Atomic Bound State Research Articles

High-order above-threshold ionization from a coherent superposition of states

Quantum theory of high-order above-threshold ionization (HATI) of atoms, prepared in a coherent superposition of bound states, by a strong laser field is formulated. Numerical results are obtained using the solutions of the time-dependent Schr\"odinger equation and the improved strong-field approximation. As an example, coherent superposition of the excited $2s$ and $2p$ states of the He atom is used. Applying a two-level model, it is shown how the relative amplitude and phase of the states in this coherent superposition can be controlled with a weak resonant laser pulse. Numerical results presented for HATI by a strong nonresonant probe laser pulse confirm that the photoelectron spectra and the momentum distributions strongly depend on the relative phase of the states in the prepared coherent superposition. For the case of HATI by a strong resonant laser pulse, we modify our strong-field-approximation theory by applying the two-level model to describe the time evolution of the atomic bound state before the instant of ionization. Contrary to the HATI from a single state by a long laser pulse, the corresponding photoelectron spectra of HATI from the coherent superposition of states depend on the carrier-envelope phase of the resonant ionizing pulse. Therefore, the strong-field ionization from a coherent superposition of states by a resonant laser pulse can be used to determine the carrier-envelope phase for long pulses for which the standard methods such as stereo--above-threshold ionization technique fail. The results strongly depend on the relative amplitude and phase of states in the coherent superposition of states, which can be controlled with a weak resonant laser pulse.

Ultrahigh-order harmonic generation in the subnanometer wavelength range: the role of finite atomic size

As shown by recent theoretical studies, intense ultrafast laser sources of long-wave infrared range are capable, in principle, of generating ultrahigh-order harmonics in the wavelength range of the atomic or even subatomic scale. Under these conditions the atom as an elementary emitter can no longer be considered within the framework of the point dipole model generally accepted in the theory of high-order harmonic generation. It can be expected that the non-pointness of an atomic dipole will lead to a change in both the power of the radiation emitted by it and its directivity pattern. In this paper, we study these effects in detail using the example of the hydrogen atom. The analysis was carried out within the widely used recollision model, according to which the high-frequency dipole moment responsible for the generation of high harmonics by an atomic system is induced as a result of the interference of the de Broglie wave of the recolliding electron with the wave function of the atomic bound state. Taking into account the non-pointness of the induced dipole, the dependences of the power and directivity pattern of its radiation on the wavelength of the emitted photon are found. In particular, a universal atomic dipole non-pointness factor is obtained in an explicit form, which depends on the wavelength and emission angle of the harmonic photon and makes it possible to calculate the frequency and angular characteristics of the emitted harmonics based on the results obtained in the point dipole approximation.

Momentum distribution of the electron pair from the charged lepton flavor violating process μ−e−→e−e− in muonic atoms with a polarized muon

The $\mu^-e^-\to e^-e^-$ process in a muonic atom is one of the promising probes to study the charged lepton flavor violation (CLFV). We have investigated the angular distribution of electrons from the polarized muon of the atomic bound state. The parity violating asymmetric distribution of electrons is analyzed by using lepton wave functions under the Coulomb interaction of a finite nuclear charge distribution. It is found that the asymmetry parameters of electrons are very sensitive to the chiral structure of the CLFV interaction and the contact/photonic interaction. Therefore, together with the atomic number dependence of the decay rate studied in our previous work, the angular distribution of electrons from a polarized muon should be a very useful tool to constrain the model beyond the standard model.

Effective field theories for van der Waals interactions

Van der Waals interactions between two neutral but polarizable systems at a separation $R$ much larger than the typical size of the systems are at the core of a broad sweep of contemporary problems in settings ranging from atomic, molecular and condensed matter physics to strong interactions and gravity. We reexamine the dispersive van der Waals interactions between two hydrogen atoms. The novelty of the analysis resides in the usage of nonrelativistic EFTs of QED. In this framework, the van der Waals potential acquires the meaning of a matching coefficient in an EFT suited to describe the low energy dynamics of an atom pair. It may be computed systematically as a series in $R$ times some typical atomic scale and in the fine structure constant $\alpha$. The van der Waals potential gets short range contributions and radiative corrections, which we compute in dimensional regularization and renormalize here for the first time. Results are given in $d$ spacetime dimensions. One can distinguish among different regimes depending on the relative size between $1/R$ and the typical atomic bound state energy $m\alpha^2$. Each regime is characterized by a specific hierarchy of scales and a corresponding tower of EFTs. The short distance regime is characterized by $1/R \gg m\alpha^2$ and the LO van der Waals potential is the London potential. We compute also NNNLO corrections. In the long distance regime we have $1/R\ll m\alpha^2$. In this regime, the van der Waals potential contains contact terms, which are parametrically larger than the Casimir-Polder potential that describes the potential at large distances. In the EFT the Casimir-Polder potential counts as a NNNLO effect. In the intermediate distance regime, $1/R\sim m\alpha^2$, a significantly more complex potential is obtained which we compare with the two previous limiting cases. We conclude commenting on the hadronic van der Waals case.

Atomic bound state and scattering properties of effective momentum-dependent potentials.

Effective classical dynamics provide a potentially powerful avenue for modeling large-scale dynamical quantum systems. We have examined the accuracy of a Hamiltonian-based approach that employs effective momentum-dependent potentials (MDPs) within a molecular-dynamics framework through studies of atomic ground states, excited states, ionization energies, and scattering properties of continuum states. Working exclusively with the Kirschbaum-Wilets (KW) formulation with empirical MDPs [C. L. Kirschbaum and L. Wilets, Phys. Rev. A 21, 834 (1980)0556-279110.1103/PhysRevA.21.834], optimization leads to very accurate ground-state energies for several elements (e.g., N, F, Ne, Al, S, Ar, and Ca) relative to Hartree-Fock values. The KW MDP parameters obtained are found to be correlated, thereby revealing some degree of transferability in the empirically determined parameters. We have studied excited-state orbits of electron-ion pair to analyze the consequences of the MDP on the classical Coulomb catastrophe. From the optimized ground-state energies, we find that the experimental first- and second-ionization energies are fairly well predicted. Finally, electron-ion scattering was examined by comparing the predicted momentum transfer cross section to a semiclassical phase-shift calculation; optimizing the MDP parameters for the scattering process yielded rather poor results, suggesting a limitation of the use of the KW MDPs for plasmas.

Improved strong-field approximation and quantum-orbit theory: Application to ionization by a bicircular laser field

A theory of above-threshold ionization of atoms by a strong laser field is formulated. Two versions of the strong-field approximation (SFA) are considered, the direct SFA and the improved SFA, which do not and do, respectively, take into account rescattering of the freed electron off the parent ion. The atomic bound state is included in two different ways: as an expansion in terms of Slater-type orbitals or as an asymptotic wave function. Even though we are using the single-active-electron approximation, multielectron effects are taken into account in two ways: by a proper choice of the ground state and by an adequate definition of the ionization rate. For the case of the asymptotic bound-state wave functions, using the saddle-point method, a simple expression for the $T$-matrix element is derived for both the direct and the improved SFA. The theory is applied to ionization by a bicircular field, which consists of two coplanar counterrotating circularly polarized components with frequencies that are integer multiples of a fundamental frequency $\ensuremath{\omega}$. Special emphasis is on the $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ case. In this case, the threefold rotational symmetry of the field carries over to the velocity map of the liberated electrons, for both the direct and the improved SFA. The results obtained are analyzed in detail using the quantum-orbit formalism, which gives good physical insight into the above-threshold ionization process. For this purpose, a specific classification of the saddle-point solutions is introduced for both the backward-scattered and the forward-scattered electrons. The high-energy backward-scattering quantum orbits are similar to those discovered for high-order harmonic generation. The short forward-scattering quantum orbits for a bicircular field are similar to those of a linearly polarized field. The conclusion is that these orbits are universal, i.e., they do not depend much on the shape of the laser field.

Electronic Structure of Helium Atom in a Quantum Dot**TKM Gratefully Acknowledges Financial Support under Grant No. 37(3)/14/27/2014-BRNS from the Department of Atomic Energy, BRNS, Government of India. SB Acknowledges Financial Support under Grant No. PSW-160/14-15(ERO) from University Grants Commission, Government of India

Bound and resonance states of helium atom have been investigated inside a quantum dot by using explicitly correlated Hylleraas type basis set within the framework of stabilization method. To be specific, precise energy eigenvalues of bound 1sns (1Se) (n = 1–6) states and the resonance parameters i.e. positions and widths of 1Se states due to 2sns (n = 2–5) and 2pnp (n = 2–5) configurations of confined helium below N = 2 ionization threshold of He+ have been estimated. The two-parameter (Depth and Width) finite oscillator potential is used to represent the confining potential due to the quantum dot. It has been explicitly demonstrated that the electronic structural properties become sensitive functions of the dot size. It is observed from the calculations of ionization potential that the stability of an impurity ion within a quantum dot may be manipulated by varying the confinement parameters. A possibility of controlling the autoionization lifetime of doubly excited states of two-electron ions by tuning the width of the quantum cavity is also discussed here.

Michel decay spectrum for a muon bound to a nucleus

The spectrum of electrons from muons decaying in an atomic bound state is significantly modified by their interaction with the nucleus. Somewhat unexpectedly, its first measurement, at the Canadian laboratory TRIUMF, differed from basic theory. We show, using a combination of techniques developed in atomic, nuclear, and high-energy physics, that radiative corrections eliminate the discrepancy. In addition to solving that outstanding problem, our more precise predictions are potentially useful for interpreting future high-statistics muon experiments that aim to search for exotic interactions at $10^{-16}$ sensitivity.

Classical study of atomic bound state dynamics in circularly polarized ultrastrong fields

We investigate hydrogen-like atoms in ultrastrong fields up to 1000 au (3 × 1022 W cm−2). We find the influence of the magnetic component (Blaser) of the external ultrastrong field introduces perturbations for the bound states of the atom. For intensities up to 1 × 1019 W cm−2 the changes in the trajectory energies and Poincaré plots are on the order of a few per cent. While small, the changes from Blaser with circular polarized (CP) light can result in a several-fold decrease in the ionization probability at the highest intensities for the bound states, where ionization approaches 50%. For these highest intensities, we find the Lorentz force from Blaser exerts a force on the bound electron perpendicular to the rotating plane of the CP light. Since these trajectories are then aligned away from the minimum in the potential barrier it is stabilized against tunnelling ionization. The results provide a classical understanding for ionization in ultrastrong fields and indicate that relativistic effects in ultrastrong field ionization may most easily be seen with CP fields.

Invisible decay of muonium: Tests of the standard model and searches for new physics

In the Standard Model there are several canonical examples of pure leptonic processes involving the muon, the electron and the corresponding neutrinos which are connected by the crossing symmetry: i) the decay of muon, ii) the inverse muon decay, and iii) the annihilation of a muon and an electron into two neutrinos. Although the first two reactions have been observed and measured since long ago, the third process, resulting in the invisible final state, has never been experimentally tested. It may go either directly, or, at low energies, via the annihilation of a muon and an electron from an atomic bound state, called muonium (M=\mu^+e^-). The M\to \nu_\mu \nu_e decay is expected to be a very rare process, with the branching fraction predicted to be Br(M\to \nu_\mu\nu_e) = 6.6 10^{-12} with respect to the ordinary muon decay rate. Using the reported experimental results on precision measurements of the positive muon lifetime by the MuLan Collaboration, we set the first limit Br(M \to invisible) < 5.7 10^{-6}, while still leaving a big gap of about six orders of magnitude between this bound and the predictions. To improve substantially the limit, we proposed to perform an experiment dedicated to the sensitive search for the M\to invisible decay. A feasibility study of the experimental setup shows that the sensitivity of the search for this decay mode in branching fraction Br(M\to invisible) at the level of 10^{-12} could be achieved. If the proposed search results in a substantially higher branching fraction than predicted, say Br(M \to invisible) < 10^{-10}, this would unambiguously indicate the presence of new physics. We point out that such a possibility may occur due the muonium-mirror muonium conversion in the mirror matter model. A result in agreement with the Standard Model prediction would be a clean check of the pure leptonic bound state annihilation.

Magneto-electric response functions for simple atomic systems

We consider a simple atomic two-body bound state system that is overall charge neutral and placed in a static electric and magnetic field, and calculate the magneto-electric response function as a function of frequency. This is done from first principles using a two-particle Hamiltonian for both an harmonic oscillator and Coulomb binding potential. In the high frequency limit, the response function falls off as 1/ω 2 whilst at low frequencies it tends to a constant value.

Polarized atomic radiative emission in electric and magnetic fields1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

A reduced density matrix approach is employed to provide a general theoretical description of polarized radiative emission during single-photon transitions from bound and auto-ionizing states of many-electron atomic systems in the presence of a general arrangement of static (or quasi-static) electric and magnetic fields. Polarized radiative emission from partially ionized atomic systems can occur as a result of the excitation of the radiating atomic states by electrons or ions with an anisotropic velocity distribution, which can be produced in an electron or ion beam experiment, and in a non-equilibrium plasma environment. Polarized radiative emission can also be produced or modified during the excitation of the atomic system in the presence of electric and magnetic fields, and electromagnetic fields. In electric and magnetic fields, the normally overlapping angular momentum projection components of atomic spectral lines can be substantially shifted from their field-free positions and split into spectroscopically resolvable (and inherently polarized) features. Because of the breakdown of the field-free angular momentum and parity selection rules, otherwise forbidden components of atomic spectral lines can be generated. Using a representation based on the field-free many-electron atomic states, the Stark–Zeeman patterns can be determined by a diagonalization of the atomic Hamiltonian in the presence of electric and magnetic fields. In the density operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic bound or auto-ionizing states. A general expression for the matrix elements of the detected-photon density operator is obtained and provides a unified framework for the analysis of the spectral intensity, angular distribution, and polarization of the Stark–Zeeman patterns. From a unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the more comprehensive reduced density matrix approach, the non-equilibrium atomic state kinetics and the homogeneous spectral line shapes can be systematically and self-consistently described.

Some Studies of Atomic and Molecular Bound States on a Nanosphere

Some Studies of Atomic and Molecular Bound States on a Nanosphere

Toward the Application of Three-Dimensional Approach to Few-body Atomic Bound States

The first step toward the application of an effective non partial wave (PW) numerical approach to few-body atomic bound states has been taken. The two-body transition amplitude which appears in the kernel of three-dimensional Faddeev-Yakubovsky integral equations is calculated as function of two-body Jacobi momentum vectors, i.e. as a function of the magnitude of initial and final momentum vectors and the angle between them. For numerical calculation the realistic interatomic interactions HFDHE2, HFD-B, LM2M2 and TTY are used. The angular and momentum dependence of the fully off-shell transition amplitude is studied at negative energies. It has been numerically shown that, similar to the nuclear case, the transition amplitude exhibits a characteristic angular behavior in the vicinity of 4He dimer pole.

PossibleS-wave bound-states of two pseudoscalar mesons

AbstractUsing the potentials derived from vector-meson-exchanges, the KK¯, DK, BK¯, DD¯,BB¯, BD, DK¯ , BKand BD¯ systems are studied. Possible S-wave bound-states of twopseudoscalar mesons are discussed. We find that systems of DB, DD¯, BB¯ and DKwithisospin 0 are likely to form S-wavebound states via strong interactionswhile the othersareunlikely to be bound by the strong interaction sector alone. With the Coulomb potential,the K + K − system can form an atomic bound state - the kaonium. The influence of theone-meson-exchange potential on the ground state energy of the kaonium and its decaywidths to ππand πηare evaluated. 1 Introduction Since the 1970’s, the possible existence of the nuclear-like bound states of mesons has beenone of the interesting subjects in hadron physics. Some hardrons such as the ψ(4040) [1],η(1440) [2], f 1 (1420) [3], f J (1720) [4], and the f 0 (980) and a 0 (980) [5, 6, 7, 8] were explainedas the nuclear-like bound states of mesons. To¨rnqvist [9] argued that the one-pion-exchangepotential is likely to form a few states composed of two ground-state mesons. In 2003 the BelleCollaboration reported a new narrow charmonium state at 3872±0.6(stat)±0.5(syst) MeVand with a width <2.3MeV(95% C.L.), which has been confirmed by several experiments[10, 11, 12, 13]. Almost immediately, To¨rnqvist [14] claimed that this state is the one hepredicted long ago. Indeed the proximity of the X to D

Parametrizations and dynamical analysis of angle-integrated cross sections for double photoionization including nondipole effects

Similarly to differential cross sections for one-electron photoionization, the doubly differential cross section for double photoionization (DPI) may be conveniently described by four parameters: the singly differential (with respect to energy sharing) cross section $({\ensuremath{\sigma}}_{0})$, the dipole asymmetry parameter $(\ensuremath{\beta})$, and two nondipole asymmetry parameters ($\ensuremath{\gamma}$ and $\ensuremath{\delta}$). Here we derive two model-independent representations for these parameters for DPI from a $^{1}S_{0}$ atomic bound state: (i) in terms of one-dimensional integrals of the polarization-invariant DPI amplitudes and (ii) in terms of the exact two-electron reduced matrix elements. For DPI of He at excess energies, ${E}_{\mathrm{exc}}$, of 100 eV, 450 eV, and 1 keV, we present numerical results for the asymmetry parameters within the framework of the convergent close-coupling theory and compare them with results of lowest-order (in the interelectron interaction) perturbation theory (LOPT). The results for ${E}_{\mathrm{exc}}=1\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ exhibit a nondipole asymmetry that is large enough to be easily measured experimentally. We find excellent agreement between our LOPT results and other theoretical predictions and experimental data for total cross sections and ratios of double to single ionization cross sections for $K$-shell DPI from several multielectron atoms.

The first cold antihydrogen

Antihydrogen, the atomic bound state of an antiproton and a positron, was produced at low energy for the first time by the ATHENA experiment, marking an important first step for precision studies of atomic antimatter. This paper describes the first production and some subsequent developments.

Confinement and high-order harmonic generation by a repulsive potential

The dynamics of an electron wave packet in the presence of laser radiation and of a one-dimensional repulsive soft-core potential is investigated. For different laser intensities and for different initial positions of the electron wave packet, these results are compared with those for an attractive potential. The repulsive potential is capable of confining the electron quite efficiently under appropriate conditions. In these conditions, the electron is shown to emit a high harmonic spectrum similar to that emitted by the more conventional attractive potential. It is thus argued that recombination into an atomic bound state as required by the three step model is not essential for the emission of high harmonics.

Correlated eikonal initial state in ion-atom collisions

An approximation is developed to deal with the ionization of atoms by bare charged ions. In this method the transition amplitude describing the three-body final state is evaluated using a continuum correlated wave and that for the initial state by an analytical continuation of the ${\ensuremath{\Phi}}_{2}$ model to complex momenta. This procedure introduces in the atomic bound state a kinematical correlation with the projectile motion. Doubly differential cross sections (DDCS's) are computed for collisions of ${\mathrm{H}}^{+}$ and ${\mathrm{F}}^{9+}$ ions with He atoms. Results for the DDCS's in the forward direction are compared with experimental data and other theoretical models. We find an enhancement of the distribution for low energy electrons and that the asymmetry of the electron capture to the continuum (ECC) peak is correctly described.

Existence criteria for stabilization from the scaling behaviour of ionization probabilities

We provide a systematic derivation of the scaling behaviour of various quantities and, in particular, establish the scale invariance of the ionization probability. We discuss the gauge invariance of the scaling properties and the manner in which they can be exploited as a consistency check in explicit analytical expressions, in perturbation theory, in the Kramers-Henneberger and Floquet approximations, in upper and lower bound estimates and fully numerical solutions of the time dependent Schrödinger equation. The scaling invariance leads to a differential equation which has to be satisfied by the ionization probability and which yields an alternative criterion for the existence of atomic bound state stabilization.