Resonance Wave Functions Research Articles

Formation and conversion of high-peak-power structured beams by an Nd:YVO4/Cr4+:YAG laser subject to tight-focusing off-axis pumping

A compact Nd:YVO4/Cr4+:YAG passively Q-switched laser in a near-hemispherical resonator is exploited to realize high-peak-power pulsed beams with high spatial degrees of freedom. Beneficial from the advantages of strong intracavity beam focusing as well as the point-like excitation condition for the proposed cavity design, various high-order structured pulses as coherent superpositions of multiple degenerate eigenmodes are stably generated under different off-axis pump schemes. Besides, by employing external-cavity astigmatic mode conversion (AMC), the oval-shaped and chessboard-like structured pulses under on-axis and 1D off-axis pumping are transformed into exotic modes with polygonal and figure-eight-shaped envelopes to further enrich the spatial complexity of the generated fields. With well-defined beam structures that are reconstructed using the analytical resonant wave functions of the resonator, the phase structures of AMC pulsed fields are numerically resolved to present a variety of singularity arrays. Experimental results reveal that the overall peak power of the on-axis and off-axis generated structured pulses respectively exceeds 600 W and 1 kW while maintaining good pulse train stability with peak-to-peak amplitude fluctuation to be less than 10% and 15%.

Reactant-Product Decoupling Technique Using the Intermediate Coordinate Method.

Although the reactant-product decoupling (RPD) technique was proposed over two decades ago, it remains an efficient approach for calculating product state-resolved information on some simple direct reactions using the quantum wave packet method. In the past, usually the RPD technique employed the collocation method to transform the wave function between reactant and product arrangements, which requires quite large computational efforts. In this work, the intermediate coordinate (IC) method is employed to realize the RPD technique. Numerical examples demonstrate that this new IC RPD (IRPD) technique has superior computational efficiency compared with the original method employing the collocation method. Especially, the new IRPD technique significantly saves disk space and computer memory. To illustrate the features of our new method, the total reaction probabilities of the H + H2, H + Br2, and F + H2 reactions with J = 0 and the differential cross sections of the H + H2 and F + H2 reactions at a series of collision energy are calculated and presented. With this efficient and effective new RPD technique, the Li + HF reaction, which involves sharp resonances with long-range wave functions in the van der Waals wells in both the reactant and product arrangements, is also calculated with several J at the product state-resolved level to reveal the ability of the RPD technique for describing resonance wave functions. With these numerical examples, it is found that, for the reaction with resonances, the RPD approach should be applied carefully. Otherwise, it is very possible that the resonances could disappear with the application of the RPD technique.

Resonance Energy and Wavefunction of $${}^{{31}}$$Ne: a Calculation Using Supersymmetric Quantum Mechanics

Resonance Energy and Wavefunction of $${}^{{31}}$$Ne: a Calculation Using Supersymmetric Quantum Mechanics

Resonance Structure of 8Be within the Two-Cluster Resonating Group Method

A microscopic two-cluster model is applied to study the elastic alpha-alpha scattering and the resonance structure of 8Be. The model is an algebraic version of the Resonating Group Method (RGM), which involves the complete set of oscillator functions to expand the wave function of a two-cluster system. The interaction of nucleons inside each cluster and the interaction between clusters are determined by the well-known semirealistic nucleon-nucleon potentials which are employed in calculations. They differ by a size of the core at small distances between nucleons and realize the strong, moderate, and weak cores. They allow us to study dependence of calculated quantities on the shape of a nucleon-nucleon potential. The detailed analysis of resonance wave functions is carried out in the oscillator, coordinate, and momentum spaces. Effects of the Pauli principle on the wave functions of the 8Be continuous spectrum states are thoroughly studied.

A Unique QP Partitioning and Siegert Width Using Real-Valued Continuum-Remover Potential.

A simple, practical quantum chemical procedure is presented for computing the energy position and the decay width of autoionization resonances. It combines the L2-stabilized resonance wave function obtained using the real-valued continuum-remover (CR) potential [Y. Sajeev Chem. Phys. Lett. 2013, 587, 105-112] and the Feshbach projection operator (FPO) partitioning technique. Unlike the conventional FPO partitioning of the total wave function into its resonant space and background space components, an explicit partitioning of the total wave function into its interaction region and noninteraction region components is obtained with the help of real-valued continuum-remover potential. The molecular system is initially confined inside a CR potential which removes the electronic continuum of the molecular system in which its resonance state is embedded and, thus, unravels the space component of the resonance wave function as a bound, localized eigenstate of the confined system. The eigenfunctions of the molecular Hamiltonian represented in the space constitute a complementary, orthogonal space. A unique partition is obtained when the level-shift of the space function due to its coupling with the space is zero, and the resonance width is computed using these unique partitioned spaces. This new procedure, which we refer to as CR-FPO formalism, is formally very simple and straightforward to implement, yet its applications to the resonance state of a model Hamiltonian and to the doubly excited resonance states of atomic and molecular systems at the full-CI level are very accurate as compared to the alternative, very precise L2 methods. In addition, the CR-FPO formalism is implemented in the multireference configuration interaction (MRCI) method, and uses it for calculating the energy position and the autionization decay width of 2Πg shape resonance in N2-.

Resonance states in the simple schematic two-body model

The aim of this work is to obtain resonance states in the simple schematic two-body model. We take up two-body systems, which are described by Schrodinger equation. To obtain resonance states, we apply a simple schematic potential and complex scaling method (CSM). In the CSM, the resonance wave functions are obtained as eigenstates together with bound states by carrying out the diagonalization of the complex scaled Hamiltonian. By finding eigenvalues, we can show the distribution of resonance states in the complex energy plane. As a result, we obtain 5 and 4 resonance states for õp = 0+, 1" states, respectively.

Shannon entropy of resonant scattered state in the e–C60 elastic collision

Resonance is a remarkable feature in elastic scattering and the resonant states of e–C60 scattering are benchmarked using Shannon entropy in the present work. The resonant wavefunction, total cross-section, partial cross-sections, and scattering phase shifts are calculated for the e–C60 scattering to review the localization properties owing to resonance. Three different model interaction potentials are used in the paper to simulate the environment of the C60 shell; annular square well, Gaussian annular square well, and Lorentzian potential. This paper aims to establish a relationship between the Shannon entropy and resonant properties linked with e + C60 scattering. This work introduces the Shannon entropy as an indicator of resonance in elastic scattering and it unveils the susceptibility of entropic properties to the nature of the model potential.

Dissociative electron attachment in C2H via electronic resonances

Investigation of microwave-activated CH/H plasma used in chemical vapour deposition of diamond revealed the presence of electronically excited C (B). Using high-level electronic structure methods, we investigate electronic structure of CH and suggest possible routes for the formation of C in the ground (X) and excited (B) states via electronic resonances. To describe electronically metastable states, we employ the equation-of-motion coupled-cluster method augmented by the complex absorbing potential. The resonance wavefunctions are analysed using natural transition orbitals. We identified several resonances in CH, including the state that may lead to C (B).

Application of Supersymmetric Quantum Mechanics to Calculate Resonance Energy and Wave Function of $$^{19}$$C Halo Nucleus

Application of Supersymmetric Quantum Mechanics to Calculate Resonance Energy and Wave Function of $$^{19}$$C Halo Nucleus

Learning about the structure of giant resonances from theirγdecay

The direct $\gamma$-decays of the giant dipole resonance (GDR) and the giant quadrupole resonance (GQR) of $^{208}$Pb to low-lying states are investigated by means of a microscopic self-consistent model. The model considers effects beyond the linear response approximation. The strong sensitivity of $\gamma$-decay to the isospin of the involved states is proven. By comparing their decay widths, a much larger weight of the $3_{1}^{-}$ component in the GQR wave function of $^{208}$Pb is deduced, with respect to the weight of the $2_{1}^{+}$ component in the GDR wave function. Thus, we have shown that $\gamma$-decay is a unique probe of the resonance wave functions, and a testground for nuclear structure models.

Magnon valve effect and resonant transmission in a one-dimensional magnonic crystal

We theoretically investigate the transmission of exchange-dominated spin waves in a one-dimensional magnonic crystal (MC) with a periodic exchange bias field. By recasting the Landau-Lifshitz-Gilbert equation into an effective Schr\"odinger equation and establishing spin-wave functions, it is found that MCs with upward (up) and downward (down) magnetization, respectively, correspond to the rectangular $N$-fold barriers and wells for magnons. The broadband transmission spectra in up and down states are systematically investigated. We show the phenomena of the magnon resonant transmission in both states and calculate the resonant transmission wave functions, which are related to the magnon density. Our results also show a transmission spectra shift effect (TSSE) between up and down states, which is found to be general in this system. Furthermore, the TSSE is useful to design a type of magnon valve, the magnonic-crystal-based magnon valve (MCMV), which has a large on/off ratio and bandwidth. By high-throughput screening, 125 000 groups of parameters of the MC are calculated, and 1948 parameter groups of high-performance MCMVs are screened out. Our work clarifies the physical details of the exchange-dominated spin-wave transmission in rectangular $N$-fold barriers and wells and also provides a promising route for designing novel magnonic devices.

Ultrafast Dynamics of Electronic Resonances in Molecules Adsorbed on Metal Surfaces: A Wave Packet Propagation Approach.

We present a wave packet propagation-based method to study the electron dynamics in molecular species in the gas phase and adsorbed on metal surfaces. It is a very general method that can be employed to any system where the electron dynamics is dominated by an active electron and the coupling between the discrete and continuum electronic states is of importance. As an example, one can consider resonant molecule-surface electron transfer or molecular photoionization. Our approach is based on a computational strategy allowing incorporating ab initio inputs from quantum chemistry methods, such as density functional theory, Hartree-Fock, and coupled cluster. Thus, the electronic structure of the molecule is fully taken into account. The electron wave function is represented on a three-dimensional grid in spatial coordinates, and its temporal evolution is obtained from the solution of the time-dependent Schrödinger equation. We illustrate our method with an example of the electron dynamics of anionic states localized on organic molecules adsorbed on metal surfaces. In particular, we study resonant charge transfer from the π* orbitals of three vinyl derivatives (acrylamide, acrylonitrile, and acrolein) adsorbed on a Cu(100) surface. Electron transfer between these lowest unoccupied molecular orbitals and the metal surface is extremely fast, leading to a decay of the population of the molecular anion on the femtosecond timescale. We detail how to analyze the time-dependent electronic wave function in order to obtain the relevant information on the system: the energies and lifetimes of the molecule-localized quasistationary states, their resonant wavefunctions, and the population decay channels. In particular, we demonstrate the effect of the electronic structure of the substrate on the energy and momentum distribution of the hot electrons injected into the metal by the decaying molecular resonance.

Evolution of a Molecular Shape Resonance along a Stretching Chemical Bond.

We report experiments on laser-assisted electron recollisions that result from strong-field ionization of photoexcited I_{2} molecules in the regime of low-energy electron scattering (<25 eV impact energy). By comparing differential scattering cross sections extracted from the angle-resolved photoelectron spectra to differential scattering cross sections from quantum-scattering calculations, we demonstrate that the electron-scattering dynamics is dominated by a shape resonance. When the molecular bond stretches during the evolution of a vibrational wave packet this shape resonance shifts to lower energies, both in experiment and theory. We explain this behavior by the nature of the resonance wave function, which closely resembles an antibonding molecular orbital of I_{2}.

Toward Automated Variational Computation of Rovibrational Resonances, Including a Case Study of the H2 Dimer.

A general and semi-automatic technique, based on the complex absorbing potential (CAP) method, is developed for the variational computation and identification of rotational-vibrational resonance states. This technique is an extension of a method introduced by Tremblay and Carrington ( J. Chem. Phys. 2005, 122, 244107 ), and it employs the damped eigenvectors of a CAP-modified Hamiltonian as a basis to describe resonance wave functions. The low-lying resonances of the weakly bound Ar·NO+ complex are computed with the new and the traditional CAP techniques to test the new algorithm. As an additional, more challenging test case, the bound and resonance rovibrational states of the H2 dimer, the latter with both negative and positive binding energies, are determined, corresponding to different rotational excitations of the H2 monomers. Resonances above the first few dissociation channels of (H2)2 are computed with the new and the traditional CAP methods, revealing some new, assigned resonance quantum states not reported in the literature.

Spontaneous emission from nonhermitian perspective: complex scaling of the photon coordinates

ABSTRACTSpontaneous emission (SE) is usually studied within the framework of quantum dissipation theory. In this paper we pursue a different view of SE. Namely, we take advantage of Nonhermitian Quantum Mechanics (NHQM) and interpret SE as the decay of a Feshbach type resonance. Correspondingly, we aim at calculating the SE decay rate Γ (resonance width) and the associated resonance wavefunction via the complex scaling (CS) method. Standard application of CS in NHQM is based on scaling the dissociative coordinates of the system, . In the case of SE, the decay consists in emitting photons. Therefore the CS must be applied on (suitably defined) position coordinates of the photons. Feasibility of such a programme is demonstrated explicitly through choosing the adequate photon coordinates and performing CS of the photon wavefunctions in the position representation. It is anticipated in this way that CS makes the full resonance wavefunction square integrable, and enables thus the calculation of Γ by proceeding in complete analogy with the well established NHQM approaches. As an illustration, the standard Golden Rule formula for Γ is rederived from the CS nonhermitian perturbation theory.

Discrete-resonance-resonance transitions induced by two laser pulses with an ultrashort time delay: A formal analytic solution and quantitative applications

The paper presents a theory that solves analytically the time-dependent three-level problem of the scheme $\mathrm{discrete}\phantom{\rule{0.28em}{0ex}}|0\ensuremath{\rangle}\phantom{\rule{0.28em}{0ex}}\underset{\mathrm{as}\phantom{\rule{0.16em}{0ex}}\mathrm{pulse}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\omega}}_{1}}{\overset{\mathrm{weak}\phantom{\rule{0.16em}{0ex}}}{\ensuremath{\rightarrow}}}\phantom{\rule{0.28em}{0ex}}\mathrm{resonance}\phantom{\rule{0.28em}{0ex}}|1\ensuremath{\rangle}\phantom{\rule{0.28em}{0ex}}\underset{\mathrm{fs}\phantom{\rule{0.16em}{0ex}}\mathrm{pulse}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\omega}}_{2}}{\overset{\mathrm{moderately}\phantom{\rule{0.16em}{0ex}}\mathrm{strong}\phantom{\rule{0.16em}{0ex}}}{\ensuremath{\rightarrow}}}\phantom{\rule{0.28em}{0ex}}\mathrm{resonance}\phantom{\rule{0.28em}{0ex}}|2\ensuremath{\rangle}$, where $|0\ensuremath{\rangle}$ is a discrete state, and $|1\ensuremath{\rangle}$ and $|2\ensuremath{\rangle}$ are energy-normalized resonance states. The attosecond and femtosecond pulses with central frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ (${\ensuremath{\omega}}_{1}\ensuremath{\gg}{\ensuremath{\omega}}_{2}$) act with ultrashort time delay, ${t}_{D}$. The formalism leads to analytic expressions for photoelectron emission probabilities, ${P}_{i}(E,t)$, $i=1,2$, in the energy region of the two resonance states, whose calculation in terms of N-electron matrix elements and external control parameters can be carried out economically for any such three-level system. The problem is first solved analytically, within the rotating wave approximation, for the case where the femtosecond pulse is rectangular. The weak attosecond pulse can have any temporal shape. The final solution for two pulses with arbitrary shape (Gaussian in our case) is then achieved by fitting numerically the shape of the femtosecond pulse to a sum of rectangular pulses. The formulas for ${P}_{i}(E,t)$ involve, among other things, the Fano discrete-resonance asymmetry parameter $q$, and the resonance-resonance asymmetry parameter Q, defined by us in previous work. They also involve the complex energy poles of the two resonances, a result which accounts for the whole contribution of the open channels of energy-normalized scattering states into which they decay. The theory is applied to the calculation from first principles, using compact state-specific discrete and resonance wave functions, of observable aspects of the time-resolved dynamics associated with the processes $\mathrm{He}$ $1{s}^{2}$ $^{1}S$ $\ensuremath{\rightarrow}$ $(2s2p)$ $^{1}P^{o}$ $\ensuremath{\leftrightarrow}$ $(2{p}^{2})$ $^{1}D$. Calculations show that the $(2{p}^{2})$ $^{1}D$ resonance is 0.295 eV (4200 nm) below the energy of $(2s2p)$ $^{1}P^{o}$, (60.15 eV), and its width is 0.067 eV. For the transition $1{s}^{2}$ $^{1}S$ $\ensuremath{\rightarrow}$ $(2s2p)$ $^{1}P^{o}$, the full width at half maximum (FWHM) of the Gaussian pulse is 160 as. The few-cycle midinfrared pulse coupling the resonance states is also Gaussian, whose duration is varied in the range of a few decades of femtoseconds. Its intensity is in the range $5\ifmmode\times\else\texttimes\fi{}{10}^{10}--5\ifmmode\times\else\texttimes\fi{}{10}^{11}$ $\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2}$. The external control parameters are the intensity and the FWHM of the femtosecond pulse, as well as the ${t}_{D}$. For a given value of ${t}_{D}$, the FWHM of the second pulse is a crucial control parameter. The results include the time-resolved formation of either the $(2s2p)$ $^{1}P^{o}$ or the $(2{p}^{2})$ $^{1}D$ resonance, while they are coupled with each other. For the $(2s2p)$ $^{1}P^{o}$ state, comparison is made with the case where the time-dependent buildup of its asymmetric profile, excited from $1{s}^{2}$ $^{1}S$ by the same attosecond pulse, is calculated in the absence of coupling to another resonance. The result is in harmony with that of our earlier work on this problem. For the $(2{p}^{2})$ $^{1}D$ resonance excited from $(2s2p)$ $^{1}P^{o}$, the time-resolved buildup of its profile does not develop into an asymmetric peak due to the fact that $Q$ has the very large value of $\ensuremath{\approx}\ensuremath{-}1300$. Instead, it finishes as an Autler-Townes doublet.

State-to-state quantum dynamics of F(2P)+HO(2Π)→O(3P)+HF(1Σ+) reaction on 13A′ and 23A′′ surfaces

ABSTRACTThe state-to-state dynamics of reaction F + HO() is studied on the potential energy surfaces (PESs) of the and states. The time-dependent wave packet method, which is carried out on the graphics processing units, is used for this accurate calculation. The emphasis is on the exploration of different dynamical behaviours happening on the PESs of two excited states. The obvious vibrational and rotational inversion is found in the state-resolved integral cross section on PES, but the rotational inversion does not appear on PES. Both the total and state-resolved differential cross sections (DCSs) of the reaction on two PESs exhibit the behaviour of sideward and backward scattering, but the backward scattering of is much stronger because of its higher energy barrier, and the sideward scattering is enhanced with the increasing of collision energy. In addition, a multi-peak structure is discovered in the distribution of the product rotational state-resolved integral and DCSs, which is attributed to the quantum interference of the resonance wave functions.

Real and Imaginary Excitons: Making Sense of Resonance Wave Functions by Using Reduced State and Transition Density Matrices.

Within non-Hermitian quantum mechanics, metastable electronic states can be represented by isolated L2-integrable complex-valued wave functions with complex energies. An analysis scheme of the real and imaginary parts of resonance wave functions by using reduced transition density matrices and natural transition orbitals is presented. While the real parts of excitons describe changes in the electron density corresponding to the bound part of the resonance, the imaginary excitons can be interpreted as virtual states facilitating one-electron decay into the continuum. The different nature of real and imaginary excitons is revealed by exciton descriptors, in particular hole-particle separation and their correlation. Singular values and respective participation ratios quantify the extent of collectivity of the excitation and a number of distinct decay channels. The utility of the new tool is illustrated by the analysis of bound and metastable excited states of cyanopolyyne anions.

Dynamical resonances in $$\hbox {F}+ {\hbox {H}}_2/\hbox {HD}$$ F + H 2 / HD reaction scattering

A 3D quantum time-dependent wave packet method using reactant Jacobi coordinate for calculating reactive resonance wave functions was applied to investigate the $$\hbox {F}+{\hbox {H}}_2/\hbox {HD} \rightarrow \hbox {HF} + \hbox {H}/\hbox {D}$$ reactive resonances. By transforming the scattering resonance wave function into product Jacobi coordinates and calculating the 1D rovibrational resonance potential curves using the adiabatic bender model, the nature of the resonances was clearly deciphered. It was found that the resonances without rotational excitations enhance the reactivity; however, the resonances with rotational excitations depress the reactivity significantly. The difficulty for time-dependent method for efficiently describing the $$\hbox {F}+{\hbox {H}}_2/\hbox {HD}$$ at energies around reactive resonances is explained. The collision-energy-dependent differential cross sections around the dynamical resonance states are presented for revealing the effects of reactive resonances to the observables in a molecular crossed-beams experiment.

Matching polynomial tails to the cut-off Woods–Saxon potential

Cutting off the tail of the Woods–Saxon (WS) and generalized WS (GWS) potentials changes the distribution of the poles of the [Formula: see text]-matrix considerably. Here, we modify the tail of the cut-off WS (CWS) and cut-off generalized WS (CGWS) potentials by attaching Hermite polynomial tails to them beyond the cut. The tails reach the zero value more or less smoothly at the finite ranges of the potential. Reflections of the resonant wave functions can take place at different distances. The starting points of the pole trajectories have been reproduced not only for the real values and the moduli of the starting points, but also for the imaginary parts.