Scattering Wave Function Research Articles

Comparison of the Calculated Collision-Induced Absorption Spectra by Dense Hydrogen-Helium, Deuterium-Helium, and Tritium-Helium Gas Mixtures

We have recently determined the induced dipole surface (IDS) and potential energy surface (PES) of collisional H2-He complexes. We have used these surfaces to compute the binary collision-induced absorption spectra of H2 molecules interacting with He atoms and of D2 molecules interacting with He atoms. Here we extend these calculations to the case of T2 molecules interacting with He atoms. Whereas the electronic structure of X2-He is virtually the same for all hydrogen isotopes X = H, D, or T, the collisional dynamics and molecular scattering wave functions are different for the different collisional pairs. We have calculated spectra up to a temperature of 9000 K and frequencies up to 20,000 cm−1. Here we compare the calculated collision-induced absorption spectra for the different hydrogen isotopes. While we have observed reasonable agreement between our calculations and laboratory measurements for the collisional H2-He and D2-He complexes, there are no laboratory measurements for T2-He collisional complexes, and one must rely on the fundamental theory, supported by the agreement between theory and experiment for the other isotopes.

Computational characterization of the HOMO-2 photoemission intensity oscillations in C60

We have calculated the photoionization cross section of the HOMO, HOMO-1 and HOMO-2 photoemission bands of C60 from threshold up to 250eV of photon energy. The calculated HOMO-2/HOMO-1 intensity ratio is in excellent agreement with recent experimental data. The computational method uses a multicentric expansion of the scattering wave function and a density functional theory (DFT) Hamiltonian. Time dependent DFT calculations suggest that the oscillatory phenomenon is essentially of single particle nature. An interpretation of the experimental findings in terms of the σ–π symmetries of the ionized orbitals is provided.

The Ground Motion of Isosceles Triangular Hill in Right-Angle Plane Impacted by SH-Wave

The analytical solution to the problem of the scattering of SH-wave by isosceles triangular hill in right-angle plane is given by using the methods of complex function and multiple coordinate. Firstly, the solution region is divided into two domains, where domain I involves isosceles triangular hill and a semi-circular bottom, domain II involves a semi-circular hollow in right-angle plane. And a standing wave function is constructed which satisfies the zero-stress conditions at the triangular wedges. In domain II, the scattering wave functions which satisfy the stress free boundary conditions at the free surfaces for the right-angle plane are constructed. Secondly, based on the conditions of the displacement continuity and stress continuity at the “common border” in the domains, a series of infinite algebraic equations are given and solved by truncation. Finally, some examples for amplitude of displacement on the surface are given. Numerical results show that amplitude of displacement on the surface is influenced by isosceles triangular hill.

Crystalline In–Ga–Zn–O Density of States and Energy Band Structure Calculation Using Density Function Theory

The density of states (DOS) and energy band structure of crystalline In–Ga–Zn–O (c-IGZO) and the impact of point defects on its electronic structure are investigated by first-principles calculations based on the density function theory. The calculated DOS showed that the p-orbitals of the oxygen atoms mostly contribute to the valance band maximum (VBM) of c-IGZO. The conduction band minimum (CBM) is dominated by s-orbitals of the Zn/Ga mixture atoms, while the In atoms have the largest spatial spread of wave function. Oxygen vacancies create fully occupied defect states within the band gap and serve as deep donors. Both hydrogen substitutions and interstitials act like shallow donors, and raise the Fermi level above the CBM. Oxygen split interstitials created fully occupied defect states above VBM, while oxygen octahedral interstitials create both occupied and unoccupied states, and may serve as acceptors.

Scattered Wave Packet Formalism with Markovian Outgoing Wave Boundary Conditions for Open Quantum Systems

The scattered wave formalism is developed for a quantum subsystem interacting with the external environment through open boundaries. The total wave function is divided into incident and scattered components and Markovian outgoing wave boundary conditions are applied to the scattered wave function. This formalism significantly reduces the computational effort relative to other methods which rely on Green functions and memory kernels. The method is applied to one-dimensional barrier scattering and to a three-dimensional model for the field effect transistor.

Tests of the discretized-continuum method in three-body dipole strengths

We investigate the 6He dipole distribution in a three-body α+n+n model. Two approaches are used to describe the three-body 1− continuum: the discretized-continuum method, where the scattering wave functions are approximated by square-integrable functions, and the R-matrix formalism, where their asymptotic behaviour is taken into account. We show that some ambiguity exists in the pseudostate method, owing to the smoothing technique, necessary to derive continuous distributions. We show evidence for the important role of the halo structure in the E1 dipole strength. We also address the treatment of Pauli forbidden states in the three-body wave functions.

Coulomb singularities in scattering wave functions of spin-orbit-coupled states

We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that Δl = 0, ±2. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum l, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method. We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system.

Laser-assisted free-free transition in electron-atom collisions

The free-free transition is studied for an electron-hydrogen atom system in the ground state at very low incident energies in the presence of an external homogeneous, monochromatic, and linearly polarized laser field. The incident electron is considered to be dressed by the laser field in a nonperturbative manner by choosing the Volkov solutions in both the initial and final channels. The space part of the scattering wave function for the electron is solved numerically by taking into account the effect of electron-exchange interactions, short-range interactions, as well as of long-range interactions. The laser-assisted differential as well as total elastic cross sections are calculated for single-photon absorption or emission in the soft photon limit, the laser intensity being much less than the atomic field intensity. A strong suppression is noted in the laser-assisted cross sections as compared to the field-free situations. A significant difference is noted in the singlet and the triplet cross sections.

Impurity states on the honeycomb and the triangular lattices using the Green's function method

AbstractUsing the Green's function (GF) method, we study the effect of an impurity potential on the electronic structure of the honeycomb lattice in the one‐band tight‐binding model that contains both the nearest‐neighbor (NN) (t) and the second‐neighbor (t′) interactions. If t = 0, the honeycomb lattice goes over to the triangular lattice, a case we also discuss. The model is relevant to the case of the substitutional vacancy in graphene. If the second‐neighbor interaction is large enough (t′ > t/3), then the linear Dirac bands no longer occur at the Fermi energy and the electronic structure is therefore fundamentally changed. With only the NN interactions present, there is particle–hole symmetry, as a result of which the vacancy induces a “zero‐mode” state at the band center with its wave function entirely on the majority sublattice, i.e., on the sublattice not containing the vacancy. With the introduction of the second‐neighbor interaction, the zero‐mode state broadens into a resonance peak and its wave function spreads into both sublattices, as may be argued from the Lippmann–Schwinger equation. The zero‐mode state disappears entirely for the triangular lattice and for the honeycomb lattice as well if t′ is large. In case of graphene, t′ is relatively small, so that a well‐defined zero‐mode state occurs in the vicinity of the band center.

Reduced dimensionality spin-orbit dynamics of CH3 + HCl $\rightleftharpoons$⇌ CH4 + Cl on ab initio surfaces

A reduced dimensionality quantum scattering method is extended to the study of spin-orbit nonadiabatic transitions in the CH(3) + HCl ⇌ CH(4) + Cl((2)P(J)) reaction. Three two-dimensional potential energy surfaces are developed by fitting a 29 parameter double-Morse function to CCSD(T)/IB//MP2/cc-pV(T+d)Z-dk ab initio data; interaction between surfaces is described by geometry-dependent spin-orbit coupling functions fit to MCSCF/cc-pV(T+d)Z-dk ab initio data. Spectator modes are treated adiabatically via inclusion of curvilinear projected frequencies. The total scattering wave function is expanded in a vibronic basis set and close-coupled equations are solved via R-matrix propagation. Ground state thermal rate constants for forward and reverse reactions agree well with experiment. Multi-surface reaction probabilities, integral cross sections, and initial-state selected branching ratios all highlight the importance of vibrational energy in mediating nonadiabatic transition. Electronically excited state dynamics are seen to play a small but significant role as consistent with experimental conclusions.

Role of nuclear dynamics in the asymmetric molecular-frame photoelectron angular distributions for C 1sphotoejection from CO2

We report the results of semiclassical calculations of the asymmetric molecular-frame photoelectron angular distributions for C 1$s$ ionization of CO${}_{2}$ measured with respect to the CO${}^{+}$ and ${\mathrm{O}}^{+}$ ions produced by subsequent Auger decay, and show how the decay event can be used to probe ultrafast molecular dynamics of the transient cation. The fixed-nuclei photoionization amplitudes were constructed using variationally obtained electron--molecular-ion scattering wave functions. The amplitudes are then used in a semiclassical manner to investigate their dependence on the nuclear dynamics of the cation. The method introduced here can be used to study other core-level ionization events.

Systematic calculations on exotic α-decay half-lives of nuclei with [formula omitted], 126, 127

We present systematical calculations on the α-decay half-lives of the exotic N=125, 126, 127 isotones, including even–even, odd-A, and odd–odd nuclei, by using the modified two-potential approach within the density-dependent cluster model (DDCM). The decay widths are obtained in terms of the bound state wave function and the scattering wave function. The α-preformation factors are evaluated in a Z-dependent formula based on the microscopic two-level model. With the preformation factors including the shell effect, the calculated half-lives of α transitions to both the ground states and the excited states agree well with the experimental data.

Time-saving first-principles calculation method for electron transport between jellium electrodes

We present a time-saving simulator within the framework of the density functional theory to calculate the transport properties of electrons through nanostructures suspended between semi-infinite electrodes. By introducing the Fourier transform and preconditioning conjugate-gradient algorithms into the simulator, a highly efficient performance can be achieved in determining scattering wave functions and electron-transport properties of nanostructures suspended between semi-infinite jellium electrodes. To demonstrate the performance of the present algorithms, we study the conductance of metallic nanowires and the origin of the oscillatory behavior in the conductance of an Ir nanowire. It is confirmed that the s-d(z²) channel of the Ir nanowire exhibits the transmission oscillation with a period of two-atom length, which is also dominant in the experimentally obtained conductance trace.

Unitary correlation in nuclear reaction theory: Separation of nuclear reactions and spectroscopic factors

We prove that the amplitudes for the (d,p), (d,pn) and (e,e'p) reactions determining the asymptotic behavior of the exact scattering wave functions in the corresponding channels are invariant under unitary correlation operators while the spectroscopic factors are not. Moreover, the exact reaction amplitudes are not parametrized in terms of the spectroscopic factors and cannot provide a tool to determine the spectroscopic factors.

Strong oscillations in the nondipole corrections to the photoelectron angular distributions fromC60

Nondipolar corrections to the photoelectron angular distributions from ${\mathrm{C}}_{60}$ have been calculated for the highest occupied molecular orbital (HOMO), HOMO-1, and HOMO-2 photoemission bands. The computational method employed takes advantage of a parallel algorithm that uses a multicentric expansion of bound- and scattering-wave functions and a density-functional theory one-particle Hamiltonian. First-order nondipolar asymmetry parameters have been calculated from thresholds of up to 160 eV of photon energy. Strong oscillations, reminiscent of those found in the ratio of the HOMO and HOMO-1 partial cross sections, have been observed in the nondipolar asymmetry parameters as well. The oscillations have the same period, but a different phase, compared to the ones that characterize the HOMO-HOMO-$1$ intensity ratio.

Variational description of continuum states in terms of integral relations

Two integral relations derived from the Kohn Variational Principle (KVP) are used for describing scattering states. In usual applications the KVP requires the explicit form of the asymptotic behavior of the scattering wave function. This is not the case when the integral relations are applied since, due to their short range nature, the only condition for the scattering wave function $\Psi$ is that it be the solution of $(H-E)\Psi=0$ in the internal region. Several examples are analyzed for the computation of phase-shifts from bound state type wave functions or, in the case of the scattering of charged particles, it is possible to obtain phase-shifts using free asymptotic conditions. As a final example we discuss the use of the integral relations in the case of the Hyperspherical Adiabatic method.

Treatment of the two-body Coulomb problem as a short-range potential

The scattering wave function and the transition amplitude for the two-body Coulomb problem are written as power series of the Sommerfeld parameter. Making use of a mathematical study of the nth derivatives of Kummer function with respect to its first parameter, the series coefficients are expressed analytically in terms of multivariable hypergeometric functions. We establish the connection with the Born series based on the free particle Green's function and show its applicability to long-range potentials. We also relate our analysis to recent works on the distorted-wave theory for the Coulomb problem. For the transition amplitude, the Born series is presented and compared to the series obtained from the exact well-known Rutherford result. Since the two series differ, care must be taken when extracting the relevant information about the scattering. Finally, implications for three-body problems are discussed.

Asymmetric molecular-frame photoelectron angular distributions for C 1s photoejection from CO2; a theoretical study

We report the results of ab initio calculations of cross sections and molecular-frame photoelectron angular distributions for C 1s ionization of CO2, and propose a mechanism for the recently observed asymmetry of those angular distributions with respect to the CO+ and O+ ions produced by subsequent Auger decay. The fixed-nuclei, photoionization amplitudes were constructed using variationally obtained electron-molecular ion scattering wave functions. We have also carried out electronic structure calculations which identified a dissociative state of the CO2++ dication that is likely populated following Auger decay. We show that a proper accounting of vibrational motion in the computation of the photoelectron angular distributions, along with reasonable assumptions about the nuclear dissociation dynamics, gives results in good agreement with recent experimental observations.

Solutions to the three-body collisions breakup: A Sturmians approach

We study the dynamics of a three-body collisions breakup process. We write the solution as a sum of a scattered wave function and a defined initial state, which leads to a non-homogeneous Schrödinger equation. The scattering term is expanded in a basis of positive energy Sturmian functions with outgoing wave boundary conditions. The non-homogeneous Schrödinger equation is transformed into an algebraic problem which is solved with standard matrix techniques. We show that our wave function converges and gives excellent results when compared with simple, exact analytical models.

Comment on the orthogonality of the Macdonald functions of imaginary order

Recently, Yakubovich [Opuscula Math. 26 (2006) 161–172] and Passian et al. [J. Math. Anal. Appl. 360 (2009) 380–390] have presented alternative proofs of an orthogonality relation obeyed by the Macdonald functions of imaginary order. In this note, we show that the validity of that relation may be also proven in a simpler way by applying a technique occasionally used in mathematical physics to normalize scattering wave functions to the Dirac delta distribution.