Continuum Wave Research Articles

Attosecond photoemission dynamics encoded in real-valued continuum wave functions

The dynamics of photoemission is fully encoded in the continuum wave functions selected by the transitions. Using numerical simulations on simple benchmark models, we show how scattering phase shifts and photoemission delays can be retrieved from this unambiguously defined class of wave functions. In contrast with standard scattering waves inherited from collision theory, they are real-valued for one-photon transitions and provide a clear-cut interpretation of the delays recently discussed in the framework of attosecond science.

Effect of Debye Plasma on Hydrogenic Photoionization Cross Section

In this work, we have studied the effect of plasma screening on the ground and excited state photoionization cross section \((\sigma)\) of hydrogenic system. We have considered weakly coupled plasma where the screening of nuclear charge by plasma free electrons is represented by Debye-Huckel potential. Using this potential, radial Schrodinger equation is solved numerically to obtain the bound and free state wave functions, and transition matrix elements. Adaptive step size controlled Runge-Kutta method is used for numerical integration. Use of adaptive method for grid generation ensures lesser computational time as compared to uniform grid system. Using the methodology, we have computed photoionization cross section from \(1s\) ground state and excited \(2p\) state of hydrogenic system. Strong enhancements in \(\sigma\) are observed which are generally termed as shape resonances. It is noted that these resonances occur for specific screening values where bound states are pressure ionized to enter the quasi-bound regime. The changes in the phase and amplitude of continuum wave functions also lead to appearance of Cooper minimum in \(\sigma\) of excited \(2s\) state. We have compared the results with existing theoretical and experimental data wherever they are available.

APPARENT CROSS-FIELD SUPERSLOW PROPAGATION OF MAGNETOHYDRODYNAMIC WAVES IN SOLAR PLASMAS

In this paper we show that the phase mixing of continuum Alfv\'{e}n waves and/or continuum slow waves in magnetic structures of the solar atmosphere as, e.g., coronal arcades, can create the illusion of wave propagation across the magnetic field. This phenomenon could be erroneously interpreted as fast magnetosonic waves. The cross-field propagation due to phase mixing of continuum waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfv\'{e}n and slow spectra in 2D Cartesian equilibrium models with a purely poloidal magnetic field. We show that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfv\'{e}n waves and continuum slow waves that naturally live on those structures and phase mix as time evolves. The apparent cross-field phase velocity is related to the spatial variation of the local Alfv\'{e}n/slow frequency across the magnetic surfaces and is slower than the Alfv\'{e}n/sound velocities for typical coronal conditions. Understanding the nature of the apparent cross-field propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations.

Theoretical study of photo-double ionization of CO2 in the equal energy sharing regime using Dyson orbitals and the parameterized three center continuum wave function

The theoretical procedure for the determination of the multiply differential cross sections (MDCS) applied recently [, ] to the vertical photo-double ionization of a diatomic N2 molecule is extended to the three center CO2 molecule producing dissociative dication. Dyson orbitals for the bound active electrons are introduced, and the parameterized three-center continuum wave function in its correlated form is used to describe the two ejected electrons. The variation of the MDCS for the coincidence detection of the two ejected electrons, for a randomly orientated internuclear axis is studied. The comparison of our results to those obtained by the Gaussian parametrization formula shows the similarities and the differences between the behavior of an atomic target and CO2.

Sturmian approach to study photoionization of molecules

SynopsisWe explore the implementation of generalized Sturmian functions for the study of ionization of molecules by photon or electron impact. A first part is devoted to finding a good enough description of the molecular model scattering potential and imposing accurate asymptotic boundary conditions to the molecular continuum wave functions. A second part deals with the calculation, within a generalized Sturmian approach, of single ionization cross sections for small molecules such as CH4, H2O and NH3. Issues related to the random molecular orientation are addressed.

Exact solution to the Coulomb wave using the linearized phase-amplitude method

The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

Double photoionization of helium: a generalized Sturmian approach

In this work we study the double photoionization of helium induced by low intensities laser fields in the regime where only one photon absorption occurs. The method proposed here is based on a Generalized Sturmian Functions (GSF) spectral approach which allows the imposition of outgoing boundary conditions for both ejected electrons. These, in turn, construct an hyperspherical flux characteristic of double continuum wave functions. We compare our calculated cross sections at 20 and 40 eV above threshold with absolute and relative measurements, and with other calculations. Our results definitively demonstrate the applicability of the GSF approach for dealing with break-up Coulomb problems.

The three-center parameterized continuum wave function and Dyson orbitals for the determination of the triply differential cross section of the simple ionization of CO2 by electron impact

Synopsis(e,2e) ionization of the linear three center CO2 molecules by fast electron impact.

Three-Body Continuum Wave Functions with a Box Boundary Condition

In this work we investigate the connection between discretized three-body continuum wave functions, in particular via a box boundary condition, and the wave functions computed with the correct asymptotics. The three-body wave functions are in both cases obtained by means of the adiabatic expansion method. The information concerning all the possible incoming and outgoing channels, which appears naturally when the continuum is not discretized, seems to be lost when the discretization is implemented. In this work we show that both methods are fully equivalent, and the full information contained in the three-body wave function is actually preserved in the discrete spectrum. Therefore, in those cases when the asymptotic behaviour is not known analytically, i.e., when the Coulomb interaction is involved, the discretization technique can be safely used.

Positron creation probabilities in low-energy heavy-ion collisions

The previously developed technique for calculation of ionization probabilities in low-energy heavy-ion collisions [A.I. Bondarev et al., Phys. Scr. T156 , 014054 (2013)] is extended to evaluation of positron creation probabilities. The differential probabilities are evaluated by two alternative methods. The first one uses hydrogenic continuum wave functions, while the second one uses discretized continuum wave functions corresponding to a finite basis expansion. These methods are applied to the calculation of the differential positron creation probabilities in the U91 + (1s )-U92+ collision. The results obtained by both methods are found in good agreement.

Influence of photo-inscription conditions on the radiation-response of fiber Bragg gratings.

We compared the sensitivity to X-rays of several fiber Bragg gratings (FBGs) written in the standard telecommunication fiber Corning SMF28 with different techniques. Standard gratings were manufactured with phase-mask and UV lasers, continuum wave (cw) at 244 nm or pulsed in the nanosecond domain at 248 nm, in a pre-hydrogenated fiber. Others gratings were written by exposures to a femtosecond IR-laser (800 nm), with both phase-mask and point by point techniques. The response of these FBGs was studied under X-rays at room temperature and 100°C, by highlighting their similarities and differences. Independently of the inscription technique, the two types of fs-FBGs have showed no big difference up to 1 MGy(SiO(2)) dose. A discussion on the causes of the radiation-induced peak change is also reported.

Hartree-Fock calculation of the differential photoionization cross sections of small Li clusters.

Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li2-8 are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li2 are in a good agreement with the available theoretical data, whereas those computed for Li3-8 clusters can be considered as theoretical predictions.

Triple−αcontinuum structure and Hoyle resonance ofC12using the hyperspherical slow variable discretization

We develop a method for calculating the bound and continuum energy spectrum of three particles interacting through both short-range and Coulomb potentials. Our method combines hyperspherical coordinates with the slow variable discretization approach. A complex absorbing potential is employed to describe accurately the continuum wave functions. The method is well known in atomic and molecular physics. It is extended here to nuclear physics, with a special emphasis on the long-range Coulomb interaction. The method is applied to compute the energy spectrum of $^{12}\mathrm{C}$ in a $3\ensuremath{\alpha}$-particle model, focusing on an accurate calculation of the Hoyle resonance width of the narrow near-threshold ${J}_{n}^{\ensuremath{\pi}}={0}_{2}^{+}$ state, which plays an important role in stellar nucleosynthesis. We employ an effective $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ interaction potential which reproduces both the energy and width of $^{8}\mathrm{Be}$, while a three-body force is added in order to fix the $^{12}\mathrm{C}$ energy levels at the experimental values. We also analyze the structure of the bound and resonance states by calculating the wave functions and one-dimensional distribution functions.

Solitary Wave Generation from Constant Continuous Wave in Asymmetric Oppositely Directed Waveguide Coupler

In a model which describes asymmetric oppositely directed nonlinear coupler it was observed in numerical simulations a phenomenon of solitary wave generation from the input constant continuous wave set at the entrance of a waveguide with negative refraction. The period of solitary wave formation decreases with increase of the continuum wave amplitude.

(e,2e) simple ionization of CO2 by fast electron impact: use of three-center parameterized continuum wave function and Dyson orbitals

The variation of the triple differential cross section of the (e,2e) simple ionization of CO2 with the direction of the ejected electron is studied. The calculations are performed in the frame of a perturbative first Born procedure, using a three-center Dyson type description for the 1πg bound electron and an approximate three-center continuum solution of the corresponding Schrödinger equation for a specific wave vector for the free ejected electron, which satisfies the correct asymptotic boundary condition up to the order . Empirical values for the screening of the three nuclei of the target and for the Sommerfeld parameters of the three-center Coulomb continuum function are introduced. The results are compared to existing experimental results and a theoretical result obtained by the same approach, using a Hartree–Fock Slater type orbital.

Waves in continua with extreme microstructures

The effective properties of a material may be generally defined as those that describe the limiting case where the wavelength of propagation is infinite compared to the characteristic scale of the microstructure. Generally, the limit of vanishingly small microstructural scale in a heterogeneous elastic medium results in an effective homogeneous medium that is again elastic. We show that for materials with extreme microstructures, the limiting effective medium can be quite exotic, including polar materials, or multiphase continuum. These continuum models naturally give rise to unusual effective properties including negative or anisotropic mass. Though unusual, these properties have straightforward interpretations in terms of the laws of classical mechanics. Finally, we discuss wave propagation in these structures and find dispersion curves with multiple branches.

Electron impact ionization of helium: test of screening potential in the final state

The triple differential cross sections for electron impact ionization of a helium atom is studied using the 70.6 eV incident electron. The initial state which includes both bound and continuum wave functions is calculated using the Hartree–Fock approximation. The final state continuum electron wave functions are computed in the potential of the core. The interaction potential between the two continuum electrons in the final state is approximated with the screening potential determined variationally. It is found that there is qualitative agreement between the present triple differential cross section results and the available experimental and the other theoretical data for equal and unequal sharing of 46 eV excess energy by the two final state continuum electrons. It is concluded that the screening potential which is an approximation to the actual Coulomb interaction potential between the two final state continuum electrons can produce qualitative agreement with the experiment.

Computational aspects of the continuum quaternionic wave functions for hydrogen

Over the past few years considerable attention has been given to the role played by the Hydrogen Continuum Wave Functions (HCWFs) in quantum theory. The HCWFs arise via the method of separation of variables for the time-independent Schrödinger equation in spherical coordinates. The HCWFs are composed of products of a radial part involving associated Laguerre polynomials multiplied by exponential factors and an angular part that is the spherical harmonics. In the present paper we introduce the continuum wave functions for hydrogen within quaternionic analysis ((R)QHCWFs), a result which is not available in the existing literature. In particular, the underlying functions are of three real variables and take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4). We prove that the (R)QHCWFs are orthonormal to one another. The representation of these functions in terms of the HCWFs are explicitly given, from which several recurrence formulae for fast computer implementations can be derived. A summary of fundamental properties and further computation of the hydrogen-like atom transforms of the (R)QHCWFs are also discussed. We address all the above and explore some basic facts of the arising quaternionic function theory. As an application, we provide the reader with plot simulations that demonstrate the effectiveness of our approach.(R)QHCWFs are new in the literature and have some consequences that are now under investigation.

Intrinsic power oscillations generated by the backaction of continuum on solitons and its implications on the transfer functions of a mode-locked laser.

Soliton mode locking is an essential technique for building compact mode-locked lasers with multigigahertz repetition rates. In this scheme, pulses behave like dissipative solitons due to the presence of gain, loss, frequency filtering, and nonlinear absorption in the cavity. The continuum waves that radiate from the perturbed soliton act back on the soliton, resulting in periodic changes in the electric field of the pulse. We find that, in the presence of gain filtering or two-photon absorption, this field modulation is converted to power modulation, which is observable from the radio-frequency spectrum of the laser's output power. We investigate its physical origin in the context of soliton perturbation theory. For comparison, we also perform numerical simulations and experiments.

Relativistic effects in the photoionization of hydrogen-like ions with screened Coulomb interaction

The relativistic effects in the photoionization of hydrogen-like ion with screened Coulomb interaction of Yukawa type are studied for a broad range of screening lengths and photoelectron energies. The bound and continuum wave functions have been determined by solving the Dirac equation. The study is focused on the relativistic effects manifested in the characteristic features of photoionization cross section for electric dipole nl→ε,l±1 transitions: shape resonances, Cooper minima and cross section enhancements due to near-zero-energy states. It is shown that the main source of relativistic effects in these cross section features is the fine-structure splitting of bound state energy levels. The relativistic effects are studied in the photoionization of Fe25+ ion, as an example.