev. Lett. 86, 4005). We identify the doorways to fast indirect DR as complex resonance manifolds, which couple closed channels having both high and low principal quantum numbers. This sheds new light on the competition between direct and indirect DR pathways, and suggests the reason why previous theory underestimated the DR rate by an order of magnitude.

Determination of Astrophysical 13N(p,γ)14OS-factors from the Asymptotic Normalization Coefficient of 14C→ 13C + n

The angular distribution of the 13C(d,p)14C reaction isreanalysed using the Johnson–Soper approach. The squaredasymptotic normalization coefficient (ANC) of virtual decay14C → 13C + n is then derived to be 21.4±5.0 fm−1. The squared ANC and spectroscopic factor (SF)of 14O → 13N + p are extracted to be 30.4±7.1 fm−1 and 1.94±0.45, respectively. Theastrophysical S-factors and reaction rates of13N(p,γ)14O are determined from the ANC of14O → 13N + p using the R-matrix approach.

Breit‐Pauli R ‐Matrix Calculation for Electron Collision Rates in O iv

Electron collision excitation strengths and rates for infrared and ultraviolet lines arising from transitions between the fine-structure levels of the 2s22p, 2s2p2, 2p3, 2s23s, 2s23p, 2s23d, 2s2p3s, 2s2p3p, 2s2p3d, 2s24s, and 2s24p configurations of O IV have been calculated using Breit-Pauli R-matrix approach. Configuration-interaction wave functions have been used for an accurate representation of target levels. These wave functions give excitation energies that are in close agreement with experiment. Oscillator strengths and transition probabilities for UV and EUV lines compare very well with previous calculations. The Rydberg series of resonances converging to the excited levels are explicitly included in the scattering calculation and are found to make substantial contribution to collision strengths. The effective collision strengths are obtained by integrating total collision strengths over a Maxwellian distribution of electron energies, and these are presented over a wide temperature range suitable for modeling of astrophysical plasmas. Significant qualitative and quantitative differences with earlier results of effective collision strengths are noted.

N13(d,n)O14reaction and the astrophysicalN13(p,γ)O14reaction rate

$^{13}$N($p,\gamma$)$^{14}$O is one of the key reactions in the hot CNO cycle which occurs at stellar temperatures around $T_9$ $\geq$ 0.1. Up to now, some uncertainties still exist for the direct capture component in this reaction, thus an independent measurement is of importance. In present work, the angular distribution of the $^{13}$N($d,n$)$^{14}$O reaction at $E_{\rm{c.m.}}$ = 8.9 MeV has been measured in inverse kinematics, for the first time. Based on the distorted wave Born approximation (DWBA) analysis, the nuclear asymptotic normalization coefficient (ANC), $C^{^{14}O}_{1,1/2}$, for the ground state of $^{14}$O $\to$ $^{13}$N + $p$ is derived to be $5.42 \pm 0.48$ fm$^{-1/2}$. The $^{13}$N($p,\gamma$)$^{14}$O reaction is analyzed with the R-matrix approach, its astrophysical S-factors and reaction rates at energies of astrophysical relevance are then determined with the ANC. The implications of the present reaction rates on the evolution of novae are then discussed with the reaction network calculations.

Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems

Rational Lax hierarchies introduced by Krichever are generalized. A systematic construction of infinite multi-Hamiltonian hierarchies and related conserved quantities is presented. The method is based on the classical R-matrix approach applied to Poisson algebras. A proof that Poisson operators constructed near different points of Laurent expansion of Lax functions are equal is given. All results are illustrated by several examples.

Structure ofN12usingC11+presonance scattering

The level structure of {sup 12}N has been investigated from 2.2 to 11.0 MeV in excitation energy using a {sup 11}C + p resonance interaction with thick targets and inverse kinematics. Excitation functions were fitted using an R-matrix approach. Sixteen levels in {sup 12}N were included in the analysis, several of them are new. Spin-parity assignments, excitation energies and widths are proposed for these levels. To fit the high energy part of the excitation function, imaginary phase shifts had to be added to the phase shifts generated by the hard sphere scattering.

Resonant photoionization of singly charged sulfur

Resonance structures in the photoionization of S{sup +} for the removal of a 3p or 3s electron from the ground 3s{sup 2}3p{sup 3} {sup 4}S{sup o} and excited metastable {sup 2}D{sup o} and {sup 2}P{sup o} states have been studied in the B-spline R-matrix approach. The nonorthogonal orbitals have been used for an accurate representation of the initial S{sup +} bound states, the final S{sup 2+} ion plus photoelectron states and S{sup 2+} thresholds. Calculations have been carried out in 17- and 27-state close-coupling approximations. The relativistic effects have been incorporated in the Breit-Pauli Hamiltonian. Photoionization cross sections are dominated by 3s{sup 2}3p{sup 2}({sup 1}D)ns {sup 2}D, 3s{sup 2}3p{sup 2}({sup 1}D)nd {sup 2}F, {sup 2}D, {sup 2}P, and 3s3p{sup 3}({sup 5}S{sup o}, {sup 3}S{sup o}, {sup 3}D{sup o}, {sup 3}P{sup o})np {sup 4}P Rydberg series of autoionizing resonances. The resonance states are identified and analyzed to obtain resonance positions E{sub r}, effective quantum numbers n{sup *}, and widths {gamma}{sub r} using a procedure of eigenphase gradients. The resonance line shape and correlation parameters have also been determined. Photoionization cross sections have been calculated in both length and velocity formulations that exhibit very good agreement (within 5%) with each other formore » most photon energies. Our results are compared with a recent merged ion-photon beam experiment. Significant discrepancies between the theoretically predicted and experimentally measured resonance structures and continuum cross sections are noted.« less

(e, eγ)-coincidence studies to determine spin-resolved Stokes parameters of the 185 nm emission line in mercury

Direct measurements of the three Stokes parameters (polarization components) P1, P2 and P3 of the VUV Hg transition 6s6p1P1 → 6s21S0 (185 nm) have been carried out at electron impact energies of 15 eV, 50 eV and 100 eV. Within the experimental uncertainty, no influence of the electron spin was discovered for scattering angles θ ⩽ 30°. At 15 eV excitation energy and scattering angles θ ⩾ 80°, increasing spin effects become apparent. The experimental data are compared to theoretical predictions from a first-order full-relativistic distorted-wave model, a five-state Breit–Pauli R-matrix (close-coupling) approach, and a convergent close-coupling model, in which relativistic effects are accounted for by adding non-relativistic amplitudes using known intermediate-coupling coefficients. At scattering angles θ ⩽ 15°, all of the theories reproduce the experimental data well, whereas the CCC model exhibits the best overall agreement with experiment at large scattering angles.

TheB8neutrino spectrum

Knowledge of the energy spectrum of $^8$B neutrinos is an important ingredient for interpreting experiments that detect energetic neutrinos from the Sun. The neutrino spectrum deviates from the allowed approximation because of the broad alpha-unstable $^8$Be final state and recoil order corrections to the beta decay. We have measured the total energy of the alpha particles emitted following the beta decay of $^8$B. The measured spectrum is inconsistent with some previous measurements, in particular with a recent experiment of comparable precision. The beta decay strength function for the transition from $^8$B to the accessible excitation energies in $^8$Be is fit to the alpha energy spectrum using the R-matrix approach. Both the positron and neutrino energy spectra, corrected for recoil order effects, are constructed from the strength function. The positron spectrum is in good agreement with a previous direct measurement. The neutrino spectrum disagrees with previous experiments, particularly for neutrino energies above 12 MeV.

Influence of chaos on the fusion enhancement by electron screening

We study the effect of screening by bound electrons in low energy nuclear reactions. We use molecular dynamics to simulate the reactions involving many electrons: D+d, D+D, 3He+d, 3He+D, 6Li+d, 6Li+D, 7Li+p, 7Li+ H. Quantum effects corresponding to the Pauli and Heisenberg principles are enforced by constraints in terms of the phase space occupancy. In addition to the well-known adiabatic and sudden limits, we propose a new “dissipative limit” which is expected to be important not only at high energies but in the extremely low energy region. The dissipative limit is associated with the chaotic behavior of the electronic motion. It affects also the magnitude of the enhancement factor. We discuss also numerical experiments using polarized targets. The derived enhancement factors in our simulation are in agreement with those extracted within the R-matrix approach.

Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras

The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in (1) for systems with finite number of degrees of freedom is generalized to infinite- dimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to the exceptional algebras E6 and E7. The involutions of the local integrals of motion are proved by means of the classical R-matrix approach.

Triple-differential cross-section measurements of electron-impact ionization of argon3sin the backward scattering direction

The triple-differential cross section for the electron-impact ionization of the 3s orbital of argon has been measured over the complete backward scattering direction of the ejected electron, using a magnetic angle changer in a conventional (e,2e) spectrometer. The results reveal the position and relative magnitude of the recoil scattering peak in the cross section for this target, and enable a detailed comparison with recently published calculations of argon 3s ionization which have been performed using a hybrid distorted-wave Born approximation--R-matrix approach. These theoretical calculations show dramatically improved agreement with the experimental results, in comparison with earlier approaches, but puzzling discrepancies still remain.

BSR: B-spline atomic R-matrix codes

BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron–atom and electron–ion scattering, and radiative processes such as bound–bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit–Pauli Hamiltonian. New version program summary Title of program: BSR Catalogue identifier: ADWY Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PC Operating systems under which the new version has been tested: UNIX, Windows XP Programming language used: FORTRAN 95 Memory required to execute with typical data: Typically 256–512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problem No. of bits in a word: 8 No. of processors used: 1 Has the code been vectorized or parallelized?: no No. of lines in distributed program, including test data, etc.: 69 943 No. of bytes in distributed program, including test data, etc.: 746 450 Peripherals used: scratch disk store; permanent disk store Distribution format: tar.gz Nature of physical problem: This program uses the R-matrix method to calculate electron–atom and electron–ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit–Pauli terms in the Hamiltonian. Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput. Phys. Comm. 92 (1995) 290].

Electron collisions with an ozone molecule using the R-matrix method

Elastic integral, differential and momentum transfer cross sections for electron collisions with an O3 molecule have been calculated in a 16-state R-matrix approach. The 16 target states have symmetries X1A1, 13B2, 13B1, 13A2, 11B1, 11A2, 23B2, 21A1, 11B2, 23A2, 21A2, 23B1, 21B2, 21B1, 31A1 and 13A1 and have been represented by configuration interaction (CI) wavefunctions. In our CI model, we keep the core 6 electrons frozen in doubly occupied molecular orbitals 1a1, 2a1 and 1b2. The complete active space consists of 18 valence electrons that are allowed to move freely among 12 molecular orbitals: 3a1, 4a1, 5a1, 6a1, 7a1, 1b1, 2b1, 2b2, 3b2, 4b2, 5b2 and 1a2. This CI model gave an adequate description of the vertical spectrum of these excited states which span the energy range 0–10 eV and also gave a good representation of the charge cloud of the ground state at its equilibrium geometry which provided a dipole moment of 0.61 D in good accord with the experimental value 0.53 D. Our calculations detect one bound O−3 state (2B1) at the equilibrium geometry of the O3 molecule. We also find two broad shape resonances in 2A1 and 2B2 symmetries out of which the 2A1 resonance supports dissociative electron attachment when an O–O bond is stretched beyond 3.1 a0. Born correction is applied for the elastic and the dipole allowed transitions to account for partial waves higher than l = 4 that are excluded in the R-matrix calculation. Elastic and excitation cross sections are presented for incident electron energies up to 15 eV and our results are compared with the other theoretical and experimental works.

Influence of the electronic chaotic motion on the fusion dynamics at astrophysical energies

We perform semi-classical molecular dynamics simulations of screening by bound electrons in low energy nuclear reactions. In our simulations quantum effects corresponding to the Pauli and Heisenberg principle are enforced by constraints. In addition to the well-known adiabatic and sudden limits, we propose a new “dissipative limit” which is expected to be important not only at high energies but in the extremely low energy region. The dissipative limit is associated with the chaotic behavior of the electronic motion. It affects also the magnitude of the enhancement factor. We discuss also numerical experiments using polarized targets. The derived enhancement factors in our simulation are in agreement with those extracted within the R-matrix approach.

AB INITIO R-MATRIX/MULTI-CHANNEL QUANTUM DEFECT THEORY APPROACH TO STUDY MOLECULAR CORE EXCITATION AND IONIZATION: GSCF4R

The ab initio program package named GSCF4R, which is based on the polyatomic R-matrix/MQDT (multi-channel quantum defect theory), has been developed using Gaussian type basis functions for the bound and continuum states to analyze the near edge feature of molecular inner shell excitations. The GSCF4R code is constructed by improvement and extension of the ordinal static exchange (STEX) approach. The R-matrix approach used in GSCF4R is beyond multi-channel multi-reference extensions of STEX, since it is based on the close coupling method augmented with the correlation term solved in the inner part of the R-matrix sphere. Simplification of the input data in GSCF4R has demonstrated that the R-matrix/MQDT method could be widely used in analysis of the molecular inner shell excitation and ionization. The quantum defects of the Rydberg states converging to the lowest valence ionized state NO +(1∑+) and the lowest N1 s ionized state N ⋆ O +(3Π) have been calculated.