Continuum Wave Research Articles

An Orbital Basis Set for Double Photoionization of Atoms and Molecules.

The ab initio theoretical treatment of one-photon double photoionization processes has been limited to atoms and diatomic molecules by the challenges posed by large grid-based representations of the double ionized continuum wave function. To provide a path for extensions to polyatomics, an energy-adapted orbital basis approach is demonstrated that reduces the dimensions of such representations and simultaneously allows larger time steps in time-dependent computational descriptions of double ionization. Additionally, an algorithm that exploits the diagonal nature of the two-electron integrals in the grid basis and dramatically accelerates the transformation between grid and orbital representations is presented. Excellent agreement between the present results and benchmark theoretical calculations is found for H- and Be atoms, as well as the hydrogen molecule, including for the triply differential cross sections that relate the angular distribution and energy sharing of all of the particles in the molecular frame.

Luminescence enhancement of carbon dots synthesized by intense CW laser at 450 nm irradiating biocompatible solutions

Carbon dots (CDs) were synthesized by a continuum wave (CW) laser system irradiating vegetable charcoal placed in a Phosphate-Buffered Saline (PBS) solution. The laser operates at 450 nm with an output power of 50 W and 1 mm2 spot size, irradiating the carbon target for 1–3 h. The used charcoal consists of amorphous carbon that gives rise to CDs in liquids revealing high luminescence in the blue region. The formation of CDs is due to photo-thermal and photo-chemical effects induced by the prolonged laser irradiation inducing carbon atom ejection, scissions, radical formation, chemical bond breaking, molecular detachment bounded by weakened bonds and van de Walls forces, and nanoparticle functionalization in the used solution. The measurements have been concerned with the laser ablation yield, the Fourier Transmission Infrared (FTIR) spectroscopy, the UV-Vis optical spectroscopy, and the luminescence yield induced by UV excitation lamp at 365 nm wavelength. The main luminescence peak is observed at about 480 nm, characteristic of the blue color, with less significant involvement of the near regions at about 450 nm and 520 nm. Results suggest that CDs luminescence can be enhanced by the laser irradiation time, the PBS concentration, and the addition of acetic acid in the PBS solution. The presented luminescence in biocompatible solutions found many applications in different scientific fields. Overall, it is discussed its application for bioimaging in the biomedical field.

Resonating with the World: Thinking Critically about Brain Criticality in Consciousness and Cognition

Aim: Biofields combine many physiological levels, both spatially and temporally. These biofields reflect naturally resonant forms of synaptic energy reflected in growing and spreading waves of brain activity. This study aims to theoretically understand better how resonant continuum waves may be reflective of consciousness, cognition, memory, and thought. Background: The metabolic processes that maintain animal cellular and physiological functions are enhanced by physiological coherence. Internal biological-system coordination and sensitivity to particular stimuli and signal frequencies are two aspects of coherent physiology. There exists significant support for the notion that exogenous biologically and non-biologically generated energy entrains human physiological systems. All living things have resonant frequencies that are either comparable or coherent; therefore, eventually, all species will have a shared resonance. An organism’s biofield activity and resonance are what support its life and allow it to react to stimuli. Methods: As the naturally resonant forms of synaptic energy grow and spread waves of brain activity, the temporal and spatial frequency of the waves are effectively regulated by a time delay (T) in inter-layer signals in a layered structure that mimics the structure of the mammalian cortex. From ubiquitous noise, two different types of waves can arise as a function of T. One is coherent, and as T rises, so does its resonant spatial frequency. Results: Continued growth eventually causes both the wavelength and the temporal frequency to abruptly increase. Two waves expand simultaneously and randomly interfere in an area of T values as a result. Conclusion: We suggest that because of this extraordinary dualism, which has its roots in the phase relationships of amplified waves, coherent waves are essential for memory retrieval, whereas random waves represent original cognition.

Intense Continuous Wave Laser to Synthesize Luminescent Solution of Carbon Dots

Biocompatible Carbon dots (CDs) were obtained by the laser irradiation of vegetable carbon placed in a Phosphate-Buffered Saline (PBS) solution. The carbon nanoparticles were generated by a visible and continuum wave (CW) He-Ne laser beam at a 632.8 nm wavelength with 1 mm2 spot, irradiating the carbon target for times of the order of some hours. The CDs generation might be due to thermal effects induced by the prolonged laser irradiation inducing carbon atoms ejection bounded by weak van de Walls forces. Ultraviolet-visible (UV-Vis) spectroscopy, Fourier-transform infrared spectroscopy (FTIR) transmittance and luminescence measurements were employed to study the CDs synthesize. The UV excitation at a 365 nm wavelength induces visible CDs luminescence mainly at about 474 nm wavelength, giving the emitted light a characteristic blue color. The CDs luminescence in biocompatible solutions is presented and discussed in anticipation of possible applications in various sectors, such as radiation detector and material physics, engineering, microelectronics, sensors and, above all, in relation to bio-images from cell cultures and biological tissue as possible applications to the bio-medical field.

Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

Anyons obeying fractional exchange statistics arise naturally in two dimensions: Hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent exchange paths can be associated to non-trivial geometric phases for abelian anyons. Braid-anyon exchange statistics can also be found in one dimension (1D), but this requires broken Galilean invariance to distinguish different ways for two anyons to exchange. However, recently it was shown that an alternative form of exchange statistics can occur in 1D because hard-core three-body constraints also make the configuration space not simply-connected. Instead of the braid group, the topology of exchange paths and their associated non-trivial geometric phases are described by the traid group. In this article we propose a first concrete model realizing this alternative form of anyonic exchange statistics. Starting from a bosonic lattice model that implements the desired geometric phases with number-dependent Peierls phases, we then define anyonic operators so that the kinetic energy term in the Hamiltonian becomes local and quadratic with respect to them. The ground-state of this traid-anyon-Hubbard model exhibits several indications of exchange statistics intermediate between bosons and fermions, as well as signs of emergent approximate Haldane exclusion statistics. The continuum limit results in a Galilean invariant Hamiltonian with eigenstates that correspond to previously constructed continuum wave functions for traid anyons. This provides not only an a-posteriori justification of our lattice model, but also shows that our construction serves as an intuitive approach to traid anyons, i.e. anyons intrinsic to 1D.

The crucial role of granular packing structure in marine sediment acoustics

Motivated by the acoustic properties of marine sediments, we study via discrete-element method simulations the frequency dependence of dispersion and attenuation in model marine sediments. By numerically solving for the motion of each grain in a packing, rather than solving a continuum wave equation, we find that the granular packing structure, which is not explicitly considered in existing sediment-acoustics models, plays a crucial role in determining how attenuation and wave speed vary with frequency. Prior work has typically postulated a wave equation that is motivated by grain- scale forces, including viscous effects from the interstitial fluid, without explicitly considering the disordered packing structure of the grains. However, the packing structure is known to produce complex, nonlinear behavior (e.g., during shear or quasistatic compression), and how it affects dispersion and attenuation is not known. We consider linearized forces between particles (i.e., springs and dashpots), and demonstrate that the disordered packing structure leads to emergent scaling laws that do not agree with PDE-based approaches. Our results demonstrate that the granular packing structure must be explicitly considered when constructing theories for the acoustic properties of marine sediments.

Contribution of Discrete and Continuum Wave Functions in the Ground State Polarizability of Hydrogen

We analytically derive a discrete radial Green function for a hydrogenic system in terms of associated Leguerre polynomials. We investigate the polarizability of the ground-state hydrogen using the so-called length gauge approximation of electrodynamics. The polarizability is the sum of the polarization matrix elements for the negative and the positive frequency values. We estimate the contribution of discrete wavefunctions to the static ground state polarizability. We found that the contribution of continuum states dominates over that of discrete states to the polarizability by an order of magnitude.

Quantum-mechanical four-body versus semi-classical three-body theories for double charge exchange in collisions of fast alpha particles with helium targets

AbstractWithin the two-channel distorted wave second-order perturbative theoretical formalism, we study capture of both electrons from helium-like targets by heavy nuclei as projectiles at intermediate and high impact energies. The emphasis is on the four-body single-double scattering (SDS-4B) method and the three-body continuum distorted wave impact parameter method (CDW-3B-IPM). The SDS-4B method deals with the full quantum-mechanical correlative dynamics of all the four interactively participating particles (two electrons, two nuclei). The CDW-3B-IPM is a semi-classical three-body independent particle model (one electron, two nuclei), using a combinatorial calculus to describe double capture by a product of two uncorrelated probabilities, integrated over impact parameters. Both theories share a common feature in having altogether two electronic full Coulomb continuum wave functions. One such function is centered on the projectile nucleus in the entrance channel, whereas the other is centered on the target nucleus in the exit channel. These two methods satisfy the correct initial and final Coulomb boundary conditions in the asymptotic region of scattering, at infinitely large inter-particle separations. Yet, it is presently demonstrated that most of the available experimental data on total cross sections for the double capture from helium by alpha particles distinctly favor the SDS-4B method. This is especially true at intermediate energies. Such energies are critically important in versatile applications under the general umbrella of ion transport in matter, including thermonuclear fusion (plasma physics) and ion therapy (medicine).

Photoionization from the Ground and Excited Vibrational States of and Its Deuterated Isotopologues

Photoionization cross sections and rate coefficients have been calculated for all bound vibrational levels of the 1sσ g state of , HD+, and . The Born–Oppenheimer approximation is employed in our calculation of vibrationally resolved photoionization cross sections. Vibrationally resolved and local thermal equilibrium photoionization rate coefficients are presented for photon temperatures less than 50,000 K and are found to be several orders of magnitude larger than previous results in the literature. Analytic fits for the vibrationally resolved and local thermal equilibrium photoionization rate coefficients are provided. Near-threshold oscillations in the vibrationally resolved photoionization are observed. A benchmark set of photoionization cross sections are presented. Fixed-nuclei photoionization cross sections are calculated using two-center true continuum wave functions and are verified by comparison with previous calculations and are found to be in excellent agreement in all cases. Data files for our set of benchmark cross sections, rate coefficients, and fitting parameters for , HD+, and are available on Zenodo under an open-source Creative Commons Attribution license at doi:10.5281/zenodo.8304061.

Use of Gaussian-Type Functions for Describing Fast Ion-Matter Irradiation with Time-Dependent Density Functional Theory.

The electronic stopping power is an observable property that quantifies the ability of swift ions to penetrate matter to transfer energy to the electron cloud. The recent literature has proven the value of Real-Time Time-Dependent Density Functional Theory to accurately evaluate this property from first-principles, but questions remain regarding the capability of computer codes relying on atom-centered basis functions to capture the physics at play. In this Perspective, we draw attention to the fact that irradiation by swift ions triggers electron emission into the continuum, especially at the Bragg peak. We investigate the ability of Gaussian atomic orbitals (AOC), which were fitted to mimic continuum wave functions, to improve electronic stopping power predictions. AOC are added to standard correlation-consistent basis sets or STO minimal basis sets. Our benchmarks for water irradiation by fast protons clearly advocate for the use of AOC, especially near the Bragg peak. We show that AOC only need to be placed on the molecules struck by the ion. The number of AOC that are added to the usual basis set is relatively small compared to the total number of atomic orbitals, making the use of such a basis set an excellent choice from a computational cost point of view. The optimum basis set combination is applied for the calculation of the stopping power of a proton in water with encouraging agreement with experimental data.

Photoionization Cross Section for H@Cn${\text{H@C}}_{n}$ Implanted in Nonideal Classical Plasmas

AbstractIn this study, photoionization cross sections of guest hydrogen atom in endohedral fullerene () modeled by the Woods–Saxon confinement potential implanted in the nonideal classical plasma (NICP) under spherical confinement are reported for the first time in the related literature. The relevant wave equation is solved numerically via the tridiagonal matrix method and then the energy levels, bound and continuum wave functions are interpreted. Plasma effect is examined by considering plasma temperature and density and is evaluated in the photoionization process. Since the plasma modifies the discrete and continuum spectra by changing the potential energy of hydrogen atom, it closely affects the overlapping of the wave functions of ground state and continuum state. This effect has a distinct response on photoionization resonances. Using different values of endohedral confinement parameters, which means regarding different types of fullerenes, detailed analysis of energy levels, bound and continuum wave functions, and photoionization cross sections are provided by evaluating confinement width, depth, smoothing effect and distance from the spherical encompassement center. The photoionization process of implanted in the NICP (nonideal classical plasma) is highly sensitive to both plasma and endohedral confinement. At this sensitivity, Cooper resonance character is like an encoder for fullerene structure.

Antiproton impact ionization of hydrogen atom: Differential cross sections computed by Coulomb wave function discrete variable representation method

Our aim is using the Coulomb wave function discrete variable representation method (CWDVR) for the calculation of collision problem in first time. Nonrelativistic collision of antiproton with hydrogen atom is described by solving the time-dependent Schrodinger equation numerically. Two collision amplitudes are used for calculation of the differential cross sections, one of them corresponds to impact parameter of the projectile while other one is determined by projectile momentum transfer and found by Fourier transform of the first one. The ionization amplitude calculated by projecting of the wave function onto continuum wave function of the ejected electron. The differential cross sections calculated depending on projectile impact energy, scattering angle and electron ejection energy and angles, which is a result that can be measured experimentally. Our results are in good agreement with the relativistic calculation results.

Interference Phenomenon in Electron-Molecule Collisions

This article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is atomic-like, being a linear combination of the regular and irregular solutions of the wave equation. For this purpose, the elastic scattering of slow particles by a pair of non- overlapping short-range potentials has been studied. The continuum wave function of the particle is represented as a combination of a plane wave and two spherical s-waves propagating freely throughout space. The asymptotic behavior of this function determines the amplitude of elastic particle scattering in closed form. It is demonstrated that this amplitude can be represented as a partial expansion in a set of the orthonormal functions Zλ(r) other than spherical harmonics Ylm(r). General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion into a series of functions Zλ(r) and determine the scattering phases ηλ(k) for the considered two- atomic target. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.

Computing photoelectron spectra employing unique continuum functions

Molecular photoelectron spectra are commonly obtained theoretically in Fermi's Golden Rule framework, where the stationary continuum wave function is represented by slowly converging series such as the celebrated partial wave expansion. In this paper, we employ an alternative approach to address the photoionization cross section. While it gives the same cross section as the Golden Rule, this method follows a different route and has a number of advantages. The cross section is computed directly from the probability current density having the (conjugated) Dyson orbital as its source. With this, one arrives at an intuitive interpretation of the photoionization process and avoids employing a long expansion series since the continuum solution is transition-specific and thus unique. We expect this methodology to be particularly beneficial in the case of complexly shaped and delocalized Dyson orbitals.

Nonlinear optical and quantum chemical studies of Palladium benzimidazole Schiff base complex

This article presents the linear and nonlinear optics and density functional theory studies of a Palladium complex with a benzimidazole-based Schiff base. Linear absorption of the complex has been studied using a UV–Vis absorption spectrometer. Optical nonlinearity and thereby the optical limiting performance of the complex has been deliberated experimentally using a Z-scan method with a continuum wave laser of wavelength 532 nm. The NLO investigation of the complex demonstrated significant nonlinear absorption (βeff = 4.64–27.23 × 10−2 cm/W) with an imaginary part of nonlinear optical susceptibility of the third-order (Imχ(3) = 1.28–7.49 × 10−5 esu) and nonlinear refraction (n2 = 5.46–12.3 × 10−7 cm2/W) with real part of nonlinear optical susceptibility of the third-order (Reχ(3) = 3.55–8.00 × 10−5 esu). The large nonlinear absorption displayed superior optical power limiting characteristics with a threshold and clapping level of 115 W/cm2 and 35 W/cm2respectively. Theoretical studies are performed for Palladium benzimidazole Schiff base complex within Density Functional Theory (DFT) framework, using hybrid exchange-correlation B3LYP with basis set LANL2DZ. DFT-based descriptors are computed viz. energy gap between HOMO-LUMO, electronegativity, electrophilicity index, molecular hardness, and softness. Result reveals that the bond length between Pd–O is small as compared to Pd–Cl and Pd–N.

BREMS: Partial-wave calculation of spectra and angular distributions of electron-atom bremsstrahlung at electron energies less than 30 MeV (New Version Announcement)

BREMS: Partial-wave calculation of spectra and angular distributions of electron-atom bremsstrahlung at electron energies less than 30 MeV (New Version Announcement)

Franz-Keldysh and Stark Effects in Two-Dimensional Metal Halide Perovskites

The established theory of a two-dimensional (2D) Wannier exciton in a uniform electric field is used to analyze the electroabsorption response of an archetypal 2D metal halide perovskite (MHP), phenethylammonium lead iodide. The high level of agreement between the electroabsorption simulation and measurement allows for a deepened understanding of the redshift of exciton energy, according to the quadratic Stark effect, and the continuum wave function leaking, according to the Franz-Keldysh effect. We find the field dependency of each of these effects to be rich with information, yielding measurements of the exciton Bohr radius, transition dipole moment, polarizability, and reduced effective mass of the exciton. Most importantly, the band-gap energy and exciton binding energy are unambiguously determined with 1σ variance of 4 meV. The high precision of these new measurement methods opens the opportunity for determining the influence of chemical and environmental factors on the optoelectronic properties of MHPs, which would enable the fabrication of highly efficient and reproducible light-harvesting and light-emitting optoelectronic devices.8 MoreReceived 21 September 2021Revised 22 December 2021Accepted 2 February 2022DOI:https://doi.org/10.1103/PRXEnergy.1.013001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasStark effectPhysical SystemsPerovskitesQuantum wellsTechniquesOptical absorption spectroscopyCondensed Matter, Materials & Applied Physics

Two-body continuum states in noninteger geometry

Wave functions, phase shifts and corresponding elastic cross sections are investigated for two short-range interacting particles in a deformed external oscillator field. For this we use the equivalent $d$-method employing a non-integer dimension $d$. Using a square-well potential, we derive analytic expressions for scattering lengths and phase shifts. In particular, we consider the dimension, $d_E$, for infinite scattering length, where the Efimov effect occurs by addition of a third particle. We give explicitly the equivalent continuum wave functions in $d$ and ordinary three dimensional (3D) space, and show that the phase shifts are the same in both methods. Consequently the $d$-method can be used to obtain low-energy two-body elastic cross sections in an external field.

Complete characterization of attosecond photoelectron wave packets

Development of attosecond laser technology allows us to measure electron dynamics such as photoionization delays between different species or electronic states. In general, the measured photoionization phase is a mixture of the spectral phase of the extreme ultraviolet (XUV) pulse and the atomic phases inherent to the optical transitions. Hence, it is difficult to disentangle these phases independently. Here we separate these phases by using an XUV attosecond pulse train containing both even and odd harmonic orders, generated by an 800- and 400 nm laser pulse, in the presence of the infrared 800-nm pulse. We measure the photoelectron angular distributions as a function of two independently controlled delays, the XUV-IR and the 800--400 nm delays, with attosecond time resolution. We analyze the photoelectron angular distributions to determine the relative amplitudes and phases of each angular momentum component. Using an in situ technique, we determine the phases of the harmonic orders and thereby completely determine the atomic phases. Using the obtained atomic phases and amplitudes, we reconstruct the real and imaginary parts of the continuum wave functions associated with three individual photoionization pathways.

A complex Gaussian approach to molecular photoionization.

We develop and implement a Gaussian approach to calculate partial cross-sections and asymmetry parameters for molecular photoionization. Optimal sets of complex Gaussian-type orbitals (cGTOs) are first obtained by nonlinear optimization, to best fit sets of Coulomb or distorted continuum wave functions for relevant orbital quantum numbers. This allows us to represent the radial wavefunction for the outgoing electron with accurate cGTO expansions. Within a time-independent partial wave approach, we show that all the necessary transition integrals become analytical, in both length and velocity gauges, thus facilitating the numerical evaluation of photoionization observables. Illustrative results, presented for NH3 and H2 O within a one-active-electron monocentric model, validate numerically the proposed strategy based on a complex Gaussian representation of continuum states.