Resonance Wave Functions Research Articles

Resonant Capture of Low-Energy Electrons by Gas-Phase Glycine: A Quantum Dynamics Calculation

We present quantum calculations for the low-energy dynamics of electrons interacting with glycine molecules in the gas phase. The scattering equations are formulated within a symmetry-adapted, single-center expansion of both continuum and bound electrons, and the interaction forces are obtained from a combination of ab initio calculations and a nonempirical modeling of exchange plus correlation effects. Several open-channel (shape) resonances are obtained, and the features of the excess electron resonant wave functions are related to the experimental findings about the dissociative electron attachment (DEA) processes that follow the initial formation of those transient negative ions.

Silicon Germanium Nanostructures: Electronic Parameters and Optical Characteristics

The electronic states (energies of localized and resonance levels, wave functions, charge density, and density of states) and optical absorption spectra of germanium clusters in silicon matrix are studied by the pseudo-potential method. The possibility of description of cluster states of germanium in silicon using the effective mass method is explored.

Nanoscopic models for radiobiological damage: metastable precursors of dissociative electron attachment to formic acid

The HCOOH molecule represents the simplest organic acid which is also supposed to play a role in the interstellar formation of more complicated biomolecules. Its interaction with slow electrons in the gas phase is analysed in the present work with the view of providing specific structural and dynamical information on those resonant states which lead to different transient negative ions (TNIs) formation. The latter resonant states in turn guide molecular fragmentation along different pathways, forming HCOO−, O− and OH− fragments as experimentally observed. The present calculations, carried out at the equilibrium molecular geometry, indeed support the presence of two main resonances within the expected energy range and further indicate the presence of antibonding nodal planes in the excess electron resonant wave function features which could explain the observed fragmentation products formed during the subsequent dissociative break-up.

Building Scattering Cross Sections from Resonance Wave Functions

A comparative discussion is presented for methods to evaluate simultaneously both resonance and background contributions to scattering.

Electronic properties of a Cantor lattice

We present results of some investigations on the electronic properties of a non-periodic self-similar structure based on the triadic Cantor set sequence. In particular, we examine the eigenvalue spectrum of a Cantor lattice using the trace map technique widely used for the conventional quasi-periodic sequences. In addition, we show that a Cantor lattice possesses a number of resonant extended wave functions, some of which exhibit a distribution that resembles the lattice itself. We present results for the transmission coefficient of finite, but arbitrarily large Cantor lattices. We also examine in some detail, the cycles of the matrix map for such a sequence, and the variety of cyclic behaviour that one may encounter depending on the specific choices of the Hamiltonian parameters.

Signatures of a Discrete Level Spectrum and Dynamical Tunneling in the Conductance of a Large Open Quantum Dot

We simulate transport in large, strongly-open, quantum dots, which typically would be viewed as lying well within the semiclassical regime for which all energy levels can be assumed to be broadened. Contrary to this assumption, we find that resonances, which can be associated with individual eigenstates, can persist even under these conditions. Their presence yields regular fluctuations in the low temperature conductance which persist in the presence of a moderately-disordered dot potential and can be observed experimentally. Examining the resonant wave functions, we typically find them to be scarred by regular periodic orbits which are classically inaccessible from the leads. As such, our results suggest that dynamical phase-space tunneling may play a more generic role in transport through mesoscopic structures than has thus far been appreciated.

Trapped metastable anions in low-energy electron scattering from C20 clusters

Calculations are reported on scattering resonances in low-energy electron collisions with the fullerene carbon cluster C20. The quantum treatment of the scattering process is carried out using a single-center expansion of the total (bound + scattering electronic) wave function and with the electron–molecule interaction represented by a set of adiabatic multipolar effective potential curves. All resonant wave functions with scattering energies less than 20 eV are analyzed. In some of the resonant states the scattered electron density is seen to remain partly trapped inside carbon cage, although in all cases the resonant, continuum orbital density in the anionic state is primarily distributed near the surface of the cluster cage.

Stark resonances for a double quantum well: crossing scenarios, exceptional points and geometric phases

The complex energy resonances of a double δ potential well in a constant (Stark) field are studied. Varying the two system parameters (well distance and field strength) we investigate the behaviour of the resonance energies and wavefunctions both analytically and numerically. Different crossing scenarios for the real and imaginary parts of two resonance energies are observed and compared with a simple two-state model. In addition, a point in parameter space where both the real and imaginary parts of the two energies degenerate, an exceptional point, is found. Varying the system parameters around this exceptional point, the behaviour of energies and wavefunctions is discussed and the corresponding geometric phases, or Berry phases, for this non-Hermitian system are considered.

Hydrogen-enhanced clusterization of carbon in crystalline silicon

The influence of hydrogen impurities on the formation of carbon nanoclusters in carbon-enriched (>1017 cm−3) float-zone (FZ) silicon has been studied by means of EPR along with uniaxial-stress experiments. Hydrogen was incorporated by proton implantation at room temperature. As object of research, we used EPR as a signal of the earlier not identified EPR defect with S=1/2 and a C2 symmetry of g-tensor (denoted as PK4), which was observed in fast neutrons irradiated silicon. We have found that hydrogen implantation in FZ silicon with elevated content of carbon upon subsequent annealing above ∼250 °C generate most prominent EPR signal of the defect. We have revealed reliably three sets of hyperfine (hf) satellites: (1) one equivalent Si atom with strong localization (∼42%) of the resonant wave function of tetragonal symmetry; (2) four equivalent Si atoms with ∼16% of the resonant wave function; (3) weak hfi, which can be caused by an isotope of 13C from four equivalent carbon atoms. Uniaxial stress experiments reveal very large value (∼2.8 eV) of the activation energy for atomic reorientation that, along with data of piezospectroscopic tensor, are in good agreement with the cluster nature of the defect. We suggest that the presence of hydrogen leads to a strongly coordinated formation of nanocluster, which include carbon and self-interstitial atoms. It is suggested that the electronic structure of this defect corresponds to the double donor in a positive charge state.

Vibronic Resonances Arising from Conically Intersecting Electronic States

We provide here a quantum mechanical investigation of the resonance states found in a study of conically intersecting electronic surfaces. The dynamical system under investigation consists of a bound electronic state having a conical intersection with a dissociative electronic state. Quantum mechanical resonances arise from the predissociation of vibrational states of the bound potential surface via the nonadiabatic coupling to the dissociative potential surface. Resonance energies and wave functions are computed using the complex coordinate method, and the resonances are characterized in terms of contributions from states of the uncoupled potential surfaces. Key results found in this study include the following: (i) there is no correlation between resonance positions and widths in that when the resonances are ordered by their positions, the corresponding widths (and lifetimes) fluctuate irregularly; (ii) the resonance energetically below the conical intersection cannot be identified as a tunneling resonance of the lowest adiabatic potential surface since its resonance lifetime is orders of magnitude larger than the tunneling lifetime; (iii) the resonance states (even those whose positions are energetically much higher than the conical intersection) are found to arise from a small number of vibrational states of the bound diabat coupling to each other via the continuum of the dissociative diabat; and (iv) none of the resonance states emanate from a bound state of the upper adiabatic cone-shaped potential surface. We also briefly investigate the resonance energies as a function of the nonadiabatic coupling strength; the irregular behavior of the resonance lifetimes with the coupling strength is a fingerprint of the conical intersection. Furthermore, we have performed a symmetry analysis of the resonances and introduced an effective Hamiltonian which, with the aid of a simple model, yields results in agreement with numerically exact results.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular.

Exchange currents in nucleon electroexcitation

We calculate the scalar and transverse helicity amplitudes for the electromagnetic excitation of nucleon resonances as a function of the photon four-momentum transfer. The helicity amplitudes are decomposed into electromagnetic multipoles and connected to the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{N}{N}^{*}$ transition form factors. The internal N and ${N}^{*}$ dynamics is described by a constituent quark model (CQM) Hamiltonian with gluon, pion, and $\ensuremath{\sigma}$-meson exchange potentials as residual interactions. The N and ${N}^{*}$-resonance wave functions are obtained by solving the Schr\odinger equation in a harmonic oscillator basis which contains up to $N=2$ excitation quanta. For the electromagnetic current we include, in addition to the one-body current, two-body exchange currents associated with the quark-quark potentials. Exchange currents provide an effective description of the cloud of $q\overline{q}$ pairs, which together with the valence quarks are important degrees of freedom in physical hadrons. We obtain sizable contributions of the two-body exchange currents for nearly all $\ensuremath{\gamma}{\mathrm{NN}}^{*}$ amplitudes. For some observables, e.g., the $C2/M1$ ratio in the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\Delta}(1232)$ transition, and the $M1$ transition to the ${N}^{*}(1440),$ exchange currents provide the most important contribution.

Properties of microscopic nucleus-nucleus interaction for molecular resonance formation in12C+12Cand3α+3αsystems

Properties of microscopic interaction potentials between two ${}^{12}\mathrm{C}$ nuclei are discussed in connection with the formation of ${}^{12}{\mathrm{C}+}^{12}\mathrm{C}$ and $3\ensuremath{\alpha}+3\ensuremath{\alpha}$ molecular resonances. The nucleus-nucleus interactions are calculated by the double-folding procedure based on a realistic nucleon-nucleon interaction (DDM3Y) and microscopic ${}^{12}\mathrm{C}$ transition densities calculated from 3\ensuremath{\alpha}-RGM wave functions. The interaction potential can be written as the sum of the monopole part obtained from the monopole density and the multiple parts generated from the quadrupole component of the density. We discuss the role of the monopole and multipole parts of the potential separately. It is shown that the multipole part is very strong in the channels with $3\ensuremath{\alpha}+3\ensuremath{\alpha}$ structure and the energy positions of the $3\ensuremath{\alpha}+3\ensuremath{\alpha}$ molecular bands generated by the monopole potential are largely modified. The effect is moderate but non-negligible on the molecular bands with the ${}^{12}{\mathrm{C}+}^{12}\mathrm{C}$ dinuclearlike structure and largely modifies the band crossing diagram between the elastic and aligned-inelastic molecular bands. The channel coupling effect among the ${}^{12}{\mathrm{C}+}^{12}\mathrm{C}$ channels, namely, the elastic channel and the single- and mutual-${2}_{1}^{+}$ excitation channels is also investigated. Due to the strong coupling between the ground and ${2}_{1}^{+}$ states of ${}^{12}\mathrm{C},$ the resonance wave functions obtained by the coupled-channel calculation have an additional radial node compared with those of the single-channel resonances. All the results are discussed in connection with the band crossing model which was believed to be successful in describing the ${}^{12}{\mathrm{C}+}^{12}\mathrm{C}$ molecular resonances.

Multiphoton detachment rates ofH−for weak and strong fields

The time-independent Schr\"odinger problem for the ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ plus ac field system has been solved from first principles via the nonperturbative many-electron, many-photon theory (MEMPT) for a wide range of values of frequency \ensuremath{\omega} and of intensity I of linearly polarized light. The calculations obtained the multiphoton electron detachment rates (MPEDRs) as the imaginary part of a complex eigenvalue and were done for combinations of values of \ensuremath{\omega} and of I defining regimes of ``weak'' and of ``strong'' fields. Most of the results cover the cases of two-, three-,\dots{}, seven-photon electron detachment, studied as a function of frequency and of intensity. However, special cases, such as the one of $I=2\ifmmode\times\else\texttimes\fi{}{10}^{11}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ for the ${\mathrm{CO}}_{2}$ frequency of 0.117 eV, represent detachment processes into various symmetries requiring the absorption of at least 25 photons. The MEMPT results were obtained without any empirical adjustment of energies or of basis sets. The dressed-atom resonance wave function consisted of optimized function spaces for the initial and final states, including the lowest ${}^{1}S,$ ${}^{1}{P}^{o},$ and ${}^{1}D$ doubly excited states (DES). The initial state was represented by a ten-term numerical multiconfigurational Hartree-Fock wave function whose energy, -0.5275 a.u., is very close to the exact one, -0.5277 a.u., and which accounts self-consistently for electron correlation as well as for the proper magnitude of the $1s$ orbital at large values of r. The ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}\mathrm{ }\mathrm{DES}$ wave functions were correlated, yielding accurate energies. However, their presence does not affect the results at all. The results converged well when 15 photon blocks were used. In spite of the large number of absorbed photons required in cases such as the ${\mathrm{CO}}_{2}$ frequency, the calculations converged well, within the numerical accuracy of the algorithms, by using free-electron angular momenta with 1 up to 7. The systematic quantitative study of the dependence of the MPEDRs on \ensuremath{\omega} and I has led to conclusions as to the behavior at thresholds and as to the limits of validity of the predictions of the lowest-order perturbation theory. An interesting result is the appearance of intensity-dependent structures in the two-, four-, and six-photon detachment rates, which is caused by the interference of the ${}^{1}S$ and ${}^{1}D$ channels. For a number of $(I,\ensuremath{\omega})$ pairs, comparison is possible with published results obtained by earlier large-scale calculations which either started from first principles or used parametrized one-electron models. Overall, there is good agreement. We conclude that the current level of theoretical knowledge of the ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}\mathrm{MPEDR}$ spectrum is very satisfactory for a large set of experimentally possible laser parameters.

Bi-orthogonality of Resonance Wave Functions in NO2

Bi-orthogonality of Resonance Wave Functions in NO₂

From bound states to resonances: Analytic continuation of the wave function

Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the Schroedinger equation with respect to the coupling strength is exploited to analytically continue the bound-state solutions into the positive-energy region by means of Pade' approximants of the second kind. The method is here applied to single-particle wave functions of the $^{154}Sm$ and $^{131}Eu$ nuclei. A comparison of the results with the direct solution of the Schroedinger equation shows that the method can be confidently applied also in coupled-channel situations requiring high numerical accuracy.

New (S=1) EPR AA17 center in silicon — microplatelets or precursor of platelets?

New (S=1) EPR spectrum (labeled Si-AA17) is observed in irradiated high-purity hydrogen-contained silicon after annealing at ≥200°C. The AA17 defect has D3d symmetry with g∣∣=2.0028, g⊥=2.0106; A∣∣(29Si)=175.0 MHz, A⊥=89.0 MHz; and D∣∣=±33.6 MHz, D⊥=±16.8 MHz. It is paramagnetic in a neutral charge state. An analysis of 29Si hf interaction has shown that 62% of the resonant wave function belong to two equivalent silicon atoms. The magnitude of zero-field splitting (D=16.8 MHz) of AA17 has a smallest value among the known (S=1) EPR centers in silicon and indicates that the distance between two equivalent Si sites (spins) creating the S=1 state, is ∼12 Å along to 〈111〉 axis. Most suitable model of the defect is the {111} planar hexavacancy situated between two 〈111〉 dangling Si bonds separated by ∼12 Å. Each of these dangling bonds is formed as a result of saturation of the nearest Si atom by one hydrogen located at AB position.

Resonant wavefunctions and exchange effect in nanostructures

It is shown that itinerant electrons in a nanostructure have the property, in a resonance energy range, that the wavefunctions exhibiting a resonance peak all have substantially the same position dependence within the ‘quantum dot’. In the resonance energy range, they differ only by a Lorentzian function of energy including a phase factor. Consequently, for electron states with parallel spins there should be an exchange cancellation of their Coulomb interaction.

Hydrogen-induced extended complexes in silicon

New EPR spectrum, labeled Si-AA17, forms upon annealing at ⩾200°C in irradiated high-purity hydrogen-containing silicon and is stable up to ∼450°C. The AA17 defect has D3d symmetry, electronic spin S=1 and it is paramagnetic in a neutral charge state. An analysis of 29Sihf interaction has shown that 62% of the resonant wave function belongs to two equivalent silicon atoms. The magnitude of zero-field splitting (D=16.8MHz) indicates that the distance between two equivalent Si sites (spins) creating the S=1 state is ∼12Å along the 〈111〉 axis. Piezospectroscopic measurements have also shown that vacancy-like defect should be sited between equivalent Si atoms. Tentative model of the defect is the {111} planar hexavacancy centered between two 〈111〉 dangling Si bonds separated by ∼12Å. Each of these dangling bonds is formed as a result of saturation of the nearest Si atom by one hydrogen. Si-AA1 EPR spectrum associated with the formation of self-interstitial aggregates is observed simultaneously with the Si-AA17.

Scattering matrix determination by asymptotic analysis of complex scaled resonance wave functions: Model Cl+H2 nonadiabatic dynamics

It has previously been shown that partial widths of resonance states can be calculated by the asymptotic analysis of the complex scaled resonance wave function [U. Peskin, N. Moiseyev, and R. Lefebvre, J. Chem. Phys. 92, 2902 (1990)] and by the complex coordinate scattering theory [N. Moiseyev and U. Peskin, Phys. Rev. A 42, 255 (1990)]. Here we use these methods for the first time to calculate complex partial width amplitudes. The complex amplitudes are independent of the complex scaling parameters and are used for calculating the resonance contribution to the scattering matrix (the S matrix) in the case of Cl+H2 scattering described by two coupled one-dimensional potential energy curves. The background contribution to the S matrix was calculated by the use of one ClH2 potential energy curve only. The sum of the resonance and the background contributions provides accurate complex S matrix elements and transition probabilities, even at the resonance energy for which total reflection is obtained due to the interference between the two contributions.