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ABSTRACT: The R-Matrix incorporating Time (RMT) method is a new method for solving the
time-dependent Schroedinger equation for multi-electron atomic systems exposed
to intense short-pulse laser light. We have employed the RMT method to
investigate the time delay in the photoemission of an electron liberated from a
2p orbital in a neon atom with respect to one released from a 2s orbital
following absorption of an attosecond XUV pulse. Time delays due to XUV pulses
in the range 76-105 eV are presented. For an XUV pulse at the experimentally
relevant 105.2 eV, we calculate the time delay to be 10.2 +/- 1.3 attoseconds,
somewhat larger than estimated by other theoretical calculations, but still a
factor two smaller than experiment. We repeated the calculation for a photon
energy of 89.8 eV with a larger basis set capable of modelling
correlated-electron dynamics within the neon atom and the residual Ne(+) ion. A
time delay of 14.5 +/- 1.5 attoseconds was observed, compared to a 16.7 +/- 1.5
attosecond result using a single-configuration representation of the residual
Ne(+) ion.
04/2012;
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ABSTRACT: We report full-dimensionality quantum and classical calculations for double ionization of laser-driven helium at 390 nm. Good qualitative agreement is observed. We show that the classical double ionization trajectories can be divided into two distinct pathways: direct and delayed. The direct pathway, with an almost simultaneous ejection of both electrons, emerges from small laser intensities. With increasing intensity its relative importance, compared to the delayed ionization pathway, increases until it becomes the predominant pathway for total electron escape energy below around 5.25 $U_{p}$. However the delayed pathway is the predominant one for double ionization above a certain cut-off energy at all laser intensities.
05/2010;
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ABSTRACT: We present high-accuracy calculations of ionization rates of helium at UV (195 nm) wavelengths. The numerical results are obtained from full-dimensional numerical integration of the two-electron time-dependent Schrödinger equation. Comparison is made between ionization rates at 195 nm with previously obtained data at 390 nm and 780 nm. In addition, we have obtained quantitatively accurate solutions of the full-dimensional time-dependent Schrödinger equation for static-field ionization of helium. We compare our numerically integrated rates with those of time-independent calculations, and obtain good agreement over a wide range of intensities.
Journal of Physics Conference Series 12/2009; 194(3):032023.
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ABSTRACT: We present high-accuracy calculations of ionization rates of helium at UV (195 nm) wavelengths. The data are obtained from full-dimensionality integrations of the helium-laser time-dependent Schrödinger equation. Comparison is made with our previously obtained data at 390 nm and 780 nm. We show that scaling laws introduced by Parker et al extend unmodified from the near-infrared limit into the UV limit. Static-field ionization rates of helium are also obtained, again from time-dependent full-dimensionality integrations of the helium Schrödinger equation. We compare the static-field ionization results with those of Scrinzi et al and Themelis et al, who also treat the full-dimensional helium atom, but with time-independent methods. Good agreement is obtained.
Journal of Physics B Atomic Molecular and Optical Physics 06/2009; 42(13):134011. · 1.88 Impact Factor
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ABSTRACT: In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.
Phys. Rev. A. 12/2008; 78(6).
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ABSTRACT: The X-ray free electron lasers currently being built promise light of sufficient intensity to cause direct double photoionization of the inner K-shells of Ne and Ar atoms. The Ne and Ar K-shell electrons experience a binding energy that is almost the same in the neutral atom as in the corresponding two-electron ion, Ne 8þ or Ar 16þ . We report on new numerical methods we have implemented for calculating double ionization rates for these two-electron positive ions interacting with an intense X-ray free electron laser pulse. The numerical method builds upon an existing code (HELIUM) for solving the full-dimensional time-dependent Schroinger equation that, operating within the electric dipole approximation, has found successful application in the optical to XUV wavelength range. The primary extensions to HELIUM are the inclusion of magnetic dipole and electric quadrupole interaction terms appropriate to extreme laser intensities and wavelengths approaching atomic dimensions.
Journal of Modern Optics 10/2008; 55:2541-2555. · 1.17 Impact Factor
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ABSTRACT: In this work we present the theoretical framework for the solution of the time-dependent Schr\"{o}dinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron's coordinates separated over two regions, that is regions $I$ and $II$. In region $I$ the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wavefunction. In region $II$ a grid representation of the wavefunction is considered and propagation in space and time is obtained through the finite-differences method. It appears this is the first time a combination of basis set and grid methods has been put forward for tackling multi-region time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multi-electron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely that beyond a certain distance (encompassing region $I$) a single ejected electron is distinguishable from the other electrons of the multi-electron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field. Comment: 13 pages, 6 figures, submitted
10/2008;
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ABSTRACT: We present a numerical and theoretical study of intense-field single-electron ionization of helium at 390 nm and 780 nm. Accurate ionization rates (over an intensity range of (0.175–34) × 1014 W cm−2, at 390 nm, and (0.275–14.4) × 1014 W cm−2 at 780 nm) are obtained from full-dimensionality integrations of the time-dependent helium-laser Schrödinger equation. We show that the power law of lowest order perturbation theory, modified with a ponderomotive-shifted ionization potential, is capable of modelling the ionization rates over an intensity range that extends up to two orders of magnitude higher than that applicable to perturbation theory alone. Writing the modified perturbation theory in terms of scaled wavelength and intensity variables, we obtain to first approximation a single ionization law for both the 390 nm and 780 nm cases. To model the data in the high intensity limit as well as in the low, a new function is introduced for the rate. This function has, in part, a resemblance to that derived from tunnelling theory but, importantly, retains the correct frequency-dependence and scaling behaviour derived from the perturbative-like models at lower intensities. Comparison with the predictions of classical ADK tunnelling theory confirms that ADK performs poorly in the frequency and intensity domain treated here.
Journal of Physics B Atomic Molecular and Optical Physics 04/2007; 40(10):1729. · 1.88 Impact Factor
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ABSTRACT: We simulate the dynamics of H2+ and HD+ by direct solution of the time-dependent Schroedinger equation for the electronic and nuclear motion for the interaction of intense femtosecond pulses. On these timescales the rotational motion, even for such light molecules, is frozen. Therefore it is a reasonable assumption that the nuclear alignment is fixed during the pulse interaction and that rotation can be neglected. In terms of vibrational relaxation, and since the nuclei are light, vibration will be important over femtosecond timescales. Although homonuclear diatomics are IR-inactive, in an intense field one can create vibrational excitation through continuum coupling. To show the effect of vibration, consider a first approximation in which the nuclei are infinitely massive so they maintain their positions at a fixed bond length of R=2 a.u., throughout the process.
05/2006;
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ABSTRACT: Electron energy distributions of singly and doubly ionized helium in an intense 390 nm laser field have been measured at two intensities (0.8 PW/cm2 and 1.1 PW/cm2, where PW is defined as 10(15) W/cm2). Numerical solutions of the full-dimensional time-dependent helium Schrödinger equation show excellent agreement with the experimental measurements. The high-energy portion of the two-electron energy distributions reveals an unexpected 5U(p) cutoff for the double ionization (DI) process and leads to a proposed model for DI below the quasiclassical threshold.
Physical Review Letters 05/2006; 96(13):133001. · 7.37 Impact Factor
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ABSTRACT: We compare single-electron multiphoton ionization rates of He obtained by the R-matrix Floquet approach with those obtained by the numerical integration of the time-dependent Schrödinger equation. The calculations are performed at a laser wavelength of 390 nm, a wavelength accessible to Ti:sapphire lasers via frequency doubling. For intensities between 1 × 1014 W cm−2 and 2.5 × 1014 W cm−2, we find general agreement between the two approaches within 10%. Over this range of intensities we further find our single-ionization rates typically two orders of magnitude greater than those predicted by the ADK model. The ionization rates are strongly enhanced by resonances. This resonance structure is strongly distorted by the laser field: the 1s3d 1D state lies below the 1s3s 1S state at the present intensities.
Journal of Physics B Atomic Molecular and Optical Physics 06/2005; 38(13):L207. · 1.88 Impact Factor
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ABSTRACT: We present a practical and efficient computational method for the solution of the time-dependent full-dimensionality Schrödinger equation for two-electron atoms in intense laser fields. The method, incorporating electric quadrupole and magnetic dipole terms, is a generalization of an approach within the dipole approximation that has previously found successful application at wavelengths from the visible to the XUV. We discuss the computational demands of non-dipole calculations for helium. We deduce from our helium formulation the equivalent formulation for hydrogen and report calculations we have performed on this atom beyond the dipole approximation, producing results that are found to be in good agreement with literature values obtained by a different method.
Journal of Physics B Atomic Molecular and Optical Physics 01/2005; 38(3):237. · 1.88 Impact Factor
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ABSTRACT: The full-dimensional time-dependent Schrödinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium, the hydrogen atom and the hydrogen molecular ion are presented. At very high laser intensity, above the saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments.
The Journal of Chemical Physics 07/2004; 120(21):10046-55. · 3.33 Impact Factor
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ABSTRACT: The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium and hydrogen atoms and molecules are presented. At very high intensity above saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments. Comment: 10 pages, 9 figure, 4 tables
02/2004;
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ABSTRACT: Intense-field ionization of the hydrogen molecular ion by linearly-polarized light is modelled by direct solution of the fixed-nuclei time-dependent Schr\"odinger equation and compared with recent experiments. Parallel transitions are calculated using algorithms which exploit massively parallel computers. We identify and calculate dynamic tunnelling ionization resonances that depend on laser wavelength and intensity, and molecular bond length. Results for $\lambda \sim 1064$ nm are consistent with static tunnelling ionization. At shorter wavelengths $\lambda \sim 790 $ nm large dynamic corrections are observed. The results agree very well with recent experimental measurements of the ion spectra. Our results reproduce the single peak resonance and provide accurate ionization rate estimates at high intensities. At lower intensities our results confirm a double peak in the ionization rate as the bond length varies. Comment: 8 pages, 3 figures
02/2004;
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ABSTRACT: We present calculations of the time delay between single and double ionization of helium, obtained from full-dimensionality numerical integrations of the helium–laser Schrödinger equation. The notion of a quantum mechanical time delay is defined in terms of the interval between correlated bursts of single and double ionization. Calculations are performed at 390 and 780 nm in laser intensities that range from 2 × 1014 to 14 × 1014 W cm−2. We find results consistent with the rescattering model of double ionization but supporting its classical interpretation only at 780 nm.
Journal of Physics B Atomic Molecular and Optical Physics 10/2003; 36(21):L393. · 1.88 Impact Factor
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ABSTRACT: Single- and multiphoton detachment rates have been calculated for K− using the R-matrix Floquet approach. Single-photon detachment rates, obtained at a laser field peak intensity of 109 W cm−2, are discussed and compared with other theoretical work. Two-photon detachment rates at the same intensity have also been obtained, and similarities with results from earlier calculations for Li− and Na− are discussed. Three-photon rates are also presented at this laser intensity, and are compared and contrasted with those arising in the single-photon case, since both involve resonance structure with 1Po symmetry. The influence of resonances such as the 5s2 1Se doubly excited state and excitations of the residual atom are also considered.
Journal of Physics B Atomic Molecular and Optical Physics 04/2003; 36(9):1795. · 1.88 Impact Factor
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ABSTRACT: We present calculations of intense-field multiphoton ionization processes in helium at XUV wavelengths. The calculations are obtained from a full-dimensional integration of the two-electron time-dependent Schrödinger equation. A momentum-space analysis of the ionizing two-electron wavepacket reveals the existence of double-electron above threshold ionization (DATI). In momentum-space two distinct forms of DATI are resolved, namely non-sequential and sequential. In non-sequential DATI correlated electrons resonantly absorb and share energy in integer units of ωlaser.
Journal of Physics B Atomic Molecular and Optical Physics 01/2001; 34(3):L69. · 1.88 Impact Factor
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ABSTRACT: The R-matrix theory of photoionization described by Burke and Taylor (1975) is used to obtain cross sections for the photoionization of ground-state carbon and oxygen atoms. The calculations are the first to couple systematically all channels corresponding to the 2s22p1, 2s2pq+1 and 2p1+2 configurations of the residual ion. The results are in good agreement with experiment where comparison is possible.
Journal of Physics B Atomic and Molecular Physics 01/2001; 9(12):L353.
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ABSTRACT: We present calculations of single- and double-ionization rates of helium at 390 nm, accurate to within 10%, obtained from a full-dimensional integration of the time-dependent Schrödinger equation. The theoretical results are compared with experimental data at the same wavelength. Excellent agreement is obtained, allowing for likely uncertainties in the experimental determination of laser intensity.
Journal of Physics B Atomic Molecular and Optical Physics 09/2000; 33(20):L691. · 1.88 Impact Factor
