Model Of Helium Atom Research Articles

Mountain pass frozen planet orbits in the helium atom model

We seek frozen planet orbits for the helium atom through an application of the mountain pass lemma to the Lagrangian action functional. Our method applies to a wide class of gravitational-like interaction potentials, thus generalising the results in Cieliebak, Frauenfelder, and Volkov [Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), 379–455]. We also let the charges of the two electrons tend to zero and perform an asymptotic analysis to prove convergence to a limit trajectory having a collision-reflection singularity between the electrons.

High electron mobility in heavily sulfur-doped 4H-SiC

The Hall electron mobility in sulfur-doped 4H-SiC over a wide range of S concentration was investigated. Sulfur (S) works as a double donor in SiC. The electron concentration in the S+-implanted layers saturates when the S concentration exceeds 1×1018 cm−3 and the net donor concentration of the S+-implanted layer with S concentration of 1×1019 cm−3 is 4×1018 cm−3, indicating that the solubility or activation limit of S+-implanted SiC is about 2×1018 cm−3. The S+-implanted SiC with a S concentration of 1×1018 cm−3 exhibits an electron mobility of 598 cm2/V s, which is more than twice as high as that in N-doped SiC with the same doping concentration (268 cm2/V s). The temperature dependence of the electron mobility in S+-implanted SiC is reproduced in the wide temperature range by the calculation of the electron mobility adopting the helium atom model for neutral-impurity scattering.

Ionization and recombination times of the long trajectory in high-order harmonic generation

Measuring the ionization and recombination times in high-order harmonic generation driven by strong laser fields is of fundamental importance in attosecond science and vital for assessing the temporal accuracy of trajectory-resolved high-harmonic spectroscopy. We investigate the effect of the electron-core interaction on the ionization and recombination times of the long trajectory in high-order harmonic generation. Using a classical model and the analytical $R$-matrix theory for helium, it is found that the attractive interaction leads to a 30-as shift of the ionization times for the long trajectory. By numerically solving the time-dependent Schr\"odinger equation for a helium atom model, we demonstrate that this small time shift can be probed by using orthogonally polarized two-color fields with high probe frequencies.

Revealing Coulomb time shifts in high-order harmonic generation by frequency-dependent streaking

When an atom is ionized by a strong laser pulse, the field can drive the released electron back to the parent ion and trigger the emission of a high-order harmonic photon with a frequency that is a function of the time of ionization. The attractive Coulomb potential causes a slowdown of the outgoing electron that must be compensated by an earlier release into the accelerating field to produce the same harmonic frequency as without the Coulomb force. By numerical solution of the time-dependent Schr\"odinger equation for a helium model atom, we demonstrate that such a subtle time shift of about 35 attoseconds is measurable by streaking with a weak, orthogonally polarized field combined with a complex-time trajectory interpretation. A comparison of results for high and low streaking frequency shows that only the high-frequency method measures the Coulomb shift well. This is confirmed by a classical trajectory model and by the analytical $R$-matrix theory.

Attosecond-Scale Streaking Methods for Strong-Field Ionization by Tailored Fields

Streaking with a weak probe field is applied to ionization in a two-dimensional strong field tailored to mimic linear polarization, but without disturbance by recollision or intracycle interference. This facilitates the observation of electron-momentum-resolved times of ionization with few-attosecond precision, as demonstrated by simulations for a model helium atom. Aligning the probe field along the ionizing field provides meaningful ionization times in agreement with the attoclock concept that ionization at maximum field corresponds to the peak of the momentum distribution, which is shifted due to the Coulomb force on the outgoing electron. In contrast, this attoclock shift is invisible in orthogonal streaking. Even without a probe field, streaking happens naturally along the laser propagation direction due to the laser magnetic field. As with an orthogonal probe field, the attoclock shift is not accessible by the magnetic-field scheme. For a polar molecule, the attoclock shift depends on orientation, but this does not imply an orientation dependence in ionization time.

Attoclock with counter-rotating bicircular laser fields

The attoclock technique which maps the emission time of a photoelectron to its detection angle is an important tool in strong-field physics. Previously, it was implemented only with circularly or elliptically polarized laser fields. Here, we show how counter-rotating bicircular laser fields can be used as an attoclock to investigate the ionization dynamics in quasilinear polarization. This is achieved by choosing the ratio of the two field strengths in a way such that the vector potential has aspects of the attoclock and time is mapped directly to the photoelectron momentum, but the shape of the electric field corresponds to approximately linear polarization during three intervals per optical cycle. We report momentum distributions calculated by solving the time-dependent Schr\odinger equation for a model helium atom and obtain the mapping from photoelectron momentum to ionization time using a trajectory-free method. Unlike circular polarization where the time of maximal ionization rate typically deviates less than 5 attoseconds from the maximium of the electric field, we find positive ionization times of more than 10 attoseconds in the quasilinear case.

Non-LTE Effects of Helium Lines in Late-B and A Stars

A helium model atom that includes 55 He I levels and the He II ground level in a detailed consideration has been constructed to investigate the departures from local thermodynamic equilibrium (LTE) in the formation of helium lines in stars with effective temperatures from 9300 to 20 000 K. For eight stars with effective temperatures from 9380 to 17 500 K the helium abundance has been determined from He I lines. The neutral helium lines in B stars cannot be described under LTE conditions using the common helium abundance. Furthermore, the profiles of several lines cannot be described in terms of the LTE approach at all. In contrast, a satisfactory coincidence of the theoretical and observed profiles for the entire set of helium lines observed in a wide spectral range can be achieved using virtually the same helium abundance by taking into account the departures from LTE. The LTE and non-LTE helium abundances can differ by up to a factor of 2–3, depending on the stellar parameters. The higher the stellar temperature, the stronger the departures from LTE. As a rule, the lines in the blue spectral region are less affected by non- LTE effects. In the atmospheres of six stars the helium abundance corresponds, within the error limits, to the present-day solar value. A helium underabundance is observed in the atmospheres of Sirius and HD 72660 classified as hot Am stars.

Transition from strong-field sequential to nonsequential double ionization at near-infrared wavelengths and low intensities

Within a quantum-mechanical model, we investigate strong-field double ionization of a model helium atom by near-infrared, linearly polarized laser pulses at intensities far below the recollision threshold. The quantum simulations show a clear mechanism change from sequential to nonsequential double ionization (NSDI) as the laser intensity increases. For NSDI, the two-electron correlated momentum distribution exhibits a strong final-state Coulomb repulsion effect for high-energy photoelectrons, but absent for low-energy photoelectrons. This repulsion effect is ascribed to field double ionization from doubly-excited states populated by recollision of the first ionized electron when it returns to the parent ion. Such recollision-induced excited states are absent at ultraviolet wavelengths due to the very low returning kinetic energies, resulting to the absence of final-state repulsion effect in NSDI.

Tunneling criteria and a nonadiabatic term for strong-field ionization

We investigate tunneling ionization of a model helium atom in a strong circularly polarized short laser pulse using the classical backpropagation method and compare ten different tunneling criteria on the same footing, aiming for a consistent classical picture of the tunneling dynamics. These tunneling criteria are categorized into velocity-based, position-based, and energy-based criteria according to different notions of a tunnel exit. We find that velocity-based criteria give consistent tunneling exit characteristics with nonadiabatic effects fully included. Other criteria are either inconsistent or only able to include nonadiabatic effects partially. Furthermore, we construct a simple tunneling rate formula, identify a term in the rate responsible for the nonadiabatic effects, and demonstrate the importance of this term.

Single-photon double ionization: renormalized-natural-orbital theory versus multi-configurational Hartree–Fock

The N-particle wavefunction has too many dimensions for a direct time propagation of a many-body system according to the time-dependent Schrödinger equation (TDSE). On the other hand, time-dependent density functional theory (TDDFT) tells us that the single-particle density is, in principle, sufficient. However, a practicable equation of motion for the accurate time evolution of the single-particle density is unknown. It is thus an obvious idea to propagate a quantity which is not as reduced as the single-particle density but less dimensional than the N-body wavefunction. Recently, we have introduced time-dependent renormalized-natural-orbital theory (TDRNOT). TDRNOT is based on the propagation of the eigenfunctions of the one-body reduced density matrix, the so-called natural orbitals. In this paper we demonstrate how TDRNOT is related to the multi-configurational time-dependent Hartree–Fock (MCTDHF) approach. We also compare the performance of MCTDHF and TDRNOT versus the TDSE for single-photon double ionization (SPDI) of a 1D helium model atom. SPDI is one of the effects where TDDFT does not work in practice, especially if one is interested in correlated photoelectron spectra, for which no explicit density functional is known.

Cosmospec: fast and detailed computation of the cosmological recombination radiation from hydrogen and helium

We present the first fast and detailed computation of the cosmological recombination radiation released during the hydrogen (redshift z ~ 1300) and helium (z ~ 2500 and z ~ 6000) recombination epochs, introducing the code CosmoSpec. Our computations include important radiative transfer effects, 500-shell bound-bound and free-bound emission for all three species, the effects of electron scattering and free-free absorption as well as interspecies (HeII --> HeI --> HI) photon feedback. The latter effect modifies the shape and amplitude of the recombination radiation and CosmoSpec improves significantly over previous treatments of it. Utilizing effective multilevel atom and conductance approaches, one calculation takes only ~ 15 seconds on a standard laptop as opposed to days for previous computations. This is an important step towards detailed forecasts and feasibility studies considering the detection of the cosmological recombination lines and what one may hope to learn from the ~ 6.1 photons emitted per hydrogen atom in the three recombination eras. We briefly illustrate some of the parameter dependencies and discuss remaining uncertainties in particular related to collisional processes and the neutral helium atom model.

Theoretical Study of Isolated Attosecond Pulse Generation with Two Methods

We theoretically investigated high-order harmonic generation and isolated attosecond pulse generation from a model of helium atom by two methods: numerically solve time dependent Schrodinger equation (TDSE) by splitting-operator method and Lewenstein’s strong field approximation theory. A left circularly polarized pulse (800 nm) is combined to a right circular polarized pulse (1200 nm) with a timedelay of 4 fs. A supercontinuum spectrum plateau with a broad bandwidth of 215 eV (from 230 to 445 eV) is obtained for the case of I0=7×10W/cm. By superposing a bandwidth of 70 eV in the plateau region, an linear polarized isolated attosecond pulse with the duration of about 56 as can be obtained. Moreover, we illustrate the quantum path control in terms of the time-frequency analysis by Morlet wavelet transform method. PACS: 32.80.Rm,42.65.Ky

The structure of approximate two electron wavefunctions in intense laser driven ionization dynamics

The structure of approximate two-electron wavefunctions in strong-field-driven ionization dynamics is investigated in depth, both theoretically and numerically. Theoretical analyses clarify that for two-electron singlet systems, the previously proposed time-dependent extended Hartree–Fock (TD-EHF) method (1995 Phys. Rev. A 51 3999) is equivalent to the multiconfiguration time-dependent Hartree–Fock method with two occupied orbitals. The latter wavefunction is further transformed into the natural expansion form, enabling the direct propagation of the natural orbitals (NOs). These methods, as well as the conventional time-dependent Hartree–Fock (TDHF) method, are numerically assessed as regards providing a description of the ionization dynamics of a one-dimensional helium atom model. This numerical analysis (i) explains the reason behind the well-known failure of the TDHF method to describe tunneling ionization, (ii) demonstrates the interpretive power of the TD-EHF wavefunction in both the original nonorthogonal formulation and the NO-based formulation, and (iii) highlights different manifestations of the electron correlation (an effect beyond the single-determinant description), in tunneling ionization, high harmonic generation, and nonsequential double ionization. Possible extensions of the NO basis approach to multielectron systems are briefly discussed.

DETAILED AND SIMPLIFIED NONEQUILIBRIUM HELIUM IONIZATION IN THE SOLAR ATMOSPHERE

Helium ionization plays an important role in the energy balance of the upper chromosphere and transition region. Helium spectral lines are also often used as diagnostics of these regions. We carry out 1D radiation-hydrodynamics simulations of the solar atmosphere and find that the helium ionization is mostly set by photoionization and direct collisional ionization, counteracted by radiative recombination cascades. By introducing an additional recombination rate mimicking the recombination cascades, we construct a simplified 3 level helium model atom consisting of only the ground states. This model atom is suitable for modeling non-equilibrium helium ionization in 3D numerical models. We perform a brief investigation of the formation of the He I 10830 and He II 304 spectral lines. Both lines show non-equilibrium features that are not recovered with statistical equilibrium models, and caution should therefore be exercised when such models are used as a basis in the interpretation of observations.

Time-dependent renormalized natural orbital theory applied to the two-electron spin-singlet case: Ground state, linear response, and autoionization

Favorably scaling numerical time-dependent many-electron techniques such as time-dependent density functional theory (TDDFT) with adiabatic exchange-correlation potentials typically fail in capturing highly correlated electron dynamics. We propose a method based on natural orbitals, i.e., the eigenfunctions of the one-body reduced density matrix, that is almost as inexpensive numerically as adiabatic TDDFT, but which is capable of describing correlated phenomena such as doubly excited states, autoionization, Fano profiles in the photoelectron spectra, and strong-field ionization in general. Equations of motion (EOMs) for natural orbitals and their occupation numbers have been derived earlier. We show that by using renormalized natural orbitals (RNOs) both can be combined into one equation governed by a hermitian effective Hamiltonian. We specialize on the two-electron spin-singlet system, known as being a ``worst case'' testing ground for TDDFT, and employ the widely used, numerically exactly solvable, one-dimensional helium model atom (in a laser field) to benchmark our approach. The solution of the full, nonlinear EOMs for the RNOs is plagued by instabilities, and resorting to linear response is not an option for the ultimate goal to study nonperturbative dynamics in intense laser fields. We therefore make two rather bold approximations: we employ the initial-state-``frozen'' effective RNO Hamiltonian for the time propagation and truncate the number of RNOs to only two per spin. Surprisingly, it turns out that even with these strong approximations we obtain a highly accurate ground state, reproduce doubly excited states, and autoionization.

Effect of electron correlation on high-order harmonic generation in helium model atom

High-order harmonic generation (HHG) of a helium model atom in an intense laser field has been numerically investigated. The influence of electron correlation on HHG is analysed by changing the strength between the electrons. The numerical results show that as the electron interaction strength becomes small, the first ionization energy increases rapidly, which results in the decrease in ionization. So the conversion efficiency of the high harmonic lying in the plateau decreases greatly, while the cutoff harmonic order in the harmonic spectrum increases.

Time and intensity dependence of total ionization of helium studied with the multi-configuration time-dependent Hartree–Fock method

We have demonstrated the use of the multi-configuration time-dependent Hartree–Fock (MCTDHF) method to compute total ionization probabilities of a 3-dimensional (3D) model helium atom interacting with a strong laser field. The time dependence and the intensity dependence of the total ionization probabilities of helium are investigated by using the MCTDHF method. The MCTDHF results are consistent with the previous theoretical expectations by directly solving the time-dependent Schrödinger equation.

Classical helium atom with radiation reaction

We study a classical model of Helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as pointed out by Dirac, in any model of classical electrodynamics of point particles involving radiation reaction one has to eliminate, from the a priori conceivable solutions of the problem, those corresponding to the emission of an infinite amount of energy. We show that the Dirac prescription solves a problem of inconsistency plaguing all available models which neglect radiation reaction, namely, the fact that in all such models most initial data lead to a spontaneous breakdown of the atom. A further modification is that the system thus acquires a peculiar form of dissipation. In particular, this makes attractive an invariant manifold of special physical interest, the zero--dipole manifold, that corresponds to motions in which no energy is radiated away (in the dipole approximation). We finally study numerically the invariant measure naturally induced by the time--evolution on such a manifold, and this corresponds to studying the formation process of the atom. Indications are given that such a measure may be singular with respect to that of Lebesgue.

Isolated attosecond pulse generated by a model helium atom exposed to the combined field

We theoretically study the high-order harmonic generation (HHG) of a model He atom exposed to a combined field of 1600 nm and 800 nm laser pulses. The changing of rising rate and falling rate with time for the combined filed during main HHG, can present the different characteristics of high-order harmonic generation from the short electron trajectories and the long electron trajectories. By superimposing several harmonics generated from He atom driven by the combined field, we could obtain shorter attosecond pulses. Finally, by adjusting the time delay between two laser pulses, we can effectively suppress the contribution of the short electron trajectories to HHG, and obtain an isolated attosecond pulse with duration 33.7 as.

Ultrafast photoionization dynamics at high laser intensities in the xuv regime

We study the ionization dynamics in the soft-x-ray regime for high intensities and short pulses for excitations near the ionization threshold. Using a one-dimensional helium atom model, we compare exact numerical solutions with time-dependent Hartree-Fock results in order to identify the role of electron-electron correlations. At moderate intensities but still in the x-ray and short-pulse regime, we find that the Hartree-Fock theory reproduces well the dynamics of the ground-state occupation, while at high intensities strong correlation effects occur for excitations close to the threshold. From their characteristic momentum distributions, we can identify contributions to the double ionization from sequential three-photon and nonsequential or sequential two-photon processes. At elevated intensities these contributions deviate from their usual intensity scaling due to saturation effects, even though the total double-ionization probability stays below 10%. Furthermore, analysis of the time evolution of the momentum distribution reveals signatures of the energy-time uncertainty which indicate a coherent regime of the dynamics.