Close-coupling Approach Research Articles

Close-coupling approach to antiproton-impact ionisation of H2 with analytical spherical averaging

Integrated cross section for single ionisation of molecular hydrogen by antiproton impact has been calculated in a wide range of impact energies from 1 keV up to 2 MeV using a close-coupling approach. For the first time all possible orientations of the molecular target have been accounted for using an ab initio analytical spherical averaging technique. Obtained results are in good agreement with experiment.

Rotational excitation of AlH by Helium and Neon at low temperature: State-to-state inelastic cross section

In this work, inelastic rotational collisions of AlH with He and Ne were studied. The CCSD (T) method was used for the computation of accurate two dimensional potential energy surfaces (2-D-PESs). In the calculation of the 2-D-PESs, AlH was frozen at the experimental value of 3.1149 a0. The recently published basis sets m-aug-cc-pV (Q+d) Z of Papajak and Truhlar, completed with bond functions placed at mid-distance between the center of mass of AlH and He/Ne atom for a better description of van der Waals interaction energy, was used throughout the computational process. The PESs of AlH–He and AlH–Ne were found to have global minima at (R=6.9a0,θ=68°) and (R=6.9a0,θ=69°) respectively, with corrresponding depths of 26.32cm−1 and 48.70cm−1. These potentials were fitted analytically and expanded in terms of Legendre polynomials, then used for the evaluation of the integral cross sections of state-to-state rotational transitions in AlH induced by the collisions with He or Ne within the close coupling approach. The rate coefficients are computed for low kinetic temperatures ranging from 3K to 300K.

Target Structure-Induced Suppression of the Ionization Cross Section for Low-Energy Antiproton-Molecular Hydrogen Collisions: Theoretical Confirmation

Theoretical confirmation of the experimentally observed phenomenon [Knudsen et al., Phys. Rev. Lett. 105, 213201 (2010)] of target structure-induced suppression of the ionization cross section for low-energy antiproton-molecular hydrogen collisions is given. To this end a novel time-dependent convergent close-coupling approach to the scattering problem that accounts for all possible orientations of the molecular target, has been developed. The approach is applied to study single ionization of molecular hydrogen on the wide energy range from 1 keV to 2 MeV with a particular emphasis on low energies. Results for the orientation-averaged total single ionization cross section are compared with available experimental data and good agreement is found at low (<20 keV) and high (>90 keV) energies. A minor discrepancy is found within a small energy gap near the maximum of the cross section.

Rotational excitation of protonated hydrogen cyanide (HCNH+) by He atom at low temperature

We report on ab initio coupled-cluster calculations of the interaction potential energy surface for the HCNH+–He complex. The aug-cc-pVTZ Gaussian basis, to which is added a set of bond functions placed at mid-distance between HCNH+ center of mass and He atom is used. The HCNH+ bonds length are set to their values at the equilibrium geometry, i.e., r e [HC]=1.0780 A, r e [CN]=1.1339 A and r e [NH]=1.0126 A. The interaction energy presents a global minimum located $266.9~\mathrm{cm^{-1}}$ below the HCNH+–He dissociation limit. Using the interaction potential obtained, we have computed rotational excitation cross sections in the close-coupling approach and downward rate coefficients at low temperature (T≤120 K). It is expected that the data worked out in this study may be beneficial for further astrophysical investigations as well as laboratory experiments.

Collisional shift and broadening of the 2p-2sspectral lines in muonic helium ions

In connection with the recently proposed Lamb-shift experiments at Paul Scherrer Institute in ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}4}{\mathrm{He}}^{+}$ and ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}3}{\mathrm{He}}^{+}$ by using the laser-spectroscopy method, the pressure shift and width of the $2p$-$2s$ spectral lines in muonic-helium ions were studied in the present paper within the fully quantum-mechanical close-coupling approach. The calculations of the $S$ matrix as well as of the energy-dependent shift and width were made for collisional energies $E={10}^{\ensuremath{-}5}--1$ eV. The shift and width averaged over energy were obtained for target temperatures up to 350 K. It is shown that the fine-structure effect does not exceed a few percent. The isotopic effect is very small and can be neglected for the shift at $T\ensuremath{\ge}150$ K, contrary to the width, for which the isotopic effect becomes much more pronounced at $T\ensuremath{\ge}150$ K. At density $N=2.4145\ifmmode\times\else\texttimes\fi{}{10}^{18}$ atom/cm${}^{3}$ corresponding to the target pressure 100 mbar ($T=300$ K) the predicted values of the shifts are equal to 35 (50) MHz for ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}3}{\mathrm{He}}^{+}$ and 33 (35) MHz for ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}4}{\mathrm{He}}^{+}$ respectively for upper (lower) values of the $2p$-$2s$ energy-level separation. At the same conditions the values of the widths are equal to 2.4 (13.6) MHz for ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}3}{\mathrm{He}}^{+}$ and 2.0 (3.0) MHz for ${\ensuremath{\mu}}^{\phantom{\rule{0.16em}{0ex}}4}{\mathrm{He}}^{+}$.

Fully differential cross section for O8+-impact ionization of Li

We present various differential cross sections for the single ionization of Li by O${}^{8+}$ ions. We use a time-dependent, close-coupling approach to model the evolution of a one-active-electron wave function in the field of the incoming projectile for a range of impact parameters. In addition, a Fourier transform approach is used to extract differential cross sections for a specific projectile momentum transfer value. This scheme allows us to incorporate information about the interaction of the two heavy nuclei [the so-called nuclear-nuclear (NN) interaction] and to assess its influence in the differential cross sections. We find noticeable differences in the shape of the differential cross sections when we include (neglect) the NN interaction. Our single-differential cross-section calculation shows excellent agreement with experimental data. In addition, recent measured double-differential cross sections as a function of electron energy and transverse momentum transfer are reasonably well reproduced by our theoretical calculations.

Excitation cross sections for Li3 +, Ne10 + and Ar18 ++H(1s) collisions of interest in fusion plasma diagnostics

We have calculated state-selective excitation cross sections in fully stripped Li3 +, Ne10 + and Ar18 ++H(1s) collisions from low (1 keV/amu) to high (1000 keV/amu) impact energies, relevant in fusion plasma diagnostics. In order to cover this broad impact energy range, three different theoretical methods have been employed: the semi-classical molecular and one-centre atomic-orbital close-coupling approaches, and the classical trajectory Monte Carlo method. Recommended partial excitation cross sections are provided by merging the results obtained with each method in the energy range where they are the most accurate.

ROTATIONAL QUENCHING OF ROTATIONALLY EXCITED H2O IN COLLISIONS WITH He

Theoretical rotational quenching cross sections and rate coefficients of ortho- and para-H$_2$O due to collisions with He atoms are presented. The complete angular momentum close-coupling approach as well as the coupled-states approximation for angular momentum decoupling were applied to solve the scattering problem for a large range of rotationally-excited states of water. Results are obtained for quenching from initial levels 1$_{1,0}$, 2$_{1,2}$, 2$_{2,1}$, 3$_{0,3}$, 3$_{1,2}$, 3$_{2,1}$, 4$_{1,4}$, 3$_{3,0}$, and 4$_{2,3}$ of ortho-H$_2$O and from initial levels 1$_{1,1}$, 2$_{0,2}$, 2$_{1,1}$, 2$_{2,0}$, 3$_{1,3}$, 3$_{2,2}$, 4$_{0,4}$, 4$_{1,3}$, and 3$_{3,1}$ of para-H$_2$O for kinetic energies from 10$^{-5}$ to 10$^4$ cm$^{-1}$. State-to-state and total deexcitation cross sections and rate coefficients for temperatures between 0.1 and 3000 K are reported. The present state-to-state rate coefficients are found to be in good agreement with previous results obtained by Green and coworkers at high temperatures, but significant discrepancies are obtained at lower temperatures likely due to differences in the adopted potential energy surfaces. Astrophysical applications of the current rate coefficients are briefly discussed.

Collision-induced absorption and annihilation in hadronic atoms within a close-coupling approach

The induced absorption or annihilation of ${\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{\ensuremath{-}}$, and $\overline{p}$ in collisions of hadronic hydrogen atoms in excited states with ordinary hydrogen in the ground state is treated in a unified manner with the elastic scattering, Stark transition, and Coulomb de-excitation in the framework of the close-coupling approach. The close-coupling approach is generalized to include both open andclosed channels corresponding to stable and unstable states of the hadronic atom. Calculations are performed using the basis sets including all states of hadronic atoms with a principal quantum number from $n=1$ up to ${n}_{\mathrm{max}}=8$. The general features of induced-absorption cross sections are studied in a wide range of complex energy-shift values. The cross sections of all processes are calculated for ${\ensuremath{\pi}}^{\ensuremath{-}}p$, ${K}^{\ensuremath{-}}p$, and $\overline{p}p$ atoms with principal quantum numbers $n=2$--8 and kinetic energies from 0.001 up to 100 eV. The validity of the previous quantum-mechanical and semiclassical models is critically discussed.

Fully quantal close-coupling approach to antiproton-hydrogen collisions

A fully quantal close-coupling integral-equation approach to antiproton-hydrogen collisions has been developed. Integral and fully differential cross sections have been calculated.

ECC in proton-H collisions at keV projectile energy

Electron capture to the continuum is studied within a close-coupling approach, for proton-H collisions at keV projectile energy.

Convergent close coupling calculations for positron-magnesium scattering

While a two-centre convergent close-coupling approach to positron-magnesium scattering is developed, a single-centre method has been used to calculate total cross sections up to incident energies of 100 eV. The results agree very well with the measurements of Stein et al. [1] for positron energies above the ionisation threshold (7.6 eV). Similar accuracy is expected for energies below the positronium formation threshold (0.8 eV) where presently there are no experimental data to compare to. In this energy region we find a large p-wave resonance at 0.17 eV. Similar resonance behaviour was found in calculations by Mitroy and Bromley [2] at an energy of 0.1 eV.

Application of the time-dependent close-coupling approach to few-body atomic and molecular ionizing collisions

We review the recent progress made in applying the time-dependent close-coupling approach to ionizing collisions of electrons, photons, and ions with small atoms and molecules. The last twenty years have seen a proliferation of non-perturbative approaches applied to fundamental atomic and molecular scattering processes. Such processes form the building blocks of describing the dynamics of plasmas over a wide range of temperatures and densities, and also provide insight into the long-range Coulomb interactions between charged particles. Studies of the few-body Coulomb problem presented in electron, photon, or ion-impact ionization of small atoms and molecules, by direct solution of the time-dependent Schrodinger equation, are particularly useful because the complicated three-body boundary conditions of more than one continuum particle in a Coulomb potential are not required. With the continuing growth and increasing availability of high-performance computing resources, such methods can now be applied to a wide variety of scattering processes. The recent progress made using such a time-dependent approach is described in this colloquium. In this paper, we focus on the recent results obtained for one-, two-, and three-electron systems, thus building on a previous review of the time-dependent close-coupling method [M.S. Pindzola et al., J. Phys. B 40, R39 (2007)], which also described the application to multi-electron targets.

Fully differential cross section for single ionization in energetic C6+-He collisions

The quantum-mechanical convergent close-coupling approach has been used to calculate the fully differential cross section for the single ionization of helium by C${}^{6+}$ ions at 100 MeV/amu. This allows one to test the quality of approximations used in standard approaches to the problem, particularly in geometries that are out of the scattering plane, where there is a strong disagreement between calculations and measurements. The obtained results show that the fully quantum-mechanical treatment of the internuclear motion does not enable one to get any better agreement with experimental data. In addition, we have performed calculations for the precise geometry where experimental data were collected, i.e., in the plane perpendicular to the momentum-transfer direction. We conclude that this rotation also has a minor effect on the shape of the cross section.

Ab initio potential energy surface and rotationally inelastic collisions of hydroxide of lithium (LiH) with argon (Ar): State-to-state inelastic rotational cross section

In this work, the inelastic collision of hydroxide of lithium with argon is studied for a fixed experimental value of the LiH bond length 3.0139bohr using an ab initio energy surface. The potential energy surface (PES) for the LiH(X1Σ+)–Ar(1S) Van der Waals system is calculated accurately at the ab initio coupled-cluster [CCSD(T)] with an aug-cc-pVQZ Gaussian basis set for the H and Ar atoms and cc-pVQZ Gaussian basis set for the Li atom. In this calculation, the basis set superposition error (BSSE) was corrected at all geometries with the counterpoise procedure of Boys and Bernadi. The interaction potential has a global minimum at θ=180° and at an equilibrium distance R=5.30bohr with a well depth of 525.13cm−1. This potential already fitted analytically and expanded in terms of Legendre polynomials is employed to evaluate the state-to-state rotational cross sections over a range of energies up to 6452.584cm−1. The calculations of cross sections are done in the close coupling (CC) approach. The features present on low collision energy some resonances and are related to the anisotropic interaction potential. We have compared the cross sections in LiH–Ar at 6452.584cm−1 with the available experiment one of Wilcomb and Dagdigian and the earlier calculations of Bhattacharyya et al. However, we have found that the results show a good agreement especially for j=1→0 transition.

Kinetic energy distributions of muonic and pionic hydrogen atoms

The kinetic energy distributions of μ − p and π − p atoms at a time of the radiative np→1s transitions and charge-exchange reaction (in case of π − p) have been studied in the improved version of extended standard cascade model (ESCM). Ab initio quantum-mechanical calculations of the differential and integral cross sections of the elastic scattering, Stark transitions, Coulomb deexcitation (CD), and induced absorption (in case of pionic hydrogen) have been performed in a framework of the close-coupling approach for the states of exotic atoms with \(n\leqslant 8\) and relative motion energies \(E \geqslant 0.0001\) eV. The calculated X-ray yields and kinetic energy distributions are in good agreement with the known experimental data. The initial (n, l, E)-distributions of the exotic atoms and target motion are explicitly taken into account.

Induced absorption and annihilation in hadronic hydrogen atoms

The induced absorption or annihilation in the collisions of the hydrogen hadronic atoms in the excited states with ordinary hydrogen have been described in a unified manner with the elastic scattering, Stark transitions, and Coulomb de-excitation in the framework of a close-coupling approach including both the open and closed channels corresponding to both the stationary and non-stationary states of hadronic atom. The general features of the induced absorption cross sections have been studied in a wide range of the complex energy-shift values. The total and differential cross sections of all processes have been calculated for π − p, K − p, and \(\bar p p\) atoms with the principal quantum numbers n = 2 − 8 and kinetic energy from 0.001 eV up to 100 eV.

Elastic scattering and rotational excitation of nitrogen molecules by sodium atoms

A quantal study of the rotational excitation of nitrogen molecules by sodium atoms is carried out. We present the two-dimensional potential energy surface of the NaN(2) complex, with the N(2) molecule treated as a rigid rotor. The interaction potential is computed using the spin unrestricted coupled-cluster method with single, double, and perturbative triple excitations (UCCSD(T)). The long-range part of the potential is constructed from the dynamic electric dipole polarizabilities of Na and N(2). The total, differential, and momentum transfer cross sections for rotationally elastic and inelastic transitions are calculated using the close-coupling approach for energies between 5 cm(-1) and 1500 cm(-1). The collisional and momentum transfer rate coefficients are calculated for temperatures between 100 K and 300 K, corresponding to the conditions under which Na-N(2) collisions occur in the mesosphere.

Collision induced rotational excitation of AlF (X 1Σ+) by para-H2 (j=0)

Rotational excitation cross sections and rate coefficients of AlF collisions with para-H2 are computed at low temperature, i.e., for T≤70 K. Prior to collisional calculations, a four-dimensional (4D) potential energy surface (PES) for the AlF-H2 system is calculated at the ab initio Coupled-Cluster level of the theory with an aug-cc-pVQZ Gaussian basis set. This 4D-PES is further reduced to a two-dimensional (2D) PES based on the considerations related to collisional studies with para-H2. The [Al-F] and [H-H] bond lengths are frozen at their experimental equilibrium value r e =1.654369 bohr and r e =1.4011 bohr respectively. The interaction energy presents a global minimum located ∼63 cm−1 below the AlF-H2 dissociation limit. With this PES, cross sections are determined in the Close-Coupling (CC) approach and rate coefficients are inferred by averaging the cross sections over a Maxwell-Boltzman distribution of kinetic energies. These quantities are significantly magnified in comparison with their AlF-He counterparts. The already observed propensity towards ΔJ=1 transitions for AlF-He remains.

Fully differential cross sections for the single ionization of He by C6 + ions

We present fully differential cross sections for the single ionization of He by C6 + ions. A time-dependent close-coupling approach is used to describe the two-electron wavefunction in the field of the projectile for a range of impact parameters, and a Fourier transform approach is used to extract fully differential cross sections for a specific momentum transfer. Our calculations are compared to the measurements of Schulz et al (2003 Nature 422 48) and we find very good agreement in the scattering plane and good qualitative agreement in the perpendicular plane. In particular, our calculations in the perpendicular plane find a similar ‘double-peak’ structure in the angular distributions to those seen experimentally. We also discuss the various checks made on our calculations by comparing to a one-electron time-dependent calculation.